Keywords: material modelling, non-linear, anisotropic, damage, stress-softening, residual-strain.

It is oftened found that when an initially isotropic (in its stress-free undeformed virgin state) material is deformed it becomes anisotropic, softened and incurs residual strain; anisotropicity, softening behaviour and residual strain are induced by deformation. Examples of materials having these properties are elastic-plastic, filled rubber and some deformation damaged materials. To desrcibe these properties we developed a phenomenological three dimensional anisotropic model via an energy function which depends on the right stretch tensor. We use the principal stretches as strain magnitude measures and define unloading points as

where , and are functions of and ,

and are the principal directions of the right stretch tensor.

To handle residual strain we introduce a modified strain which is a function of the principal stretches and the unloading points. The energy function is postulated to be a function of the principal stretches and the unloading points. A symmetric positive definte Lagrangean softening tensor which is coaxial with the right stretch tensor is introduced in the constitutive equation.The norm of the softening tensor is not greater than 1. The energy function is postulated to take the form

where are the modified principal stretches. The energy function has the property

where is an isotropic scalar function for the virgin material and are the eigenvalues of . is a function of principal stretches and the unloading points.

The Biot stress is thus given by

Specific forms for the energy function are proposed which appear to simplify both the analysis of the three dimensional model and the evaluation of the parameter values from experimental data. Results demonstrating the effects of anisotropic stress softening are obtained for several types of homogeneous deformations. The theoretical results compare well, qualitatively and quantatively, with several experimental data exhibiting anisotropic behaviour. Numerical problems for this type of material is discussed.

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