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On the deformation of porous spherical bodies under radial surface traction

De Cicco Simona

Journal of Theoretical and Applied Mechanics

2023

Vol. 61 nr 2

305--316

The paper deals with the linear theory of elastic materials with voids based on the concept of volume fraction. In this model, the interstitial pores are vacuous and can contract or stretch. The change in the volume fraction is measured by a scalar function, so that independent kinematical variables are four: the components of displacements and the volume fraction function. The equilibrium problem of elastic spherical bodies under radial surface traction is solved. The solution is given in closed form and applied to study three special cases. Explicit formulas of the displacement, stress distribution and volume fraction function are given.

Some boundary value problems for a micropolar porous elastic body

Janjgava R., Gulua B., Tsotniashvili S.

Archives of Mechanics

2020

Vol. 72, nr 6

485--509

The paper reviews the static equilibrium of a micropolar porous elastic material. We assume that the body under consideration is an elastic Cosserat media with voids, however, it can also be considered as an elastic microstretch solid, since the basic differential equations and mathematical formulations of boundary value problems in these two cases are actually identical. As regards the three-dimensional case, the existence and uniqueness of a weak solution of some boundary value problems are proved. The two-dimensional system of equations corresponding to a plane deformation case is written in a complex form and its general solution is presented with the use of two analytic functions of a complex variable and two solutions of the Helmholtz equations. On the basis of the constructed general representation, specific boundary value problems are solved for a circle and an infinite plane with a circular hole.