Continuum Damage Mechanics

In the last five decades, continuum damage mechanics has proven to be a valuable tool to study material degradation. Many damage models have been developed that allow an accurate description of damage processes for a wide range of materials. At the same time, much effort has been expended to develop robust algorithms for obtaining numerical solutions to problems with damage. Some of the models have already been implemented in commercial finite element codes and have become a valuable tool in helping engineers predict behavior of engineering structures. In this article, a general framework for modeling damage, based on the theory of irreversible thermodynamics with internal variables, is outlined. Special attention is devoted to issues related to the numerical implementation of material models with damage, such as mesh sensitivity of the solution and convergence difficulties. Keywords: continuum damage mechanics; finite element method; mesh sensitivity; viscous regularization; convergence difficulties

[1]  Jinyang Zheng,et al.  Recent developments on damage modeling and finite element analysis for composite laminates: A review , 2010 .

[2]  Robert L. Taylor,et al.  A constitutive model for anisotropic damage in fiber-composites , 1995 .

[3]  Zenon Mróz,et al.  A continuum model for plastic-brittle behaviour of rock and concrete , 1979 .

[4]  Sumio Murakami,et al.  Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics , 1997 .

[5]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part II – Computational implementation and validation , 2007 .

[6]  M. Kachanov.  On the Concept of Damage in Creep and in the Brittle-Elastic Range , 1994 .

[7]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

[8]  Z. Hashin.  Failure Criteria for Unidirectional Fiber Composites , 1980 .

[9]  Stephen W. Tsai,et al.  A General Theory of Strength for Anisotropic Materials , 1971 .

[10]  Ireneusz Lapczyk,et al.  Progressive damage modeling in fiber-reinforced materials , 2007 .

[11]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[12]  Gilles Pijaudier-Cabot,et al.  Measurement of Characteristic Length of Nonlocal Continuum , 1989 .

[13]  George Z. Voyiadjis,et al.  Gradient-enhanced Coupled Plasticity-anisotropic Damage Model for Concrete Fracture: Computational Aspects and Applications , 2009 .

[14]  J. Chaboche,et al.  A new formulation of continuum damage mechanics (CDM) for composite materials , 1997 .

[15]  J. Oliver.  A consistent characteristic length for smeared cracking models , 1989 .

[16]  Z. Hashin,et al.  A Fatigue Failure Criterion for Fiber Reinforced Materials , 1973 .

[17]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[18]  Rodney S. Thomson,et al.  Review of methodologies for composite material modelling incorporating failure , 2008 .

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

[20]  Wim Van Paepegem,et al.  Fatigue damage modeling of fibre-reinforced composite materials: Review , 2001 .

[21]  Pedro P. Camanho,et al.  Failure Criteria for FRP Laminates , 2005 .

[22]  Ramesh Talreja,et al.  Damage and fatigue in composites – A personal account , 2008 .

[23]  Ramesh Talreja,et al.  A continuum mechanics characterization of damage in composite materials , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  L. Sluys,et al.  Continuum Models for the Analysis of Progressive Failure in Composite Laminates , 2009 .

[25]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .

[26]  René de Borst,et al.  Some recent issues in computational failure mechanics , 2001 .

[27]  Dusan Krajcinovic,et al.  Damage tensors and the crack density distribution , 1993 .

[28]  Jiann-Wen Ju,et al.  ISOTROPIC AND ANISOTROPIC DAMAGE VARIABLES IN CONTINUUM DAMAGE MECHANICS , 1990 .

[29]  Pierre Ladevèze,et al.  Damage modelling of the elementary ply for laminated composites , 1992 .

[30]  Pedro P. Camanho,et al.  A continuum damage model for composite laminates: Part I - Constitutive model , 2007 .

[31]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .

[32]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[33]  George Z. Voyiadjis,et al.  A Finite Strain Plastic-damage Model for High Velocity Impacts using Combined Viscosity and Gradient Localization Limiters: Part II - Numerical Aspects and Simulations , 2006 .