The mechanical behavior of skin: Structures and models for the finite element analysis

Abstract Soft biological tissues are complex materials with a large structural variety, with differences in behavior, but with some common characteristics. Skin is an archetypal soft tissue which presents many common characteristics to other soft biological tissues, like being a multilayer collagen-reinforced structure, with nonlinear behavior, anisotropy, viscosity, preconditioning effects, internal stresses and tissue growth and adaptation. Departing from a detailed description of the structures of the skin and the experimental evidence, we herein analyze the different modeling approaches in the literature for the distinct aspects of the skin behavior, with attention to the implementation in finite element codes.

[1]  Walter Herzog,et al.  Towards an analytical model of soft biological tissues. , 2008, Journal of biomechanics.

[2]  Corina Stefania Drapaca,et al.  Nonlinear Constitutive Laws in Viscoelasticity , 2007 .

[3]  V. Mow,et al.  The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage. , 2000, Journal of biomechanics.

[4]  Jeffrey C Lotz,et al.  Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus , 2004, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[5]  Yasuaki Seki,et al.  Biological materials: Structure and mechanical properties , 2008 .

[6]  Mark Taylor,et al.  On the constitutive modeling of biological soft connective tissues: A general theoretical framework and explicit forms of the tensors of elasticity for strongly anisotropic continuum fiber-reinforced composites at finite strain , 2002 .

[7]  F. Montáns,et al.  Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains , 2015 .

[8]  N. G. Mccrum,et al.  The viscoelastic deformation of tendon. , 1980, Journal of biomechanics.

[9]  Andrew Taberner,et al.  Modeling the Mechanical Response of In Vivo Human Skin Under a Rich Set of Deformations , 2011, Annals of Biomedical Engineering.

[10]  D. Elliott,et al.  Interfibrillar shear stress is the loading mechanism of collagen fibrils in tendon. , 2014, Acta biomaterialia.

[11]  A. Caplan,et al.  Age-related changes in the proteoglycans of human skin. , 2000, Archives of biochemistry and biophysics.

[12]  Heng Xiao,et al.  Constitutive inequalities for an isotropic elastic strain-energy function based on Hencky's logarithmic strain tensor , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Y Lanir,et al.  Optimal design of biaxial tests for structural material characterization of flat tissues. , 1996, Journal of biomechanical engineering.

[14]  Robert P. Jenkins,et al.  Mechano-transduction and YAP-dependent matrix remodelling is required for the generation and maintenance of cancer associated fibroblasts , 2013, Nature Cell Biology.

[15]  T. Christian Gasser,et al.  The numerical implementation of invariant-based viscoelastic formulations at finite strains. An anisotropic model for the passive myocardium , 2011 .

[16]  J. C. Barbenel,et al.  Mechanical and optical anisotropy of bovine pericardium , 2006, Medical and Biological Engineering and Computing.

[17]  Markus J. Buehler,et al.  Nature designs tough collagen: Explaining the nanostructure of collagen fibrils , 2006, Proceedings of the National Academy of Sciences.

[18]  E M Arruda,et al.  Finite element modeling of human skin using an isotropic, nonlinear elastic constitutive model. , 2000, Journal of biomechanics.

[19]  Xiongqi Peng,et al.  A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus , 2006 .

[20]  Konstantin Y. Volokh,et al.  Hyperelasticity with softening for modeling materials failure , 2007 .

[21]  H. Zahouani,et al.  In vivo skin biophysical behaviour and surface topography as a function of ageing. , 2013, Journal of the mechanical behavior of biomedical materials.

[22]  J. C. Simo,et al.  On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects , 1987 .

[23]  José M. Goicolea,et al.  A regularised continuum damage model based on the mesoscopic scale for soft tissue , 2015 .

[24]  Saskia Lippens,et al.  The emerging roles of serine protease cascades in the epidermis. , 2009, Trends in biochemical sciences.

[25]  Ray Vanderby,et al.  Nonlinear Viscoelasticity in Rabbit Medial Collateral Ligament , 2004, Annals of Biomedical Engineering.

[26]  M. J. Gómez-Benito,et al.  Challenges in the Modeling of Wound Healing Mechanisms in Soft Biological Tissues , 2014, Annals of Biomedical Engineering.

[27]  A. Rachev,et al.  Deformation of blood vessels upon stretching, internal pressure, and torsion , 1980 .

[28]  Francisco J. Montáns,et al.  The relevance of transverse deformation effects in modeling soft biological tissues , 2016 .

[29]  I. LeGrice,et al.  Shear properties of passive ventricular myocardium. , 2002, American journal of physiology. Heart and circulatory physiology.

[30]  B A Trimmer,et al.  A constitutive model for muscle properties in a soft-bodied arthropod , 2007, Journal of The Royal Society Interface.

[31]  H. Haslach Maximum dissipation non-equilibrium thermodynamics and its geometric structure / Henry W. Haslach Jr. , 2011 .

[32]  Ciaran K Simms,et al.  Control of tension-compression asymmetry in Ogden hyperelasticity with application to soft tissue modelling. , 2015, Journal of the mechanical behavior of biomedical materials.

[33]  V. K. Katiyar,et al.  A new strain energy function to characterize apple and potato tissues , 2013 .

[34]  G. Holzapfel,et al.  Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. , 2008, Journal of biomechanical engineering.

[35]  Boumediene Nedjar,et al.  An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects , 2007 .

[36]  Borhan Beigzadeh,et al.  A visco-hyperelastic constitutive approach for modeling polyvinyl alcohol sponge. , 2014, Tissue & cell.

[37]  C. C. Wang,et al.  The principle of fading memory , 1965 .

[38]  Marcello Vasta,et al.  Fiber distributed hyperelastic modeling of biological tissues , 2010 .

[39]  K. Kobayashi,et al.  Force-induced Rapid Changes in Cell Fate at Midpalatal Suture Cartilage of Growing Rats , 1999, Journal of dental research.

[40]  Lallit Anand,et al.  On H. Hencky’s Approximate Strain-Energy Function for Moderate Deformations , 1979 .

[41]  Douglas Cook,et al.  Unrealistic statistics: how average constitutive coefficients can produce non-physical results. , 2014, Journal of the mechanical behavior of biomedical materials.

[42]  Y Lanir,et al.  A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. , 1979, Journal of biomechanics.

[43]  Ellen Kuhl,et al.  On the biomechanics and mechanobiology of growing skin. , 2012, Journal of theoretical biology.

[44]  Sevan Goenezen,et al.  Inverse Problems , 2008 .

[45]  James S. Davidson,et al.  Three-Dimensional Finite Element Models of the Human Pubic Symphysis with Viscohyperelastic Soft Tissues , 2006, Annals of Biomedical Engineering.

[46]  M. Collins,et al.  Aspartic acid racemization: evidence for marked longevity of elastin in human skin , 2003, The British journal of dermatology.

[47]  Aidy Ali,et al.  A review and comparison on some rubber elasticity models , 2010 .

[48]  D. J. Montgomery,et al.  The physics of rubber elasticity , 1949 .

[49]  Erwan Verron,et al.  Comparison of Hyperelastic Models for Rubber-Like Materials , 2006 .

[50]  S. Karadeniz,et al.  Constitutive equations for isotropic rubber-like materials using phenomenological approach : A bibliography (1930-2003) , 2006 .

[51]  P. Payne,et al.  Measurement of properties and function of skin. , 1991, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[52]  Francisco Chinesta,et al.  Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models , 2010 .

[53]  Gerhard A. Holzapfel,et al.  On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework , 2009 .

[54]  S. Göktepe,et al.  Computational modeling of passive myocardium , 2011 .

