Numerical calculation of effective elastic moduli for incompressible porous material

Abstract

Incompressible elastic material with a periodic system of pores is considered. Processes are studied with a typical length which is much more than the typical diameter of pores and the typical distance between pores. Porous material behaves as a certain “effective” material without pores in such processes. The method of calculation of effective moduli based on mathematical homogenization theory is described. The estimates for the effective moduli are proved. The results of numerical calculations of effective moduli for materials with spherical and cubic pores are presented. The dependence of the effective moduli on the volume fracture of pores is investigated. The explicit formulae for effective coefficients are deduced. Comparison with the effective moduli for compressible materials is performed.