Mesh-dependence of Material with Softening Behavior

Abstract The issue of mesh-dependence emerges when the conventional continuum damage model is applied to handling the softening behavior. In order to circumvent the mesh-dependence, the non-local theory is introduced into the conventional damage model and the finite element formulas are derived for two-dimensional gradient-enhanced damage model. A new element is proposed in which the basic unknown quantities are displacement, non-local equivalent strain and the gradient of non-local equivalent strain. The element and constitutive equation proposed in this article are added to the finite element software ABAQUS through user subroutine UEL. Numerical results show that the gradient-enhanced damage model can eliminate the mesh-dependence and is effective for dealing with the issue of softening behavior.

[1]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[2]  F. Feyel,et al.  Simulation of laminate composites degradation using mesoscopic non-local damage model and non-local layered shell element , 2007 .

[3]  Meng Guotao.  NONLOCAL ELASTOPLASTIC THEORY AND ITS APPLICATION , 2007 .

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

[5]  P. McAllen,et al.  Ductile Fracture by Central Bursts in Drawn 2011 Aluminium Wire , 2005 .

[6]  J. F. T. Pittman,et al.  Isoparametric Hermite elements , 1994 .

[7]  Mgd Marc Geers,et al.  On coupled gradient-dependent plasticity and damage theories with a view to localization analysis , 1999 .

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

[9]  R. Dorgan.  A nonlocal model for coupled damage-plasticity incorporating gradients of internal state variables at multiscales , 2006 .

[10]  D. Krajcinovic,et al.  Introduction to continuum damage mechanics , 1986 .

[11]  Harold Malcolm Westergaard.  Theory of Elasticity and Plasticity , 1952 .

[12]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[13]  Milan Jirásek,et al.  Non‐local damage model based on displacement averaging , 2005 .

[14]  E. Aifantis.  On the role of gradients in the localization of deformation and fracture , 1992 .

[15]  R. Tovo,et al.  An implicit gradient type of static failure criterion for mixed-mode loading , 2006 .

[16]  Alberto Carpinteri,et al.  Computational Fracture Mechanics in Concrete Technology , 1999 .

[17]  D. Borst,et al.  Fundamental issues in finite element analyses of localization of deformation , 1993 .

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

[19]  T. Drabek,et al.  Damage models for studying ductile matrix failure in composites , 2005 .

[20]  G. Houlsby,et al.  Analysis of Essential Work of Rupture using Non-local Damage-plasticity Modelling , 2005 .

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