Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms

We develop homogenization schemes and numerical algorithms for two-phase elasto-plastic composite materials and structures. A Hill-type incremental formulation enables the simulation of unloading and cyclic loadings. It also allows to handle any rate-independent model for each phase. We study the crucial issue of tangent operators: elasto-plastic (or "continuum") versus algorithmic (or "consistent"), and anisotropic versus isotropic. We apply two methods of extraction of isotropic tangent moduli. We compare mathematically the stiffnesses of various tangent operators. All rate equations are discretized in time using implicit integration. We implemented two homogenization schemes: Mori-Tanaka and a double inclusion model, and two plasticity models: classical J(2) plasticity and Chaboche's model with non-linear kinematic and isotropic hardenings. We consider composites with different properties and present several discriminating numerical simulations. In many cases, the results are validated against finite element (FE) or experimental data. We integrated our homogenization code into the FE program ABAQUS using a user material interface UMAT. A two-scale procedure allows to compute realistic structures made of non-linear composite materials within reasonable CPU time and memory usage; examples are shown. (C) 2002 Elsevier Science Ltd. All rights reserved.

[1]  Sia Nemat-Nasser,et al.  Averaging theorems in finite deformation plasticity , 1999 .

[2]  T. Bretheau,et al.  Homogénéisation en mécanique des matériaux, Tome 1 : Matériaux aléatoires élastiques et milieux périodiques , 2001 .

[3]  R. Hill.  On constitutive macro-variables for heterogeneous solids at finite strain , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  G. P. Tandon,et al.  A Theory of Particle-Reinforced Plasticity , 1988 .

[6]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[7]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[8]  M. Bornert,et al.  Homogénéisation en mécanique des matériaux, Tome 2 : Comportements non linéaires et problèmes ouverts , 2001 .

[9]  H. Böhm,et al.  A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori–Tanaka approach , 1999 .

[10]  P. Suquet,et al.  Nonlinear Composites and Microstructure Evolution , 2001 .

[11]  Dimitris C. Lagoudas,et al.  On the numerical evaluation of Eshelby's tensor and its application to elastoplastic fibrous composites , 1990 .

[12]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

[13]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[14]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[15]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[16]  D. Chandrasekharaiah,et al.  Mechanics of Deformable Solids: Linear, Nonlinear, Analytical and Computational Aspects , 2000 .

[17]  Javier Segurado,et al.  On the accuracy of mean-field approaches to simulate the plastic deformation of composites , 2002 .

[18]  Michel Bornert,et al.  An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals , 2000 .

[19]  Issam Doghri,et al.  Fully implicit integration and consistent tangent modulus in elasto‐plasticity , 1993 .

[20]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[21]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[22]  J. Hutchinson,et al.  Bounds and self-consistent estimates for creep of polycrystalline materials , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[23]  J. Llorca,et al.  A self-consistent approach to the elasto-plastic behaviour of two-phase materials including damage , 2000 .

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

[25]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[26]  Pedro Ponte Castañeda.  Exact second-order estimates for the effective mechanical properties of nonlinear composite materials , 1996 .