# Analytical and Numerical Investigation of Hardening Behavior of Porous Media

## DOI:

https://doi.org/10.25156/ptj.v9n2y2019.pp1-10## Keywords:

Elastic-plastic porous materials, Computational homogenization, Non-linear isotropic hardening, Exponential law, Three-scale homogenization## Abstract

In this study, a comparative analysis is presented between a new proposed analytical model and numerical results for macroscopic behavior of porous media with isotropic hardening in its matrix. The macroscopic behavior of a sufficiently large representative volume element (RVE), with 200 identical spherical voids, was simulated numerically using finite element method and compared with elementary volume element that contains one void. The matrix of the porous material is considered as elasto-plastic with isotropic hardening obeys exponential law for isotropic hardening. A new parameter was added with exponential law for isotropic hardening to represent the new proposed analytical model for macroscopic isotropic porous hardening. The new added parameter *B* depended only on the porosity. The results of the new proposed analytical model were compared with numerical results for different types of cyclic loading. Very good agreements were found between the numerical results and the proposed analytical model.

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*9*(2), 1-10. https://doi.org/10.25156/ptj.v9n2y2019.pp1-10

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