[55]  R. Wildnauer,et al.  Stratum corneum biomechanical properties. I. Influence of relative humidity on normal and extracted human stratum corneum. , 1971, The Journal of investigative dermatology.

[56]  Victor H. Barocas,et al.  Volume-averaging theory for the study of the mechanics of collagen networks , 2007 .

[57]  Arnab Majumdar,et al.  Mechanical interactions between collagen and proteoglycans: implications for the stability of lung tissue. , 2005, Journal of applied physiology.

[58]  R. Ogden,et al.  A pseudo–elastic model for the Mullins effect in filled rubber , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[59]  Gerhard A. Holzapfel,et al.  A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications , 2001 .

[60]  Michel Destrade,et al.  Characterization of the anisotropic mechanical properties of excised human skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[61]  D. Elliott,et al.  Modeling interlamellar interactions in angle-ply biologic laminates for annulus fibrosus tissue engineering , 2011, Biomechanics and modeling in mechanobiology.

[62]  R. Rivlin,et al.  Representation theorems in the mechanics of materials with memory , 1964 .

[63]  L. Taber Biomechanics of Growth, Remodeling, and Morphogenesis , 1995 .

[64]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials—III. self-consistent model , 1965 .

[65]  Stephen C Cowin,et al.  Tissue growth and remodeling. , 2004, Annual review of biomedical engineering.

[66]  P. Neff,et al.  Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions , 2003 .

[67]  C Edwards,et al.  The measurement of photodamage , 1992, The British journal of dermatology.

[68]  Christian Miehe,et al.  Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials , 1995 .

[69]  A. Singer,et al.  Cutaneous wound healing. , 1999, The New England journal of medicine.

[70]  A. Pipkin,et al.  Small Finite Deformations of Viscoelastic Solids , 1964 .

[71]  N. Sasaki,et al.  Stress-strain curve and Young's modulus of a collagen molecule as determined by the X-ray diffraction technique. , 1996, Journal of biomechanics.

[72]  Jingfeng Jiang,et al.  Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility , 2009, Physics in medicine and biology.

[73]  Ivonne Sgura,et al.  On worm-like chain models within the three-dimensional continuum mechanics framework , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[74]  Ivonne Sgura,et al.  Fitting hyperelastic models to experimental data , 2004 .

[75]  Andrew Taberner,et al.  Measurement of the force-displacement response of in vivo human skin under a rich set of deformations. , 2011, Medical engineering & physics.

[76]  R. Ogden,et al.  Computational method for excluding fibers under compression in modeling soft fibrous solids , 2016 .

[77]  Alexandre Delalleau,et al.  Characterization of the mechanical properties of skin by inverse analysis combined with the indentation test. , 2006, Journal of biomechanics.

[78]  Peter Wriggers,et al.  3D multiscale crack propagation using the XFEM applied to a gas turbine blade , 2014 .

[79]  S. E. James,et al.  A review of tissue-engineered skin bioconstructs available for skin reconstruction , 2010, Journal of The Royal Society Interface.

[80]  Andreas Menzel,et al.  Application of an anisotropic growth and remodelling formulation to computational structural design , 2012 .

[81]  Serdar Göktepe,et al.  A micro-macro approach to rubber-like materials—Part I: the non-affine micro-sphere model of rubber elasticity , 2004 .

[82]  A. Ibrahimbegovic Nonlinear Solid Mechanics , 2009 .

[83]  Kent N. Bachus,et al.  Soft Tissue Restraints to Lateral Patellar Translation in the Human Knee , 1998, The American journal of sports medicine.

[84]  F. Montáns,et al.  On the interpretation of the logarithmic strain tensor in an arbitrary system of representation , 2014 .

[85]  Ray W. Ogden,et al.  On anisotropic elasticity and questions concerning its Finite Element implementation , 2013, 2009.00044.

[86]  Tom Shearer,et al.  A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructure. , 2015, Journal of biomechanics.

[87]  A. Menzel,et al.  A fibre reorientation model for orthotropic multiplicative growth , 2007, Biomechanics and modeling in mechanobiology.

[88]  Julius Wolff,et al.  The Classic: On the Inner Architecture of Bones and its Importance for Bone Growth , 2010, Clinical orthopaedics and related research.

[89]  A. Grodzinsky,et al.  Swelling of articular cartilage and other connective tissues: Electromechanochemical forces , 1985, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[90]  Jeremiah G Murphy,et al.  Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants , 2013 .

[91]  A. Gefen,et al.  Simulations of skin and subcutaneous tissue loading in the buttocks while regaining weight-bearing after a push-up in wheelchair users. , 2013, Journal of the mechanical behavior of biomedical materials.

[92]  E. Caterson,et al.  Extracellular Matrix and Dermal Fibroblast Function in the Healing Wound. , 2014, Advances in wound care.

[93]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour , 1964 .

[94]  Peter Regitnig,et al.  Determination of the layer-specific distributed collagen fibre orientations in human thoracic and abdominal aortas and common iliac arteries , 2012, Journal of The Royal Society Interface.

[95]  Y. Fung Elasticity of soft tissues in simple elongation. , 1967, The American journal of physiology.

[96]  F. Silver,et al.  Viscoelastic properties of human skin and processed dermis , 2001, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[97]  M. F. Ahmad,et al.  A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type , 1999 .

[98]  K. Madison,et al.  Barrier function of the skin: "la raison d'être" of the epidermis. , 2003, The Journal of investigative dermatology.

[99]  B. Boyce,et al.  An inverse finite element method for determining the anisotropic properties of the cornea , 2011, Biomechanics and modeling in mechanobiology.

[100]  Giuseppe Saccomandi,et al.  Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials with Limiting Chain Extensibility , 1999 .

[101]  G. Chagnon,et al.  Hyperelastic Energy Densities for Soft Biological Tissues: A Review , 2015 .

[102]  Andreas Menzel,et al.  A micro‐sphere‐based remodelling formulation for anisotropic biological tissues , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[103]  Gerhard A. Holzapfel,et al.  On the tension–compression switch in soft fibrous solids , 2015 .

[104]  Jaeyoung Lim,et al.  Mechanical response of pig skin under dynamic tensile loading , 2011, International Journal of Impact Engineering.

[105]  W. D. Wilson,et al.  Strain-energy density function for rubberlike materials , 1979 .

[106]  E. Peña A rate dependent directional damage model for fibred materials: application to soft biological tissues , 2011 .

[107]  M. Nalls,et al.  Genome-Wide Association Study of Retinopathy in Individuals without Diabetes , 2013, PloS one.

[108]  Pedro Ponte Castañeda Exact second-order estimates for the effective mechanical properties of nonlinear composite materials , 1996 .

[109]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[110]  T. Gibson,et al.  Directional variation in extensibility of human skin in vivo. , 1969, Journal of biomechanics.

[111]  H. Zahouani,et al.  In vivo measurements of the elastic mechanical properties of human skin by indentation tests. , 2008, Medical engineering & physics.

[112]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[113]  P. Nielsen,et al.  Mechanical characterisation of in vivo human skin using a 3D force-sensitive micro-robot and finite element analysis , 2011, Biomechanics and modeling in mechanobiology.

[114]  T J Joyce,et al.  Resolving the viscoelasticity and anisotropy dependence of the mechanical properties of skin from a porcine model , 2016, Biomechanics and modeling in mechanobiology.

[115]  J. Humphrey,et al.  Determination of a constitutive relation for passive myocardium: II. Parameter estimation. , 1990, Journal of biomechanical engineering.

[116]  Gregory J. Gerling,et al.  Compressive Viscoelasticity of Freshly Excised Mouse Skin Is Dependent on Specimen Thickness, Strain Level and Rate , 2015, PloS one.

