# Elastoplastic Analysis of Plane Stress Problems for Porous Plastic Material

## TL;DR

This paper develops a mesoscale damage model to analyze how voids in materials affect their mechanical behavior under stress.

## Contribution

A new mesoscale damage model is proposed by incorporating void volume fraction into a yield function for porous plastic materials.

## Key findings

- Higher void volume fractions reduce radial stress and displacement but have minimal effect on circumferential stress.
- Material near voids experiences higher stress and displacement, reaching yield state faster.
- Numerical solutions show consistent curve patterns despite varying void volume fractions.

## Abstract

Considering the impact of void damage on the mechanical properties of materials, based on the two-parameter yield criterion, combined with the associated flow rule and the upper bound theorem, the void volume fraction is introduced into the macroscopic yield function, resulting in a mesoscale damage model. Two material parameters in the model are defined using yield strength and Poisson’s ratio, respectively. The yield surface of the model is presented for different void volume fractions and Poisson’s ratios. Using the mesoscale damage model, combined with the positive flow rule, the constitutive relationship of the material is established, and an elastoplastic analysis is performed for axisymmetric plane stress problems. Under the Prager hypothesis, a set of differential equations is derived to solve the problem, yielding numerical solutions. The influence of void volume fraction on the stress field and displacement field is qualitatively discussed. The research results show that when the void volume fraction is constant, the closer to the void opening, the larger the absolute value of radial stress and displacement, and the faster the material flows, with the material reaching the yield state first. As the void volume fraction increases, both the absolute value of radial stress and displacement decrease relatively. In contrast, the change in circumferential stress is relatively small, but the patterns of the numerical result curves tend to be consistent.