An anisotropic fibre-matrix material model at finite elastic-plastic strains

In this paper a constitutive model for anisotropic finite strain plasticity, which considers the major effects of the macroscopic behaviour of matrix-fibre materials, is presented. As essential feature matrix and fibres are treated separately, which allows as many bundles of fibres as desired. The free energy function is additively split into a part related to the matrix and in parts corresponding to the fibres. Usually the free energy function is defined by the integrity basis of the main variable and structural tensors, which leads to complicated numerical schemes. Here, the continuum is considered as superimposed of the isotropic matrix and further one-dimensional continua each of them represents one bundle of fibres. The deformation gradient applies to all continua introducing a constraint, which links the different continua. One of the most striking features of the model is its suitability for a numerical treatment.

[1]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

[2]  Paul Steinmann,et al.  On the spatial formulation of anisotropic multiplicative elasto-plasticity , 2003 .

[3]  Peter Wriggers,et al.  A stabilization technique to avoid hourglassing in finite elasticity , 2000 .

[4]  E. Stein,et al.  Fast transient dynamic plane stress analysis of orthotropic Hill-type solids at finite elastoplastic strains , 1996 .

[5]  Stefanie Reese,et al.  Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation , 2003 .

[6]  Christian Miehe,et al.  A constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric , 1998 .

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

[8]  F. Gruttmann,et al.  A simple orthotropic finite elasto–plasticity model based on generalized stress–strain measures , 2002 .

[9]  A. Spencer.  Anisotropic Invariants and Additional Results for Invariant and Tensor Representations , 1987 .

[10]  R. Borst,et al.  Studies in anisotropic plasticity with reference to the Hill criterion , 1990 .

[11]  Sven Klinkel,et al.  Elastic and plastic analysis of thin-walled structures using improved hexahedral elements , 2002 .

[12]  M. Lambrecht,et al.  Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials , 2002 .

[13]  Carlo Sansour,et al.  Large viscoplastic deformations of shells. Theory and finite element formulation , 1998 .

[14]  Carlo Sansour,et al.  On the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law , 2003 .

[15]  Y. Macheret,et al.  An experimental study of elastic-plastic behavior of a fibrous boron-aluminum composite , 1988 .

[16]  R. Hill.  The mathematical theory of plasticity , 1950 .

[17]  A. Spencer.  Plasticity theory for fibre-reinforced composites , 1992 .

[18]  J. Lubliner,et al.  Definition of a general implicit orthotropic yield criterion , 2003 .

[19]  I. THEORY AND FINITE ELEMENT FORMULATION , 1993 .

[20]  Jia Lu,et al.  On the formulation and numerical solution of problems in anisotropic finite plasticity , 2001 .

[21]  J. P. Boehler,et al.  Introduction to the Invariant Formulation of Anisotropic Constitutive Equations , 1987 .

[22]  Peter Wriggers,et al.  Finite element modelling of orthotropic material behaviour in pneumatic membranes , 2001 .