[117]  F. Montáns,et al.  Determination of the WYPiWYG strain energy density of skin through finite element analysis of the experiments on circular specimens , 2017 .

[118]  Nam-Ho Kim Introduction to Nonlinear Finite Element Analysis , 2014 .

[119]  G. Holzapfel,et al.  A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis , 2002 .

[120]  James C. Weaver,et al.  Hydrogels with tunable stress relaxation regulate stem cell fate and activity , 2015, Nature materials.

[121]  O. Bruhns,et al.  Hypo-Elasticity Model Based upon the Logarithmic Stress Rate , 1997 .

[122]  D. Borst,et al.  Fundamental issues in finite element analyses of localization of deformation , 1993 .

[123]  Manuel Doblaré,et al.  An anisotropic pseudo-elastic approach for modelling Mullins effect in fibrous biological materials , 2009 .

[124]  Abbas Samani,et al.  Measurement of the hyperelastic properties of tissue slices with tumour inclusion. , 2008, Physics in medicine and biology.

[125]  Ellen Kuhl,et al.  Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery. , 2014, Computers & structures.

[126]  J. Murphy Evolution of anisotropy in soft tissue , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[127]  Y C Fung,et al.  Three-dimensional stress distribution in arteries. , 1983, Journal of biomechanical engineering.

[128]  Lallit Anand,et al.  Moderate deformations in extension-torsion of incompressible isotropic elastic materials , 1986 .

[129]  Silvestro Micera,et al.  Stiffening by fiber reinforcement in soft materials: a hyperelastic theory at large strains and its application. , 2011, Journal of the mechanical behavior of biomedical materials.

[130]  R. Haut The effects of orientation and location on the strength of dorsal rat skin in high and low speed tensile failure experiments. , 1989, Journal of biomechanical engineering.

[131]  Theodore T. Tower,et al.  Fiber Alignment Imaging During Mechanical Testing of Soft Tissues , 2002, Annals of Biomedical Engineering.

[132]  Mika Vihavainen,et al.  The Fixation Strength of Six Hamstring Tendon Graft Fixation Devices in Anterior Cruciate Ligament Reconstruction: Part II: Tibial Site * , 2003, The American journal of sports medicine.

[133]  C. G. Lyons,et al.  Viscoelastic properties of passive skeletal muscle in compression-cyclic behaviour. , 2009, Journal of biomechanics.

[134]  S. L. Evans,et al.  Measuring the mechanical properties of human skin in vivo using digital image correlation and finite element modelling , 2009 .

[135]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[136]  Bernard Querleux,et al.  Computational Biophysics of the Skin , 2014 .

[137]  Skin non-linear viscoelastic properties cannot be predicted using quasi-linear viscoelasticity , 2010, Proceedings of the 2010 IEEE 36th Annual Northeast Bioengineering Conference (NEBEC).

[138]  M. Marco,et al.  Estimation of the reinforcement factor ξ for calculating the transverse stiffness E2 with the Halpin–Tsai equations using the finite element method , 2015 .

[139]  K. Bathe Finite Element Procedures , 1995 .

[140]  C. G. Lyons,et al.  Viscoelastic properties of passive skeletal muscle in compression: stress-relaxation behaviour and constitutive modelling. , 2008, Journal of biomechanics.

[141]  Ronald S. Rivlin,et al.  The mechanics of non-linear materials with memory , 1959 .

[142]  Marcos Latorre,et al.  Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle. , 2017, Journal of biomechanical engineering.

[143]  Georges Limbert,et al.  A mechanistic insight into the mechanical role of the stratum corneum during stretching and compression of the skin. , 2015, Journal of the mechanical behavior of biomedical materials.

[144]  Ellen Kuhl,et al.  On the effect of prestrain and residual stress in thin biological membranes. , 2013, Journal of the mechanics and physics of solids.

[145]  J. M. Goicolea,et al.  On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics , 2007 .

[146]  G. Borelli Borelli's On the Movement of Animals - On the Force of Percussion , 2014 .

[147]  Maria A. Holland,et al.  Growth on demand: reviewing the mechanobiology of stretched skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[148]  Brian J. Briscoe,et al.  Friction and lubrication of human skin , 2007 .

[149]  A. Douglas,et al.  Physically based strain invariant set for materials exhibiting transversely isotropic behavior , 2001 .

[150]  Joseph J O'Hagan,et al.  Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples , 2009, Physics in medicine and biology.

[151]  Thao D Nguyen,et al.  Full-field bulge test for planar anisotropic tissues: part II--a thin shell method for determining material parameters and comparison of two distributed fiber modeling approaches. , 2013, Acta biomaterialia.

[152]  G. Genin,et al.  A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials , 2015, Journal of The Royal Society Interface.

[153]  D. Balzani,et al.  Comparative analysis of damage functions for soft tissues: Properties at damage initialization , 2015 .

[154]  H Zahouani,et al.  Non contact method for in vivo assessment of skin mechanical properties for assessing effect of ageing. , 2012, Medical engineering & physics.

[155]  J. C. H. Affdl,et al.  The Halpin-Tsai Equations: A Review , 1976 .

[156]  Stefano Piccolo,et al.  Transduction of mechanical and cytoskeletal cues by YAP and TAZ , 2012, Nature Reviews Molecular Cell Biology.

[157]  G. Holzapfel,et al.  An orthotropic viscoelastic model for the passive myocardium: continuum basis and numerical treatment , 2016, Computer methods in biomechanics and biomedical engineering.

[158]  François Berthod,et al.  Collagen-Based Biomaterials for Tissue Engineering Applications , 2010, Materials.

[159]  K. Seffen,et al.  Temperature-dependent mechanical behaviours of skin tissue , 2008 .

[160]  K. Langer,et al.  On the anatomy and physiology of the skin: I. The cleavability of the cutis , 1978 .

[161]  Yanhang Zhang,et al.  An Experimental and Theoretical Study on the Anisotropy of Elastin Network , 2009, Annals of Biomedical Engineering.

[162]  E. Kearsley,et al.  Some Methods of Measurement of an Elastic Strain‐Energy Function of the Valanis‐Landel Type , 1980 .

[163]  G. Gelikonov,et al.  In vivo optical coherence tomography imaging of human skin: norm and pathology , 2000, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[164]  F. Montáns,et al.  A new approach to modeling isotropic damage for Mullins effect in hyperelastic materials , 2015 .

[165]  Hanif M. Ladak,et al.  Template-based finite-element mesh generation from medical images , 2005, Comput. Methods Programs Biomed..

[166]  H. Donahue,et al.  From streaming‐potentials to shear stress: 25 years of bone cell mechanotransduction , 2009, Journal of orthopaedic research : official publication of the Orthopaedic Research Society.

[167]  M. B. Rubin,et al.  An anisotropic discrete fibre model based on a generalised strain invariant with application to soft biological tissues , 2012 .

[168]  Yuye Tang,et al.  Deformation micromechanisms of collagen fibrils under uniaxial tension , 2009, Journal of The Royal Society Interface.

[169]  P. Bazant,et al.  Efficient Numerical Integration on the Surface of a Sphere , 1986 .

[170]  Ellen Kuhl,et al.  Characterization of living skin using multi-view stereo and isogeometric analysis. , 2014, Acta biomaterialia.

[171]  D'arcy W. Thompson On growth and form i , 1943 .

[172]  Cwj Cees Oomens,et al.  The relative contributions of different skin layers to the mechanical behavior of human skin in vivo using suction experiments. , 2006, Medical engineering & physics.

