Fractional Calculus in Biomechanics: A 3D Viscoelastic Model Using Regularized Fractional Derivative Kernels with Application to the Human Calcaneal Fat Pad

[1]  Alan D. Freed,et al.  An efficient algorithm for the evaluation of convolution integrals , 2006, Comput. Math. Appl..

[2]  Fathalla A. Rihan,et al.  Computational modelling with functional differential equations: Identification, selection, and sensitivity , 2005 .

[3]  Yury F. Luchko,et al.  Algorithms for the fractional calculus: A selection of numerical methods , 2005 .

[4]  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.

[5]  Louis J Soslowsky,et al.  The effect of overshooting the target strain on estimating viscoelastic properties from stress relaxation experiments. , 2004, Journal of biomechanical engineering.

[6]  Kai-Nan An,et al.  Dynamic mechanical properties of agarose gels modeled by a fractional derivative model. , 2004, Journal of biomechanical engineering.

[7]  H. Genant,et al.  Cortical and Trabecular Bone Mineral Loss From the Spine and Hip in Long‐Duration Spaceflight , 2004, Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research.

[8]  Alan D. Freed,et al.  Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.

[9]  E. Carew,et al.  The Effect of Strain Rate on the Viscoelastic Response of Aortic Valve Tissue: A Direct-Fit Approach , 2004, Annals of Biomedical Engineering.

[10]  A. Freed Transverse-Isotropic Elastic and Viscoelastic Solids , 2004 .

[11]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[12]  Klas Adolfsson Models and numerical procedures for fractional order viscoelasticity , 2003 .

[13]  Janice Miller-Young Factors affecting human heel pad mechanics : a finite element study , 2003 .

[14]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[15]  G. Baroud,et al.  Material properties of the human calcaneal fat pad in compression: experiment and theory. , 2002, Journal of biomechanics.

[16]  B Suki,et al.  Effects of collagenase and elastase on the mechanical properties of lung tissue strips. , 2000, Journal of applied physiology.

[17]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[18]  J. Douglas Polymer Science Applications of Path-Integration Integral Equations, and Fractional Calculus , 2000 .

[19]  W. Ames Mathematics in Science and Engineering , 1999 .

[20]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[21]  J A Weiss,et al.  Finite element implementation of anisotropic quasi-linear viscoelasticity using a discrete spectrum approximation. , 1998, Journal of biomechanical engineering.

[22]  B. Suki,et al.  Dynamic properties of lung parenchyma: mechanical contributions of fiber network and interstitial cells. , 1997, Journal of applied physiology.

[23]  A. I. Leonov On the Constitutive Equations for Nonisothermal Bulk Relaxation , 1996 .

[24]  Boris Rubin,et al.  Fractional Integrals and Potentials , 1996 .

[25]  S L Woo,et al.  A single integral finite strain viscoelastic model of ligaments and tendons. , 1996, Journal of biomechanical engineering.

[26]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[27]  R. Gorenflo,et al.  The Grünwald-Letnikov Difference Operator and Regularization of the Weyl Fractional Differentiation , 1994 .

[28]  R. Gorenflo,et al.  Locally controllable regularization of fractional derivatives , 1994 .

[29]  A. Barabasi,et al.  Lung tissue viscoelasticity: a mathematical framework and its molecular basis. , 1994, Journal of applied physiology.

[30]  R. Gorenflo,et al.  On the regularization of fractional differentiation of arbitrary positive order , 1994 .

[31]  The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra , 1993 .

[32]  P. Levoir,et al.  Deconvolution of polymer melt stress relaxation by the Padé-Laplace method , 1993 .

[33]  Ronald L. Bagley,et al.  Power law and fractional calculus model of viscoelasticity , 1989 .

[34]  S. Moolgavkar,et al.  A Method for Computing Profile-Likelihood- Based Confidence Intervals , 1988 .

[35]  M. Renardy A local existence and uniqueness theorem for a K-BKZ-fluid , 1985 .

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

[37]  M. Caputo,et al.  A new dissipation model based on memory mechanism , 1971 .

[38]  Francesco Mainardi,et al.  Linear models of dissipation in anelastic solids , 1971 .

[39]  Graham Williams,et al.  Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function , 1970 .

[40]  Bernard D. Coleman,et al.  On the general theory of fading memory , 1968 .

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

[42]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

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

[44]  A. S. Lodge Elastic Liquids: An Introductory Vector Treatment of Finite-Strain Polymer Rheology , 1964 .

[45]  B. Bernstein,et al.  A Study of Stress Relaxation with Finite Strain , 1963 .

[46]  M. L. Williams,et al.  THE STRUCTURAL ANALYSIS OF VISCOELASTIC MATERIALS , 1963 .

[47]  A. Kaye,et al.  Non-Newtonian flow in incompressible fluids , 1962 .

[48]  P. Flory,et al.  Thermodynamic relations for high elastic materials , 1961 .

[49]  R. Rivlin Large elastic deformations of isotropic materials IV. further developments of the general theory , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[50]  C. Zener Elasticity and anelasticity of metals , 1948 .

[51]  B. Gross,et al.  On Creep and Relaxation , 1947 .

[52]  E. Gripon Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Classe der Kaiserlichen Akademie der Wissenschaften in Wien (Comptes rendus de l'Académie des Sciences de Vienne) ; 1876 , 1874 .

[53]  R. Kohlrausch Ueber das Dellmann'sche Elektrometer , 1847 .