Deformation of porous Cosserat elastic bars

This paper is concerned with the linear theory of porous Cosserat elastic solids. We study the equilibrium of a cylindrical bar which is subjected to resultant forces and resultant moments on the ends, to body loads and to surface tractions on the lateral surface. The Almansi problem, where the body loads and the surface loading on the lateral surface are polynomials in the axial coordinate, is considered. The bar is made of an inhomogeneous and isotropic material whose constitutive coefficients are independent of the axial coordinate. The problem is reduced to the study of two-dimensional problems. The results are used to study two practical applications concerning the deformation of a circular rod. It is shown that a uniform pressure on the lateral surface produces an extension, a uniform change of the porosity, and a plane deformation. The bending by terminal couples produces a non-uniform variation of the porosity and a microrotation of the material particles.