[173]  van Dh Dick Campen,et al.  A mixture approach to the mechanics of skin. , 1987, Journal of biomechanics.

[174]  M. Boyce,et al.  A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials , 1993 .

[175]  Eric Viguier,et al.  The biomechanical properties of canine skin measured in situ by uniaxial extension. , 2014, Journal of biomechanics.

[176]  A. Akbarzadeh,et al.  An update on clinical applications of electrospun nanofibers for skin bioengineering , 2016, Artificial cells, nanomedicine, and biotechnology.

[177]  S Weghorst,et al.  Fast finite element modeling for surgical simulation. , 1999, Studies in health technology and informatics.

[178]  R. Ogden,et al.  Introducing mesoscopic information into constitutive equations for arterial walls , 2007, Biomechanics and modeling in mechanobiology.

[179]  Gregory J. Gerling,et al.  Hyperelastic Material Properties of Mouse Skin under Compression , 2013, PloS one.

[180]  Charles A. Taylor,et al.  A Computational Framework for Fluid-Solid-Growth Modeling in Cardiovascular Simulations. , 2009, Computer methods in applied mechanics and engineering.

[181]  M. B. Rubin,et al.  A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles , 2011 .

[182]  J. Humphrey,et al.  Determination of a constitutive relation for passive myocardium: I. A new functional form. , 1990, Journal of biomechanical engineering.

[183]  G Wang,et al.  ImageParser: a tool for finite element generation from three-dimensional medical images , 2004, Biomedical engineering online.

[184]  Klaus-Jürgen Bathe,et al.  Modeling large strain anisotropic elasto-plasticity with logarithmic strain and stress measures , 2011 .

[185]  Francisco J. Montáns,et al.  Understanding the need of the compression branch to characterize hyperelastic materials , 2017 .

[186]  Y. Lanir,et al.  Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin , 2001, Annals of Biomedical Engineering.

[187]  P. Corcuff,et al.  In Vivo Studies of the Evolution of Physical Properties of the Human Skin with Age , 1984, International journal of dermatology.

[188]  L. Soslowsky,et al.  Characterizing the mechanical contribution of fiber angular distribution in connective tissue: comparison of two modeling approaches , 2010, Biomechanics and modeling in mechanobiology.

[189]  L B Sandberg,et al.  Elastin structure in health and disease. , 1976, International review of connective tissue research.

[190]  J. C. Simo,et al.  An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids , 1993 .

[191]  Warren P. Mason,et al.  Introduction to polymer viscoelasticity , 1972 .

[192]  M. Ferguson,et al.  Tissue engineering of replacement skin: the crossroads of biomaterials, wound healing, embryonic development, stem cells and regeneration , 2007, Journal of The Royal Society Interface.

[193]  R. Guy,et al.  Bioavailability and bioequivalence of topical glucocorticoids. , 2008, European journal of pharmaceutics and biopharmaceutics : official journal of Arbeitsgemeinschaft fur Pharmazeutische Verfahrenstechnik e.V.

[194]  J. Gosline,et al.  Elastic proteins: biological roles and mechanical properties. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[195]  Brad Lee Boyce,et al.  Modeling the anisotropic finite-deformation viscoelastic behavior of soft fiber-reinforced composites , 2007 .

[196]  Mikhail Itskov,et al.  A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues , 2007 .

[197]  L. E. Malvern Introduction to the mechanics of a continuous medium , 1969 .

[198]  W. Kuhn,et al.  Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe , 1942 .

[199]  Xuefeng Zhao,et al.  Non-linear micromechanics of soft tissues. , 2013, International journal of non-linear mechanics.

[200]  Y. Fung,et al.  The stress-strain relationship for the skin. , 1976, Journal of biomechanics.

[201]  O. H. Yeoh,et al.  Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates , 1990 .

[202]  Victor H Barocas,et al.  Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. , 2006, Journal of biomechanical engineering.

[203]  Y. Lanir Constitutive equations for fibrous connective tissues. , 1983, Journal of biomechanics.

[204]  Martyn P Nash,et al.  Computational and experimental characterization of skin mechanics: identifying current challenges and future directions , 2013, Wiley interdisciplinary reviews. Systems biology and medicine.

[205]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[206]  Jeffrey E. Bischoff,et al.  Reduced Parameter Formulation for Incorporating Fiber Level Viscoelasticity into Tissue Level Biomechanical Models , 2006, Annals of Biomedical Engineering.

[207]  J. Burša,et al.  Poisson׳s ratio of arterial wall - Inconsistency of constitutive models with experimental data. , 2016, Journal of the mechanical behavior of biomedical materials.

[208]  José Crespo,et al.  WYPIWYG hyperelasticity for isotropic, compressible materials , 2016, Computational Mechanics.

[209]  Yi Liu,et al.  A Micromechanics Finite-Strain Constitutive Model of Fibrous Tissue. , 2011, Journal of the mechanics and physics of solids.

[210]  R. Pyeritz Ehlers-Danlos syndrome. , 2000, The New England journal of medicine.

[211]  Andreas Menzel,et al.  Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling , 2009 .

[212]  M. R. Dodge,et al.  In vitro fracture testing of submicron diameter collagen fibril specimens. , 2010, Biophysical journal.

[213]  Thao D Nguyen,et al.  Full-field bulge test for planar anisotropic tissues: part I--experimental methods applied to human skin tissue. , 2013, Acta biomaterialia.

[214]  Ge Wang,et al.  Modeling of elastic modulus evolution of cirrhotic human liver , 2004, IEEE Transactions on Biomedical Engineering.

[215]  D. Ku,et al.  3D MRI-based anisotropic FSI models with cyclic bending for human coronary atherosclerotic plaque mechanical analysis. , 2009, Journal of biomechanical engineering.

[216]  T. Biedermann,et al.  Tissue engineering of skin. , 2010, Burns : journal of the International Society for Burn Injuries.

[217]  H Alexander,et al.  Variations with age in the mechanical properties of human skin in vivo. , 2006, Journal of tissue viability.

[218]  Jung Kim,et al.  Characterization of Viscoelastic Soft Tissue Properties from In Vivo Animal Experiments and Inverse FE Parameter Estimation , 2005, MICCAI.

[219]  B Calvo,et al.  Mechanical characterization and constitutive modelling of the damage process in rectus sheath. , 2012, Journal of the mechanical behavior of biomedical materials.

[220]  Dawn M Elliott,et al.  Accurate Prediction of Stress in Fibers with Distributed Orientations Using Generalized High-Order Structure Tensors. , 2014, Mechanics of materials : an international journal.

[221]  R J Minns,et al.  The role of the fibrous components and ground substance in the mechanical properties of biological tissues: a preliminary investigation. , 1973, Journal of biomechanics.

[222]  Jouni Uitto,et al.  The role of elastin and collagen in cutaneous aging: intrinsic aging versus photoexposure. , 2008, Journal of drugs in dermatology : JDD.

[223]  G. Limbert State-of-the-Art Constitutive Models of Skin Biomechanics , 2014 .

[224]  Douglas D Cook,et al.  The generic modeling fallacy: Average biomechanical models often produce non-average results! , 2016, Journal of biomechanics.

[225]  Jay D. Humphrey,et al.  An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity , 2000 .

[226]  M. Destrade,et al.  Ray W Ogden: An Appreciation , 2015 .

[227]  D. W. Saunders,et al.  The free energy of deformation for vulcanized rubber , 1952 .

[228]  J P Stegemann,et al.  Strategies for directing the structure and function of three-dimensional collagen biomaterials across length scales. , 2014, Acta biomaterialia.

[229]  Wan Abas Wa Biaxial tension test of human skin in vivo. , 1994 .

