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.

On the time decay of solutions for non-simple elasticity with voids

“…Case (4) could be thought in a similar way. Nevertheless, this question remains unsolved for cases (1) …”

“…The classical setting of this theory was established by Nunziato and Cowin [14], Cowin and Nunziato [1] and Cowin [2]. The basic idea of these works is that the bulk density is the product of two scalar fields, the matrix material density and the volume fraction.…”

Exponential decay in one-dimensional porous-thermo-elasticity

“…The theory of porous elastic material has been established by Cowin and Nunziato [12,13,14]. In this theory the bulk density is the product of two scalar fields, the matrix material density and the volume fraction field; it is studied in the book of Ciarletta and Iesan [15].…”

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

“…For homogeneous, linear and thermally elastic medium with voids and temperature dependent mechanical properties, the basic equations in the context of the Lord andShulman (1997) model andNunziato (1983) in absence of body forces and heat source are given by Kumar and Devi (2011).…”