Combination of a non-local damage model for quasi-brittle materials with a mesh-adaptive finite element technique

Progressive fracture in quasi-brittle materials is often treated via strain softening models in continuum damage mechanics. Such constitutive relations favour spurious strain localization and ill-posedness of boundary value problems. The introduction of non-local damage models together with a characteristic length parameter controlling the size of the fracture process zone is known to regularize the problem. In order to account for the non-locality of these models, it is crucial to work with fine spatial discretizations at the damage progress zone. In this paper we present a non-local damage model in combination with a mesh-adaptive finite element technique that can help automatize the analysis of progressive fracture problems in an efficient manner. Classical two-dimensional examples are given to illustrate the presented approach. HighlightsFracture of quasi-brittle materials is treated via continuum damage mechanics.Strain localization is regularized through an integral-type non-local damage model.A mesh-adaptive finite element technique has been implemented to work along with the non-local damage model.Examples in 2D are given to illustrate the presented approach.

[1]  Jean-François Dubé,et al.  Calibration of nonlocal damage model from size effect tests , 2003 .

[2]  J. Hult.  Creep in Continua and Structures , 1974 .

[3]  Miguel Cervera,et al.  Mesh objective tensile cracking via a local continuum damage model and a crack tracking technique , 2006 .

[4]  A. Huerta,et al.  Numerical differentiation for local and global tangent operators in computational plasticity , 2000 .

[5]  B. Massicotte,et al.  Geometrical interpretation of the arc-length method , 1993 .

[6]  Miguel Cervera,et al.  Shear band localization via local J2 continuum damage mechanics , 2004 .

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

[8]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

[9]  Gilles Pijaudier-Cabot,et al.  From damage to fracture mechanics and conversely: A combined approach , 1996 .

[10]  Eugenio Oñate,et al.  Structural Analysis with the Finite Element Method , 2009 .

[11]  René Chambon,et al.  Plastic continuum with microstructure, Local Second Gradient Theories for Geomaterials : Localization Studies , 2001 .

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

[13]  E. Oñate,et al.  The finite element method in the 1990's , 1991 .

[14]  A. Hillerborg,et al.  Numerical methods to simulate softening and fracture of concrete , 1985 .

[15]  H. B. Mühlhaus.  Scherfugenanalyse bei granularem Material im Rahmen der Cosserat-Theorie , 1986 .

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

[17]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[18]  Eugenio Oñate,et al.  Adaptive Mesh Refinement Techniques for Structural Problems , 1991 .

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

[20]  A. Cemal Eringen,et al.  On nonlocal plasticity , 1981 .

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

[22]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[23]  A. Eringen,et al.  On nonlocal elasticity , 1972 .

[24]  G. Bugeda,et al.  Adaptive mesh refinement techniques for aerodynamic problems. , 1992 .

[25]  Gabriel Bugeda,et al.  A STUDY OF MESH OPTIMALITY CRITERIA IN ADAPTIVE FINITE ELEMENT ANALYSIS , 1993 .

[26]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1989 .

[27]  Eugenio Oñate,et al.  A methodology for adaptive mesh refinement in optimum shape design problems , 1994 .

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

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

[30]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[31]  J. Prévost,et al.  Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples , 1990 .

[32]  J. Lemaitre,et al.  Mécanique des matériaux solides , 1996 .

[33]  E. Oñate,et al.  Finite element nonlinear analysis of concrete structures using a “plastic-damage model” , 1990 .

[34]  Hussein M. Zbib,et al.  A Gradient-Dependent Flow Theory of Plasticity: Application to Metal and Soil Instabilities , 1989 .

[35]  Milan Jirásek,et al.  Comparison of integral-type nonlocal plasticity models for strain-softening materials , 2003 .

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