[230]  R. Timpl,et al.  The collagen superfamily. , 1995, International archives of allergy and immunology.

[231]  K. Rajagopal,et al.  Towards an understanding of the mechanics underlying aortic dissection , 2007, Biomechanics and modeling in mechanobiology.

[232]  Ellen Kuhl,et al.  Isogeometric Kirchhoff-Love shell formulations for biological membranes. , 2015, Computer methods in applied mechanics and engineering.

[233]  B. Roth,et al.  A mathematical model for electrical stimulation of a monolayer of cardiac cells. , 2004 .

[234]  S L Zeger,et al.  Biaxial stress-strain properties of canine pericardium. , 1986, Journal of molecular and cellular cardiology.

[235]  J. Ihlemann,et al.  On the thermodynamics of pseudo-elastic material models which reproduce the Mullins effect , 2014, 1408.0671.

[236]  Mary C. Boyce,et al.  Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity , 1996 .

[237]  Juan José Ródenas,et al.  Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry , 2015 .

[238]  F. Montáns,et al.  Computational anisotropic hardening multiplicative elastoplasticity based on the corrector elastic logarithmic strain rate , 2017 .

[239]  Cormac Flynn,et al.  Finite element modelling of forearm skin wrinkling , 2008, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[240]  F. Montáns,et al.  Fractional Mathematical Operators and Their Computational Approximation , 2016 .

[241]  R. Lavker,et al.  Aged skin: a study by light, transmission electron, and scanning electron microscopy. , 1987, The Journal of investigative dermatology.

[242]  Victor H. Barocas,et al.  Fiber-Network Modeling in Biomechanics: Theoretical and Analytical Approaches , 2017 .

[243]  J D Humphrey,et al.  A new constitutive formulation for characterizing the mechanical behavior of soft tissues. , 1987, Biophysical journal.

[244]  Milan Jirásek,et al.  Nonlocal models for damage and fracture: Comparison of approaches , 1998 .

[245]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[246]  H. Rothert,et al.  Formulation and implementation of three-dimensional viscoelasticity at small and finite strains , 1997 .

[247]  A new constitutive model for multi-layered collagenous tissues. , 2008, Journal of biomechanics.

[248]  K. Bathe,et al.  A finite element formulation for nonlinear incompressible elastic and inelastic analysis , 1987 .

[249]  K. Bathe,et al.  Studies of finite element procedures—stress band plots and the evaluation of finite element meshes , 1986 .

[250]  D. G. T. Strange,et al.  Extracellular-matrix tethering regulates stem-cell fate. , 2012, Nature materials.

[251]  A Viidik,et al.  The role of elastin in the mechanical properties of skin. , 1988, Journal of biomechanics.

[252]  L. DeLouise,et al.  Applications of nanotechnology in dermatology. , 2012, The Journal of investigative dermatology.

[253]  S C Cowin,et al.  How is a tissue built? , 2000, Journal of biomechanical engineering.

[254]  Sarah E. Duenwald,et al.  Stress relaxation and recovery in tendon and ligament: experiment and modeling. , 2010, Biorheology.

[255]  J E Scott,et al.  Elasticity in extracellular matrix ‘shape modules’ of tendon, cartilage, etc. A sliding proteoglycan‐filament model , 2003, The Journal of physiology.

[256]  L. Mullins Softening of Rubber by Deformation , 1969 .

[257]  D. J. Patel,et al.  Nonlinear anisotropic viscoelastic properites of canine arterial segments. , 1977, Journal of biomechanics.

[258]  J. Howard,et al.  Mechanics of Motor Proteins and the Cytoskeleton , 2001 .

[259]  Jacob Lubliner,et al.  A model of rubber viscoelasticity , 1985 .

[260]  R. Wildnauer,et al.  The mechanical properties of stratum corneum. I. The effect of water and ambient temperature on the tensile properties of newborn rat stratum corneum. , 1975, Biochimica et biophysica acta.

[261]  Paul Steinmann,et al.  Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data , 2012 .

[262]  A. N. Annaidh,et al.  Non‐invasive evaluation of skin tension lines with elastic waves , 2016, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[263]  M Doblaré,et al.  On modelling nonlinear viscoelastic effects in ligaments. , 2008, Journal of biomechanics.

[264]  Hans Gregersen,et al.  Biomechanical behaviour of oesophageal tissues: material and structural configuration, experimental data and constitutive analysis. , 2009, Medical engineering & physics.

[265]  N. Kollias,et al.  Skin Viscoelasticity Displays Site- and Age-Dependent Angular Anisotropy , 2007, Skin Pharmacology and Physiology.

[266]  J. Downs,et al.  Peripapillary and posterior scleral mechanics--part I: development of an anisotropic hyperelastic constitutive model. , 2009, Journal of biomechanical engineering.

[267]  C. Chamis,et al.  Critique on Theories Predicting Thermoelastic Properties of Fibrous Composites , 1968 .

[268]  Estefanía Peña,et al.  A formulation to model the nonlinear viscoelastic properties of the vascular tissue , 2011 .

[269]  S. Pillai,et al.  Future Prospects for Scaffolding Methods and Biomaterials in Skin Tissue Engineering: A Review , 2016, International journal of molecular sciences.

[270]  Wolfgang Muschik,et al.  Thermodynamics with Internal Variables. Part I. General Concepts , 1994 .

[271]  B. Hinz,et al.  The nano-scale mechanical properties of the extracellular matrix regulate dermal fibroblast function. , 2014, The Journal of investigative dermatology.

[272]  M. Sacks,et al.  Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II--A structural constitutive model. , 2000, Journal of biomechanical engineering.

[273]  Ellen Kuhl,et al.  Stretching skin: The physiological limit and beyond. , 2012, International journal of non-linear mechanics.

[274]  V C Mow,et al.  The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. , 1990, Journal of biomechanics.

[275]  Richard A. Regueiro,et al.  Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity , 2001 .

[276]  R. Landel,et al.  The Strain‐Energy Function of a Hyperelastic Material in Terms of the Extension Ratios , 1967 .

[277]  Klaus-Jürgen Bathe,et al.  Computational issues in large strain elasto‐plasticity: an algorithm for mixed hardening and plastic spin , 2005 .

[278]  D A Hidalgo,et al.  A Review of 716 Consecutive Free Flaps for Oncologic Surgical Defects: Refinement in Donor‐Site Selection and Technique , 1998, Plastic and reconstructive surgery.

[279]  A. Bakker,et al.  3-D schapery representation for non-linear viscoelasticity and finite element implementation , 1996 .

[280]  E Peña,et al.  Viscoelastic properties of the passive mechanical behavior of the porcine carotid artery: influence of proximal and distal positions. , 2012, Biorheology.

[281]  D W Hukins,et al.  Collagen orientation and molecular spacing during creep and stress-relaxation in soft connective tissues. , 1998, The Journal of experimental biology.

[282]  Ignacio Carol,et al.  Microplane constitutive model and computational framework for blood vessel tissue. , 2006, Journal of biomechanical engineering.

[283]  B. Mcgaw,et al.  Turnover rates of different collagen types measured by isotope ratio mass spectrometry. , 1992, Biochimica et biophysica acta.

[284]  Marcos Latorre,et al.  WYPiWYG hyperelasticity without inversion formula , 2017 .

[285]  Alessio Gizzi,et al.  Statistical characterization of the anisotropic strain energy in soft materials with distributed fibers , 2016 .

[286]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[287]  J. Scott,et al.  Tendon response to tensile stress: an ultrastructural investigation of collagen:proteoglycan interactions in stressed tendon. , 1995, Journal of anatomy.

