A fractional rate‐dependent cohesive‐zone model

© 2015 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

[1]  B. Persson,et al.  Crack propagation in rubber-like materials , 2005 .

[2]  E. Kramer,et al.  Interface fracture and viscoelastic deformation in finite size specimens , 1992 .

[3]  Whittle Gruffudd,et al.  Relaxation spectrum recovery using Fourier transforms , 2012 .

[4]  Cv Clemens Verhoosel,et al.  A phase‐field model for cohesive fracture , 2013 .

[5]  G. W. Blair The role of psychophysics in rheology , 1947 .

[6]  T. Siegmund,et al.  Vocal fold tissue failure: preliminary data and constitutive modeling. , 2004, Journal of biomechanical engineering.

[7]  Jay Fineberg,et al.  Instability in dynamic fracture , 1999 .

[8]  Karthik Ramani,et al.  Rate-dependent crack growth in adhesives II. Experiments and analysis , 2003 .

[9]  A. Beris,et al.  On the admissibility criteria for linear viscoelasticity kernels , 1993 .

[10]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[11]  M. Gilchrist,et al.  Bimodular rubber buckles early in bending , 2010, 1301.5437.

[12]  N. Valoroso,et al.  A cohesive zone model with rate-sensitivity for fast crack propagation , 2014 .

[13]  A. Thomas,et al.  The strength of highly elastic materials , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  William Alan Day,et al.  The Thermodynamics of Simple Materials with Fading Memory , 1972 .

[15]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[16]  Joseph Padovan,et al.  Computational algorithms for FE formulations involving fractional operators , 1987 .

[17]  R. Koeller Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .

[18]  M. Lambrecht,et al.  Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals , 2002 .

[19]  M. A. Crisfield,et al.  Progressive Delamination Using Interface Elements , 1998 .

[20]  David H. Allen,et al.  A micromechanical model for a viscoelastic cohesive zone , 2001 .

[21]  M. Crisfield,et al.  Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues , 2001 .

[22]  F. Feyel,et al.  Interface debonding models: a viscous regularization with a limited rate dependency , 2001 .

[23]  A. D. Drozdov,et al.  Fractional differential models in finite viscoelasticity , 1997 .

[24]  Marco Musto,et al.  A novel rate-dependent cohesive-zone model combining damage and visco-elasticity , 2013 .

[25]  Ludwig Boltzmann,et al.  Zur Theorie der elastischen Nachwirkung , 1878 .

[26]  R. Frassine,et al.  Experimental analysis of viscoelastic criteria for crack initiation and growth in polymers , 1996 .

[27]  Lothar Gaul,et al.  Finite Element Formulation of Viscoelastic Constitutive Equations Using Fractional Time Derivatives , 2002 .

[28]  A. Morro,et al.  Mathematical problems in linear viscoelasticity , 1987 .

[29]  E. Onat,et al.  On uniqueness in linear viscoelasticity , 1962 .

[30]  F. Akyildiz,et al.  On the spring-dashpot representation of linear viscoelastic behaviour , 1990 .

[31]  New class of creep-relaxation functions , 1995 .

[32]  Karthik Ramani,et al.  Rate-dependent crack growth in adhesives: I. Modeling approach , 2003 .

[33]  Shlomo Breuer,et al.  On the determination of free energy in linear viscoelastic solids , 1964 .

[34]  A. Kinloch,et al.  Fracture Behaviour of Polymers , 2013 .

[35]  Daniele Dini,et al.  Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach , 2013, Computer methods in biomechanics and biomedical engineering.

[36]  Mario Di Paola,et al.  Free energy and states of fractional-order hereditariness , 2014 .

[37]  Jean-François Molinari,et al.  A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials , 2005 .

[38]  Gérard A. Maugin,et al.  The thermomechanics of nonlinear irreversible behaviors : an introduction , 1999 .

[39]  M. T. Cicero FRACTIONAL CALCULUS AND WAVES IN LINEAR VISCOELASTICITY , 2012 .

[40]  Alberto Corigliano,et al.  Parameter identification of a time-dependent elastic-damage interface model for the simulation of debonding in composites ☆ , 2001 .

[41]  S. Govindjee,et al.  Numerical study of geometric constraint and cohesive parameters in steady-state viscoelastic crack growth , 2006 .

[42]  Mgd Marc Geers,et al.  Identification and characterization of delamination in polymer coated metal sheet , 2008 .

[43]  I. Podlubny,et al.  Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives , 2005, math-ph/0512028.

[44]  Elena Benvenuti,et al.  A regularized XFEM framework for embedded cohesive interfaces , 2008 .

[45]  I. Podlubny Fractional differential equations , 1998 .

[46]  K. Liechti,et al.  Mixed-mode, time-dependent rubber/metal debonding , 2001 .

[47]  Helmut Schiessel,et al.  Hierarchical analogues to fractional relaxation equations , 1993 .

[48]  M. Marder,et al.  Energy Balance in Dynamic Fracture, Investigated by a Potential Drop Technique , 1998 .

[49]  Alexander Lion,et al.  On the thermodynamics of fractional damping elements , 1997 .

[50]  G. I. Barenblatt THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[51]  B. Persson,et al.  Crack propagation in viscoelastic solids. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[53]  Alberto Corigliano,et al.  Rate-dependent interface models: formulation and numerical applications , 2001 .

[54]  W. S. Teo,et al.  Modelling the fracture behaviour of adhesively-bonded joints as a function of test rate , 2011 .

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

[56]  Marc G. D. Geers,et al.  Multi-scale modelling of delamination through fibrillation , 2014 .

[57]  Michael Ortiz,et al.  Nonconvex energy minimization and dislocation structures in ductile single crystals , 1999 .

[58]  M. Riesz L'intégrale de Riemann-Liouville et le problème de Cauchy , 1949 .

[59]  P. Gennes,et al.  Soft Interfaces: The 1994 Dirac Memorial Lecture , 1996 .

[60]  G. Alfano On the influence of the shape of the interface law on the application of cohesive-zone models , 2006 .

[61]  P. G. Nutting,et al.  A new general law of deformation , 1921 .

[62]  G. McKinley,et al.  Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations , 2013, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[63]  S. Eckardt,et al.  Modelling of cohesive crack growth in concrete structures with the extended finite element method , 2007 .

[64]  Giuseppe Giambanco,et al.  Mixed mode failure analysis of bonded joints with rate‐dependent interface models , 2006 .

[65]  Ismael Herrera,et al.  On dissipation inequalities and linear viscoelasticity , 1965 .

[66]  K. Adolfsson Nonlinear Fractional Order Viscoelasticity at Large Strains , 2004 .

[67]  Alberto Corigliano,et al.  Formulation, identification and use of interface models in the numerical analysis of composite delamination , 1993 .

[68]  M. Geers,et al.  On the development of a 3D cohesive zone element in the presence of large deformations , 2008 .

[69]  Ingo Müller,et al.  The Thermodynamics of Simple Materials with Fading Memory , 1972 .

[70]  Chad M. Landis,et al.  Crack velocity dependent toughness in rate dependent materials , 2000 .