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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 55

Anisotropic Stress-Softening Model for Damaged Materials

M.H.B.M. Shariff+* and M.A. Noor+

+Etisalat University, United Arab Emirates
*Teesside University, United Kingdom

Full Bibliographic Reference for this paper
M.H.B.M. Shariff, M.A. Noor, "Anisotropic Stress-Softening Model for Damaged Materials", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 55, 2004. doi:10.4203/ccp.79.55
Keywords: material modelling, non-linear, anisotropic, damage, stress-softening, residual-strain.

Summary
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

 (16)

where , and are functions of and ,

 (17)

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

 (18)

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

 (19)

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

 (20)

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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