[288]  Alireza Karimi,et al.  Determination of the axial and circumferential mechanical properties of the skin tissue using experimental testing and constitutive modeling , 2015, Computer Methods in Biomechanics and Biomedical Engineering.

[289]  Siamak Niroomandi,et al.  Model order reduction in hyperelasticity: a proper generalized decomposition approach , 2013 .

[290]  M. Tassabehji,et al.  An elastin gene mutation producing abnormal tropoelastin and abnormal elastic fibres in a patient with autosomal dominant cutis laxa. , 1998, Human molecular genetics.

[291]  J. Uitto,et al.  Elastoderma — Disease of Elastin Accumulation within the Skin , 1985 .

[292]  Michael S Sacks,et al.  Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. , 2003, Journal of biomechanical engineering.

[293]  Boon Chuan Low,et al.  YAP/TAZ as mechanosensors and mechanotransducers in regulating organ size and tumor growth , 2014, FEBS letters.

[294]  J. Willis,et al.  The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. II. Examples , 1997, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[295]  Nicola Elvassore,et al.  Role of YAP/TAZ in mechanotransduction , 2011, Nature.

[296]  A. E. Ehret,et al.  A polyconvex anisotropic strain–energy function for soft collagenous tissues , 2006, Biomechanics and modeling in mechanobiology.

[297]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[298]  F. Yin,et al.  Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. , 2001, Journal of biomechanics.

[299]  M. Bro-Nielsen,et al.  Finite element modeling in surgery simulation , 1998, Proc. IEEE.

[300]  Francisco J. Montáns,et al.  Fully anisotropic finite strain viscoelasticity based on a reverse multiplicative decomposition and logarithmic strains , 2016, 2104.02192.

[301]  E. Menzel,et al.  Two-dimensional elastic properties of human skin in terms of an incremental model at the in vivo configuration. , 1995, Medical engineering & physics.

[302]  A. Gent,et al.  Forms for the stored (strain) energy function for vulcanized rubber , 1958 .

[303]  R. Lakes,et al.  Creep and Relaxation in Ligament: Theory, Methods and Experiment , 2006 .

[304]  Sheila MacNeil,et al.  Progress and opportunities for tissue-engineered skin , 2007, Nature.

[305]  H. Haslach,et al.  Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue , 2005, Biomechanics and modeling in mechanobiology.

[306]  Y. Fung,et al.  Pseudoelasticity of arteries and the choice of its mathematical expression. , 1979, The American journal of physiology.

[307]  D. Meaney,et al.  A quasi-linear, viscoelastic, structural model of the plantar soft tissue with frequency-sensitive damping properties. , 2004, Journal of biomechanical engineering.

[308]  Paul Ackermans,et al.  Linear shear response of the upper skin layers. , 2011, Biorheology.

[309]  Jeffrey E. Bischoff,et al.  Finite element simulations of orthotropic hyperelasticity , 2002 .

[310]  Klaus-Jürgen Bathe,et al.  A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension–compression test data , 2009 .

[311]  Georges Limbert,et al.  A mesostructurally-based anisotropic continuum model for biological soft tissues--decoupled invariant formulation. , 2011, Journal of the mechanical behavior of biomedical materials.

[312]  Yoram Lanir,et al.  Multi-scale Structural Modeling of Soft Tissues Mechanics and Mechanobiology , 2017 .

[313]  S. Flatters Characterization of a model of persistent postoperative pain evoked by skin/muscle incision and retraction (SMIR) , 2008, PAIN®.

[314]  Z. Liu,et al.  The Preconditioning and Stress Relaxation of Skin Tissue , 2008 .

[315]  M. Sacks,et al.  A method to quantify the fiber kinematics of planar tissues under biaxial stretch. , 1997, Journal of biomechanics.

[316]  Ken Parsons,et al.  Human Thermal Environments: The Effects of Hot, Moderate, and Cold Environments on Human Health, Comfort and Performance , 1999 .

[317]  Miguel Ángel Martínez,et al.  Anisotropic microsphere-based approach to damage in soft fibered tissue , 2012, Biomechanics and modeling in mechanobiology.

[318]  S Niroomandi,et al.  Real‐time simulation of biological soft tissues: a PGD approach , 2013, International journal for numerical methods in biomedical engineering.

[319]  B. Moran,et al.  An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus , 2006 .

[320]  J. Uitto,et al.  The effect of photodamage on dermal extracellular matrix. , 1996, Clinics in dermatology.

[321]  J M Mansour,et al.  Dynamic measurement of the viscoelastic properties of skin. , 1991, Journal of biomechanics.

[322]  J. Fulkerson,et al.  Mechanical Evaluation of a Soft Tissue Interference Screw in Free Tendon Anterior Cruciate Ligament Graft Fixation , 2001, The American journal of sports medicine.

[323]  Gregory J. Gerling,et al.  Merkel Cells Are Essential for Light-Touch Responses , 2009, Science.

[324]  Mark Taylor,et al.  Accounting for patient variability in finite element analysis of the intact and implanted hip and knee: A review , 2013, International journal for numerical methods in biomedical engineering.

[325]  Sanjay Govindjee,et al.  A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect , 1991 .

[326]  Lutz Dürselen,et al.  Finite element modeling of soft tissues: material models, tissue interaction and challenges. , 2014, Clinical biomechanics.

[327]  Walter Noll,et al.  Foundations of Linear Viscoelasticity , 1961 .

[328]  E. Kuhl,et al.  A continuum model for remodeling in living structures , 2007 .

[329]  F P T Baaijens,et al.  Influence of hydration and experimental length scale on the mechanical response of human skin in vivo, using optical coherence tomography , 2004, Skin research and technology : official journal of International Society for Bioengineering and the Skin (ISBS) [and] International Society for Digital Imaging of Skin (ISDIS) [and] International Society for Skin Imaging.

[330]  A. Goriely,et al.  On the modeling of fiber dispersion in fiber-reinforced elastic materials , 2015 .

[331]  William Montagna,et al.  The Structure and Function of Skin , 1956, The Yale Journal of Biology and Medicine.

[332]  R. Jaenisch,et al.  Type III collagen is crucial for collagen I fibrillogenesis and for normal cardiovascular development. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[333]  Y. Fung,et al.  Residual Stress in Arteries , 1986 .

[334]  Wolfgang Ehlers,et al.  Finite Elastic Deformations in Liquid-Saturated and Empty Porous Solids , 1999 .

[335]  J. Weiss,et al.  Finite element implementation of incompressible, transversely isotropic hyperelasticity , 1996 .

[336]  Ray W. Ogden,et al.  A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber , 2003 .

[337]  T. G. Rogers,et al.  A non-linear integral representation for viscoelastic behaviour , 1968 .

[338]  C. Daly Biomechanical properties of dermis. , 1982, The Journal of investigative dermatology.

[339]  Heng Xiao,et al.  Self-consistent Eulerian rate type elasto-plasticity models based upon the logarithmic stress rate , 1999 .

[340]  H. Matsumura,et al.  Preconditioning of the distal portion of a rat random-pattern skin flap. , 2001, British journal of plastic surgery.

[341]  Abbas Samani,et al.  A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment. , 2010, Physics in medicine and biology.

[342]  K. Langer On the anatomy and physiology of the skin: III. The elasticity of the cutis , 1978 .

[343]  Byung H. Oh,et al.  Microplane Model for Progressive Fracture of Concrete and Rock , 1985 .

[344]  R. Neubert,et al.  Does human leukocyte elastase degrade intact skin elastin? , 2012, The FEBS journal.

[345]  Richard Schapery,et al.  Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic , 1971 .

[346]  Heinrich Hencky,et al.  The Elastic Behavior of Vulcanized Rubber , 1933 .

