Efficient and Reliable Nonlocal Damage Models

We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges — the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between non-adjacent finite elements associated to nonlocality — are addressed in detail. Efficiency is achieved with a suitable combination of load-stepping control technique and nonlinear solver for equilibrium equations. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. The proposed approach is illustrated by means of three application examples: the three-point bending test, the single-edge notched beam test and the Brazilian test.

[1]  Z. Bažant,et al.  Nonlocal Continuum Damage, Localization Instability and Convergence , 1988 .

[2]  Pedro Díez,et al.  Error estimation including pollution assessment for nonlinear finite element analysis , 2000 .

[3]  Pedro Díez,et al.  A posteriori error estimation for standard finite element analysis , 1998 .

[4]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[5]  C. Kelley.  Iterative Methods for Linear and Nonlinear Equations , 1987 .

[6]  Josep Sarrate,et al.  Efficient unstructured quadrilateral mesh generation , 2000 .

[7]  Milan Jirásek,et al.  Consistent tangent stiffness for nonlocal damage models , 2002 .

[8]  Antonio Huerta,et al.  Error estimation and adaptivity for nonlocal damage models , 2000 .

[9]  A. Anthoine,et al.  NUMERICAL STRATEGIES FOR SOLVING CONTINUUM DAMAGE PROBLEMS WITH SOFTENING:APPLICATION TO THE HOMOGENIZATION OF MASONRY , 1997 .

[10]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[11]  Milan Jirásek,et al.  Nonlocal models for damage and fracture: Comparison of approaches , 1998 .

[12]  Rhj Ron Peerlings,et al.  Gradient‐enhanced damage modelling of concrete fracture , 1998 .

[13]  Antonio Huerta,et al.  Discretization Influence on Regularization by Two Localization Limiters , 1994 .

[14]  Antonio Huerta,et al.  A note on a numerical benchmark test: an axisymmetric shell under ring loads , 1997 .

[15]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[16]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[17]  L. J. Sluys,et al.  On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials , 1995 .

[18]  Antonio Huerta,et al.  Locking in the incompressible limit for the element‐free Galerkin method , 2001 .

[19]  Antonio Huerta,et al.  Adaptive analysis based on error estimation for nonlocal damage models , 2001 .

[20]  Herbert A. Mang,et al.  The Fifth World Congress on Computational Mechanics , 2002 .

[21]  A. Huerta,et al.  Finite element analysis of bifurcation in nonlocal strain softening solids , 1991 .

[22]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

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

[24]  Jaime Planas,et al.  MECHANISMS OF RUPTURE IN SPLITTING TESTS , 1999 .

[25]  Wam Marcel Brekelmans,et al.  Comparison of nonlocal approaches in continuum damage mechanics , 1995 .

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

[27]  Silvio Valente,et al.  Is mode II fracture energy a real material property , 1993 .

[28]  J. Mazars.  A description of micro- and macroscale damage of concrete structures , 1986 .

[29]  Rhj Ron Peerlings,et al.  Interpolation requirements for implicit gradient-enhanced continuum damage models , 2003 .

[30]  Pedro Díez,et al.  Adaptivity based on error estimation for viscoplastic softening materials , 2000 .

[31]  Gilles Pijaudier-Cabot,et al.  Size effect and continuous damage in cementitious materials , 1991, International Journal of Fracture.

[32]  L. J. Sluys,et al.  Remeshing strategies for adaptive ALE analysis of strain localisation , 2000 .

[33]  A. Huerta,et al.  Adapting Broyden method to handle linear constraints imposed via Lagrange multipliers , 1999 .