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

Abstract

Most 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.

Stress concentration due to an elliptic hole in a porous elastic plate

“…There have been a few specific problems that have been studied within the context of this new linearization for porous elastic bodies and we feel that the constitutive relation warrants scrutiny in view of its potential applications to a wide range of important problems. Among the few studies that have been carried out with this new constitutive relation are those by Pavitra and Rajagopal to study the stress concentration due to a hole in an infinite porous elastic plate subject to both uniaxial loading (Murru and Rajagopal [22]) and biaxial loading (Murru and Rajagopal [23]). In both these problems, they found a significant increase in the stress concentration factor.…”

On the response of anisotropic elastic bodies described by implicit constitutive relations

“…In the new constitutive relations that describe the response of porous elastic solids, the stress and strain appear linearly, but the constitutive relation is not bilinear. Interestingly, recent studies concerning the stress concentration due to the presence of a hole in such porous elastic solids reveals that they can be higher by as much as 300% than in a classical linearized elastic isotropic solid (see the studies by Murru and Rajagopal [27,28] for the case of a circular hole and Vajipeyajula et al [29] in the case of an elliptic hole). Prusa et al [30] have developed an Euler-Bernoulli type of approximation to describe the response of a beam comprised of such a material.…”

Stress concentration around a circular rigid inclusion in incompressible nonlinearly elastic transversely isotropic and orthotropic thin sheets under uniaxial extension

“…In the case of a rigid circular inclusion, the location of maximum stress is dependent on the value of the Poisson’s ratio. Recently, the state of stress and strain of an elastic body described by an implicit constitutive relation which is linear in the stress and the linearized strain was introduced by Rajagopal [4] to describe the response of porous elastic solids undergoing small deformations, was used to study a body that has a circular hole, subject to uniaxial loading (see Murru and Rajagopal [5]) and biaxial loading (see Murru and Rajagopal [6]). The problem of such a body with an elliptic hole subject to biaxial loading (see Vajipeyajula et al [7]) have also been studied.…”