General solutions and completeness in elastostatics of materials with voids

The paper is concerned with the equilibrium theory of elastic materials with voids. The theory was introduced by Nunziato and Cowin in order to describe the effects of voids or empty-spaces, distributed in all media at some scale, on material properties. It gives a physical interpretation of the dilatation theory of elasticity proposed by Markov and can be considered a special case of Eringen’s theory of microstretch elastic media when the microrotations are absent. The theory of materials with voids is suitable to investigate various phenomena occurring in engineering, geomechanics as well as in biomechanics. We present the counterpart of Boussinesq-Somigliana-Galerkin (B-S-G) solution and Boussinesq-Papkovitch-Neuber (B-P-N)solution of the classical elasticity. The B-S-G solution is obtained with a heuristic method. We establish the links between the two solutions and their representation in the case of axisymmetry. The results are useful in solving axisymmetric problems for semi-infinite and infinite domains.