[347]  P. Sengupta The Laboratory Rat: Relating Its Age With Human's , 2013, International journal of preventive medicine.

[348]  K. Green,et al.  Desmosomes and hemidesmosomes: structure and function of molecular components , 1996, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[349]  Manuel Doblaré,et al.  An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects , 2007 .

[350]  Ellen Kuhl,et al.  Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin , 2015, Biomechanics and modeling in mechanobiology.

[351]  Rami Haj-Ali,et al.  Numerical finite element formulation of the Schapery non‐linear viscoelastic material model , 2004 .

[352]  C. Lim,et al.  Tissue scaffolds for skin wound healing and dermal reconstruction. , 2010, Wiley interdisciplinary reviews. Nanomedicine and nanobiotechnology.

[353]  J D Humphrey,et al.  Remodeling of a collagenous tissue at fixed lengths. , 1999, Journal of biomechanical engineering.

[354]  J. A. Bea,et al.  An experimental study of the mouse skin behaviour: damage and inelastic aspects. , 2008, Journal of biomechanics.

[355]  Daniel Balzani,et al.  Statistical approach for a continuum description of damage evolution in soft collagenous tissues , 2014 .

[356]  D. Pioletti,et al.  Non-linear viscoelastic laws for soft biological tissues , 2000 .

[357]  T. Best,et al.  The biomechanical effects of limb lengthening and botulinum toxin type A on rabbit tendon. , 2010, Journal of biomechanics.

[358]  A.J.M. Spencer,et al.  Isotropic Polynomial Invariants and Tensor Functions , 1987 .

[359]  I Vesely,et al.  The role of elastin in aortic valve mechanics. , 1997, Journal of biomechanics.

[360]  Mikhail Itskov,et al.  A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function , 2004 .

[361]  Estefanía Peña,et al.  Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data , 2017, Annals of Biomedical Engineering.

[362]  Katja Schenke-Layland,et al.  Skin tissue engineering--in vivo and in vitro applications. , 2011, Advanced drug delivery reviews.

[363]  M. Jeschke,et al.  Methodologies in creating skin substitutes , 2016, Cellular and Molecular Life Sciences.

[364]  Kristi S. Anseth,et al.  Mechanical memory and dosing influence stem cell fate , 2014, Nature materials.

[365]  J. Lévêque,et al.  Mechanical properties and Young's modulus of human skin in vivo , 2004, Archives of Dermatological Research.

[366]  F. O. Schmitt,et al.  THE STRUCTURE OF HUMAN SKIN COLLAGEN AS STUDIED WITH THE ELECTRON MICROSCOPE , 1948, The Journal of experimental medicine.

[367]  Gerhard A. Holzapfel,et al.  ON LARGE STRAIN VISCOELASTICITY: CONTINUUM FORMULATION AND FINITE ELEMENT APPLICATIONS TO ELASTOMERIC STRUCTURES , 1996 .

[368]  Paul D. Gasson,et al.  Simulating plastic surgery: from human skin tensile tests, through hyperelastic finite element models to real-time haptics. , 2010, Progress in biophysics and molecular biology.

[369]  R. M. Natal Jorge,et al.  A Comparative Study of Several Material Models for Prediction of Hyperelastic Properties: Application to Silicone‐Rubber and Soft Tissues , 2006 .

[370]  K. Grosh,et al.  Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network , 2004, q-bio/0411037.

[371]  I. Brown,et al.  A scanning electron microscope study of the effects of uniaxial tension on human skin , 1973, The British journal of dermatology.

[372]  T. Meinders,et al.  Viscoplastic regularization of local damage models: revisited , 2013 .

[373]  Sidney Fels,et al.  Simulating the three-dimensional deformation of in vivo facial skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[374]  A. Weiss,et al.  Electrospun synthetic human elastin:collagen composite scaffolds for dermal tissue engineering. , 2012, Acta biomaterialia.

[375]  Wei Liu,et al.  Collagen Tissue Engineering: Development of Novel Biomaterials and Applications , 2008, Pediatric Research.

[376]  Gerhard A Holzapfel,et al.  Comparison of a multi-layer structural model for arterial walls with a fung-type model, and issues of material stability. , 2004, Journal of biomechanical engineering.

[377]  Luigi Preziosi,et al.  The insight of mixtures theory for growth and remodeling , 2010 .

[378]  M. Sacks,et al.  Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp--Part I: Experimental results. , 2000, Journal of biomechanical engineering.

[379]  Ivan Vesely,et al.  Invariant formulation for dispersed transverse isotropy in aortic heart valves , 2005, Biomechanics and modeling in mechanobiology.

[380]  Michael S. Sacks,et al.  Structure-Based Mechanics of Tissues and Organs , 2016, Springer US.

[381]  R. Taylor,et al.  Thermomechanical analysis of viscoelastic solids , 1970 .

[382]  Robert J. Martin,et al.  Geometry of Logarithmic Strain Measures in Solid Mechanics , 2015, 1505.02203.

[383]  Morten Bro-Nielsen,et al.  Real‐time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation , 1996, Comput. Graph. Forum.

[384]  Michael D. Gilchrist,et al.  Slight compressibility and sensitivity to changes in Poisson's ratio , 2012, 1302.2735.

[385]  Klaus-Jürgen Bathe,et al.  Spurious modes in geometrically nonlinear small displacement finite elements with incompatible modes , 2014 .

[386]  Peter J. Hunter,et al.  Estimating material parameters of a structurally based constitutive relation for skin mechanics , 2011, Biomechanics and modeling in mechanobiology.

[387]  Alireza Karimi,et al.  Measurement of the viscoelastic mechanical properties of the skin tissue under uniaxial loading , 2016 .

[388]  M. E. van der Rest,et al.  Collagen family of proteins , 1991, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[389]  Y. Fung A first course in continuum mechanics , 1969 .

[390]  M. Monleón Pradas,et al.  Nonlinear viscoelastic behaviour of the flexor tendon of the human hand , 1990 .

[391]  Serdar Göktepe,et al.  A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage , 2005 .

[392]  B. Vollmar,et al.  Temporary Angiogenic Transformation of the Skin Graft Vasculature after Reperfusion , 2010, Plastic and reconstructive surgery.

[393]  J. Humphrey,et al.  A microstructurally inspired damage model for early venous thrombus. , 2016, Journal of the mechanical behavior of biomedical materials.

[394]  A D McCulloch,et al.  A three-dimensional finite element method for large elastic deformations of ventricular myocardium: I--Cylindrical and spherical polar coordinates. , 1996, Journal of biomechanical engineering.

[395]  On the tension-compression switch of the Gasser-Ogden-Holzapfel model: Analysis and a new pre-integrated proposal. , 2016, Journal of the mechanical behavior of biomedical materials.

[396]  K. Takamizawa,et al.  Strain energy density function and uniform strain hypothesis for arterial mechanics. , 1987, Journal of biomechanics.

[397]  Y Lanir,et al.  Two-dimensional mechanical properties of rabbit skin. I. Experimental system. , 1974, Journal of biomechanics.

[398]  Jay D. Humphrey,et al.  A CONSTRAINED MIXTURE MODEL FOR GROWTH AND REMODELING OF SOFT TISSUES , 2002 .

[399]  R. Ogden Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[400]  F. Montáns,et al.  Material-symmetries congruency in transversely isotropic and orthotropic hyperelastic materials , 2015 .

[401]  J D Humphrey,et al.  Perspectives on biological growth and remodeling. , 2011, Journal of the mechanics and physics of solids.

[402]  Ruikang K. Wang,et al.  Determining elastic properties of skin by measuring surface waves from an impulse mechanical stimulus using phase-sensitive optical coherence tomography , 2012, Journal of The Royal Society Interface.

