RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY

Damage of an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process. The damage is assumed to absorb a specific and prescribed amount of energy. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on a part of the boundary. Rigorous analysis by time discretization is performed.

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

[2]  Giulio Schimperna,et al.  Local existence for Frémond’s model of damage in elastic materials , 2004 .

[3]  G. D. Maso,et al.  Quasistatic Crack Growth in Nonlinear Elasticity , 2005 .

[4]  Meir Shillor,et al.  Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model , 1999 .

[5]  Leonard D. Berkovitz,et al.  Review: V. Barbu and Th. Precupanu, Convexity and optimization in Banach spaces , 1980 .

[6]  M. Frémond,et al.  Non-Smooth Thermomechanics , 2001 .

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

[8]  A. Mielke,et al.  A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle , 2002 .

[9]  A. Mielke,et al.  On rate-independent hysteresis models , 2004 .

[10]  Alexander Mielke,et al.  Chapter 6 – Evolution of Rate-Independent Systems , 2005 .

[11]  C. L. Chow,et al.  An anisotropic theory of elasticity for continuum damage mechanics , 1987 .

[12]  F. Schuricht.  Variational approach to contact problems in nonlinear elasticity , 2002 .

[13]  Michael Ortiz,et al.  A constitutive theory for the inelastic behavior of concrete , 1985 .

[14]  A. DeSimone,et al.  A Damage Mechanics Approach to Stress Softening and its Application to Rubber , 2001 .

[15]  M. Frémond,et al.  Damage, gradient of damage and principle of virtual power , 1996 .

[16]  Fu Yong,et al.  Semicontinuity Problems in the Calculus of Variations , 2000 .

[17]  Michel Frémond,et al.  Damage in concrete: the unilateral phenomenon , 1995 .

[18]  Andreas Mainik.  A rate-independent model for phase transformations in shape-memory alloys , 2004 .

[19]  R. Borst,et al.  Phenomenological nonlocal approaches based on implicit gradient-enhanced damage , 2000 .

[20]  D. Owen,et al.  A phenomenological three-dimensional rate-idependent continuum damage model for highly filled polymers: Formulation and computational aspects , 1994 .

[21]  R. de Borst,et al.  A Gradient-Enhanced Damage Approach to Fracture , 1996 .

[22]  S. Andrieux,et al.  A variational formulation for nonlocal damage models , 1999 .

[23]  Alexander Mielke,et al.  Existence results for energetic models for rate-independent systems , 2005 .

[24]  Paul Steinmann,et al.  A theoretical and computational framework for anisotropic continuum damage mechanics at large strains , 2001 .

[25]  M. Griebel,et al.  Digital Object Identifier (DOI) 10.1007/s00161-003-0127-3 Original article , 2002 .

[26]  G. Borino,et al.  A thermodynamically consistent nonlocal formulation for damaging materials , 2002 .

[27]  Michael Ortiz,et al.  An analytical study of the localized failure modes of concrete , 1987 .

[28]  J. Ball.  Some Open Problems in Elasticity , 2002 .

[29]  Christian Miehe,et al.  Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation , 2000 .

[30]  B. Dacorogna.  Direct methods in the calculus of variations , 1989 .