On damage modelling for elastic and viscoelastic materials at large strain

Abstract Geometrical and different physical nonlinearities have to be taken into account in order to model elastomeric material. In the present contribution, a novel approach of rubber elasticity is introduced. The approach considers the topological constraints as well as the limited extensibility of network chains in filled rubber. Subsequently, a formulation of finite viscoelastic damage is derived. With this description at hand, softening effects as well as time and frequency dependency of the material can be characterized. The goal of the present paper is twofold. Firstly, the constitutive formulations are introduced. Moreover, computational aspects are stressed. The shown approaches are presented in a format ready for a finite element implementation.

[1]  Alan Muhr,et al.  Constitutive Models for Rubber , 1999 .

[2]  J. Lemaître.  How to use damage mechanics , 1984 .

[3]  Christian Miehe,et al.  Computation of isotropic tensor functions , 1993 .

[4]  K. N. Morman.  The Generalized Strain Measure With Application to Nonhomogeneous Deformations in Rubber-Like Solids , 1986 .

[5]  Jean-Louis Chaboche,et al.  Continuous damage mechanics — A tool to describe phenomena before crack initiation☆ , 1981 .

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

[7]  J. Chaboche.  Continuum Damage Mechanics: Part I—General Concepts , 1988 .

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

[9]  Gert Heinrich,et al.  Polymere Netzwerke : Entwicklungsstand der molekular-statistischen Theorie , 1995 .

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

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

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

[13]  Sanjay Govindjee,et al.  Mullins' effect and the strain amplitude dependence of the storage modulus , 1992 .

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

[15]  M. Kaliske,et al.  An extended tube-model for rubber elasticity : Statistical-mechanical theory and finite element implementation , 1999 .

[16]  J. C. Simo,et al.  Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms , 1991 .

[17]  M. Kaliske,et al.  Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity , 1997 .