[403]  Oliver A. Shergold,et al.  The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates , 2006 .

[404]  M. Yamauchi,et al.  Aging and cross-linking of skin collagen. , 1988, Biochemical and biophysical research communications.

[405]  Kenneth M. Yamada,et al.  Cell migration in 3D matrix. , 2005, Current opinion in cell biology.

[406]  R. Christensen Theory of viscoelasticity : an introduction , 1971 .

[407]  Elías Cueto,et al.  Real time simulation for computational surgery: a review , 2014, Advanced Modeling and Simulation in Engineering Sciences.

[408]  P. Hunter,et al.  Computational Mechanics of the Heart , 2000 .

[409]  D. Schneider,et al.  In vitro biaxial stress-strain response of human skin. , 1984, Archives of otolaryngology.

[410]  Jeffrey E. Bischoff,et al.  A microstructurally based orthotropic hyperelastic constitutive law , 2002 .

[411]  Jay D. Humphrey,et al.  Computer Methods in Membrane Biomechanics , 1998 .

[412]  L. Mullins Effect of Stretching on the Properties of Rubber , 1948 .

[413]  I. Braverman,et al.  Studies in cutaneous aging: I. The elastic fiber network. , 1982, The Journal of investigative dermatology.

[414]  Victor H Barocas,et al.  A coupled fiber-matrix model demonstrates highly inhomogeneous microstructural interactions in soft tissues under tensile load. , 2013, Journal of biomechanical engineering.

[415]  John C Gardiner,et al.  Ligament material behavior is nonlinear, viscoelastic and rate-independent under shear loading. , 2002, Journal of biomechanics.

[416]  T. Beda,et al.  An approach for hyperelastic model-building and parameters estimation a review of constitutive models , 2014 .

[417]  F. Foster,et al.  Ultrasonic and viscoelastic properties of skin under transverse mechanical stress in vitro. , 1998, Ultrasound in medicine & biology.

[418]  J. Uitto,et al.  Extracellular matrix of the skin: 50 years of progress. , 1989, The Journal of investigative dermatology.

[419]  J. S. Bergström,et al.  Mechanics of Solid Polymers: Theory and Computational Modeling , 2015 .

[420]  Gerhard A. Holzapfel,et al.  On Fiber Dispersion Models: Exclusion of Compressed Fibers and Spurious Model Comparisons , 2017 .

[421]  A. Menzel,et al.  An anisotropic micro-sphere approach applied to the modelling of soft biological tissues , 2010 .

[422]  M. Rest,et al.  Collagens: diversity at the molecular and supramolecular levels , 1993 .

[423]  Manuel Doblaré,et al.  An uncoupled directional damage model for fibred biological soft tissues. Formulation and computational aspects , 2007 .

[424]  C. Roy,et al.  The Elastic Properties of the Arterial Wall , 1881, The Journal of physiology.

[425]  Ellen Kuhl,et al.  Frontiers in growth and remodeling. , 2012, Mechanics research communications.

[426]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[427]  Francisco J. Montáns,et al.  Extension of the Sussman-Bathe spline-based hyperelastic model to incompressible transversely isotropic materials , 2013 .

[428]  J D Humphrey,et al.  Stress, strain, and mechanotransduction in cells. , 2001, Journal of biomechanical engineering.

[429]  C. Harding,et al.  Filaggrin breakdown to water binding compounds during development of the rat stratum corneum is controlled by the water activity of the environment. , 1986, Developmental biology.

[430]  Arnab Majumdar,et al.  Lung and alveolar wall elastic and hysteretic behavior in rats: effects of in vivo elastase treatment. , 2003, Journal of applied physiology.

[431]  R. Ogden,et al.  A robust anisotropic hyperelastic formulation for the modelling of soft tissue. , 2014, Journal of the mechanical behavior of biomedical materials.

[432]  K. McCloskey,et al.  Can shear stress direct stem cell fate? , 2009, Biotechnology progress.

[433]  O. Yeoh Some Forms of the Strain Energy Function for Rubber , 1993 .

[434]  Nancy A. Monteiro-Riviere,et al.  Skin Penetration of Engineered Nanomaterials , 2013 .

[435]  J. Bijlsma,et al.  Effect of Collagen Turnover on the Accumulation of Advanced Glycation End Products* , 2000, The Journal of Biological Chemistry.

[436]  Francisco J. Montáns,et al.  WYPiWYG Damage Mechanics for Soft Materials: A Data-Driven Approach , 2017 .

[437]  A. Gefen,et al.  Are in vivo and in situ brain tissues mechanically similar? , 2004, Journal of biomechanics.

[438]  R. Ogden,et al.  Hyperelastic modelling of arterial layers with distributed collagen fibre orientations , 2006, Journal of The Royal Society Interface.

[439]  M. Boyce,et al.  Constitutive models of rubber elasticity: A review , 2000 .

[440]  Sergio Oller,et al.  A generalized finite‐strain damage model for quasi‐incompressible hyperelasticity using hybrid formulation , 2016 .

[441]  Christopher J. Ploch,et al.  Author ' s personal copy Growing skin : A computational model for skin expansion in reconstructive surgery , 2011 .

[442]  D. R. Veronda,et al.  Mechanical characterization of skin-finite deformations. , 1970, Journal of biomechanics.

[443]  B. J. Mac Donald,et al.  At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials , 2013, Computational Mechanics.

[444]  Gerhard A Holzapfel,et al.  Modelling non-symmetric collagen fibre dispersion in arterial walls , 2015, Journal of The Royal Society Interface.

[445]  J Bonnoit,et al.  A Visco-hyperelastic Model With Damage for the Knee Ligaments Under Dynamic Constraints , 2002, Computer methods in biomechanics and biomedical engineering.

[446]  S. Reese,et al.  A theory of finite viscoelasticity and numerical aspects , 1998 .

[447]  J. Sherratt,et al.  Theoretical models of wound healing: past successes and future challenges. , 2002, Comptes rendus biologies.

[448]  I. Sakuma,et al.  Combined compression and elongation experiments and non-linear modelling of liver tissue for surgical simulation , 2004, Medical and Biological Engineering and Computing.

[449]  Jay D. Humphrey,et al.  Review Paper: Continuum biomechanics of soft biological tissues , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[450]  Begoña Calvo,et al.  Determination of passive viscoelastic response of the abdominal muscle and related constitutive modeling: stress-relaxation behavior. , 2014, Journal of the mechanical behavior of biomedical materials.

[451]  James C Birchall,et al.  An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. , 2013, Journal of the mechanical behavior of biomedical materials.

[452]  C. G. Lyons,et al.  A validated model of passive muscle in compression. , 2006, Journal of biomechanics.

[453]  M. Sacks Biaxial Mechanical Evaluation of Planar Biological Materials , 2000 .

[454]  Anke Stoll,et al.  Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review , 2015, Biomedizinische Technik. Biomedical engineering.

[455]  F. Montáns,et al.  Stress and strain mapping tensors and general work-conjugacy in large strain continuum mechanics , 2016 .

[456]  V. Barocas,et al.  Multiscale, structure-based modeling for the elastic mechanical behavior of arterial walls. , 2007, Journal of biomechanical engineering.

[457]  I. Vesely,et al.  Role of Preconditioning and Recovery Time in Repeated Testing of Aortic Valve Tissues: Validation Through Quasilinear Viscoelastic Theory , 2000, Annals of Biomedical Engineering.

[458]  R P Vito,et al.  Two-dimensional stress-strain relationship for canine pericardium. , 1990, Journal of biomechanical engineering.