Stress concentration due to the bi‐axial deformation of a plate of a porous elastic body with a hole

Abstract

AbstractMost solid bodies are porous and in such bodies we expect the material properties to vary with porosity and hence with the density. Such bodies whose properties depend on the density cannot be described by the classical linearized elastic constitutive relation when they are undergoing small deformations, as the material moduli cannot depend on density. A constitutive relation which is valid in the small displacement gradient range wherein the material moduli are dependent on the density can be developed by linearizing implicit constitutive relations for describing elastic bodies introduced recently by Rajagopal [1]. In this paper, we determine the stress concentration due to a hole in a slab that is subject to biaxial loading in a body described by such a constitutive relation. We find that the stress concentration can be much as 147% higher than that for classical linearized elasticity for the range of loadings considered in the study.