THEORETICAL AND NUMERICAL ISSUES ON DUCTILE FAILURE PREDICTION - AN OVERVIEW

The main goal of this paper is to give a general overview of some of the recent advances accomplished in the description of ductile damage, both from a theoretical and numerical point of view. To start with, the classical local theory with regard to the thermodynamics of irreversible processes is reviewed where a general elasto-plastic damage model is established. It is also highlighted the assumptions and limitations behind the classical theory when the constitutive equations are obtained from the solution of a constrained maximisation problem. Recent advances on the non-local modelling of ductile damage are also addressed where we shed some light on the principles and consequences of non-locality in elasto-plastic damage models. The issues regarding the efficient numerical implementation of both local and non-local theories are also discussed where special attention is devoted to the implementation of non-local models. In particular, a novel computational strategy, suitable for implementations in commercial programs, is presented for the explicit finite element code LS-DYNA in detail. A FORTRAN code excerpt is given in which the main steps for the implementation of the model are schematically depicted. The effectiveness of the non-local model is assessed through the simulation of an axisymmetric specimen and a sheet metal forming process. It is shown that in both cases the non-local numerical strategy is able to diminish the pathological mesh dependency inherently present in local elasto-plastic damage models.

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

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

[3]  F. A. McClintock,et al.  A Criterion for Ductile Fracture by the Growth of Holes , 1968 .

[4]  P. Fuschi,et al.  A Thermodynamic Approach to Nonlocal Plasticity and Related Variational Principles , 1999 .

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

[6]  Joseph Datsko,et al.  Material Properties and Manufacturing Processes , 1966 .

[7]  E. A. de Souza Neto,et al.  A fast, one-equation integration algorithm for the Lemaitre ductile damage model , 2002 .

[8]  R. Frias,et al.  A comparison of meshless and finite element approaches to ductile damage in forming processes , 2007 .

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

[10]  M. Brünig,et al.  Numerical Analysis of Nonlocal Anisotropic Continuum Damage , 2007 .

[11]  Susumu Shima,et al.  Consideration of basic equations, and their application, in the forming of metal powders and porous metals , 1978 .

[12]  Ron Peerlings,et al.  A nonlocal triaxiality-dependent ductile damage model for finite strain plasticity , 2006 .

[13]  E. A. de Souza Neto,et al.  A model for elastoplastic damage at finite strains: algorithmic issues and applications , 1994 .

[14]  Wei Hua Tai,et al.  A new damage mechanics criterion for ductile fracture , 1987 .

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

[16]  A. Atkins,et al.  Possible explanation for unexpected departures in hydrostatic tension-fracture strain relations , 1981 .

[17]  P. Fuschi,et al.  A thermodynamically consistent formulation of nonlocal and gradient plasticity , 1998 .

[18]  Matti Ristinmaa,et al.  FE-formulation of a nonlocal plasticity theory , 1996 .

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

[20]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[21]  J. M. A. César de Sá,et al.  Damage modelling in metal forming problems using an implicit non-local gradient model , 2006 .

[22]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[23]  A. Freudenthal,et al.  The inelastic behavior of engineering materials and structures , 1951, The Journal of the Royal Aeronautical Society.

[24]  F. M. Andrade Pires,et al.  Improvement of the numerical prediction of ductile failure with an integral nonlocal damage model , 2009 .

[25]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[26]  Mgd Marc Geers,et al.  Strongly non‐local gradient‐enhanced finite strain elastoplasticity , 2003 .

[27]  F. Parrinello,et al.  A symmetric nonlocal damage theory , 2003 .

[28]  Milan Jirásek,et al.  Nonlocal damage mechanics , 2007, Encyclopedia of Continuum Mechanics.

[29]  J. E. Reaugh,et al.  A Plastic-Strain, Mean-Stress Criterion for Ductile Fracture , 1978 .

[30]  F. Pires,et al.  Local and Nonlocal Modeling of Ductile Damage , 2010 .

[31]  F. M. Andrade Pires,et al.  A Ductile Damage Nonlocal Model of Integral-type at Finite Strains: Formulation and Numerical Issues , 2011 .

[32]  Viggo Tvergaard,et al.  Effects of nonlocal damage in porous plastic solids , 1995 .

[33]  F. Pires,et al.  Nonlocal integreal formulation for a plasticity-induced damage model , 2009 .