Effect of pore shape on the effective behavior of viscoelastic porous media

Closed-form solutions for rheological effective properties of linear non-ageing viscoelastic porous media containing spherical pores or penny shaped cracks were recently derived by using the micromechanical method. The aim of this paper is to extend such developments to the case of spheroidal pores and to analyze the pore shape effect on the overall viscoelastic properties of porous materials. The viscoelastic Hill and localization tensors as well as the homogeneous viscoelastic stiffness tensors are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. They are functions of the aspect ratio of the pores, the porosity and the rheological viscoelastic moduli of the solid phase that is modeled by the Generalized Maxwell rheology made of a spring in parallel with n Maxwell series. Then the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace-Carson (LC) transform procedure. Finally, the relaxation and creep bulk and shear moduli as well as the relaxation and creep Poisson ratio are obtained for the isotropic case with random orientation distribution of the spheroidal pores. The developed approach is validated against the exact solution obtained by numerical inverse LC transform. It is also compared with a series of previously developed solutions for simpler problems. A sensitivity analysis shows that the effects of the aspect ratio of the pores on the effective viscoelastic properties of the whole medium are significant for the case of oblate pores. Contrarily, such effect is very slight for the case of elongated pores. The difference between the creep and the relaxation Poisson ratios is also discussed.