Micromechanical models for porous and cellular materials in linear elasticity and viscoelasticity

Due to their interesting properties and diverse applications, porous solids and cellular materials are the focus of many researchers. This paper deals with the prediction of the macroscopic elastic and linear viscoelastic properties of these materials based on their microstructure. Hence, a comparative study of several micromechanical models is conducted for both porous solids and open cell foams. Analytical beam theory models based on tetrakaidecahedron representation of the microstructure are studied for cellular materials. The applicability of common Mean Field (MF) theoretical models is examined and compared for porous solids in the whole range of porosity. The linear viscoelastic behavior is deduced from elastic results using the correspondence principle for both cellular and porous solids. Finite Element (FE) analyses are carried out in order to assess the quality of analytical solutions in elasticity and viscoelasticity. Unit cell FE models under periodic boundary conditions were developed for cellular materials and Representative Volume Elements (RVEs) were generated to represent the porous solids. Finally, the potential of MF models suitable for highly porous solids to predict the response of cellular materials is investigated.