On stress analysis for cracks in elastic materials with voids

TL;DR

This paper analyzes stress concentration around cracks in porous elastic materials using integral equations and Fourier transforms, revealing higher stress factors in materials with voids, especially for larger cracks.

Contribution

It introduces a method to reduce stress analysis in porous elastic materials to integral equations and studies the impact of porosity on stress concentration factors.

Findings

Stress concentration factor is higher in porous materials than in classical elastic media.

Porosity effects become more significant for larger cracks.

Numerical methods effectively solve hypersingular and Fredholm integral equations.

Abstract

The paper deals with classical problem for cracks dislocated in a certain very specific porous elastic material, described by a Cowin-Nunziato model. We propose a method based upon a reducing of stress concentration problem for cracks to some integral equations. By applying Fourier integral transforms the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. In the axially symmetric case, for the penny-shaped crack, the problem is reduced to a regular Fredholm integral equation of the second kind. In the both cases we study stress-concentration factor, and investigate its behavior versus porosity of the material. More in particular the stress concentration factor in the medium with voids is always higher, under the same conditions, than in the classical elastic medium made of material of the skeleton. Further, as can be seen, the influence of the porosity becomes more significant for larger cracks; that is also quite natural from a physical point of view.