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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
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
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
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
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. purchase the full-text of this paper (price £20)
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