Linear elastic materials with voids

Abstract

A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed.

In the two year period between the submission of this manuscript and the receipt of the page proof, there have been some extensions of the results reported here. In the context of the theory described, the classical pressure vessel problems and the problem of the stress distribution around a circular hole in a field have uniaxial tension have been solved [19,22]. The solution given in the present paper for the pure bending of a beam when the rate effect of the theory is absent is extended to case when the rate effect is present in [21]. The various implications of the rate effect in the void volume deformation are pursued all the subsequent works [19,20,21,22].