Finite element modeling of porous thermoelastic composites with account for their microstructure

The paper discusses approaches to the determination of the effective moduli of porous anisotropic thermoelastic composite materials based on the effective moduli method, modeling of the representative volumes with account for microstructure and finite element technologies of solving static thermoelastic problems for heterogeneous bodies. The paper formulates a set of boundary-value problems of thermoelasticity with boundary conditions of the first kind that enables computing all effective stiffness moduli, thermal conductivity moduli and coefficients of thermal stresses for porous anisotropic material. The technology of the finite element method is described for the numerical solution of boundary-value thermoelastic problems in the representative volume of a porous material. A range of the simulation methods for the inner structure of the representative volumes in cubic finite element lattice is represented by the way of giving properties of the porous material to a certain number of finite elements. The methods considered are the simple random method, the method that supports the connectivity of the skeleton for the porosity up to 90%, the Witten-Sander method that enables us to obtain a cluster from the pores of fractal type, and the growing from the plane method that forms several clusters from the pores in the vicinity of one of the edges of the cubic lattice. The example considered is the model of porous silicon that is taken as a material of cubic symmetry. The computation results allow analyzing the influence of various structures of the representative volumes on the effective moduli. The comparison of the computed effective characteristics of porous silicon with a range of known analytical and numerical results has been carried out. The results of the test computations have demonstrated that the effective material properties of porous thermoelastic composites can strongly depend on the models of their representative volumes.