Finite element modeling of effective properties of elastic materials with random nanosized porosity

An integrated approach for determination of the effective properties of anisotropic porous elastic materials with a nanoscale stochastic porosity structure is presented. This approach includes an effective moduli method of composite mechanics, modeling of representative volumes and finite element method. The Gurtin-Murdoch model of surface stresses on the boundaries between material and pores is used for taking into account the nanodimension of pores. The general methodology for determination of the effective properties of porous composites is demonstrated for a two-phase composite with special conditions of stresses discontinuity on the phase interfaces. The mathematical statements of boundary value problems and the resulting formulae to determine the complete set of effective constants of the two-phase composites with arbitrary anisotropy and surface properties are described; the generalized statements is formulated and the finite element approximations are given. It is noted that the homogenization problem for the composites under study can be solved using the known finite element software and choosing the shell finite elements with the options of membrane stiffness only for taking into consideration the surface interphase stresses. It is also shown that the homogenization procedures for porous composites with surface stresses can be considered as special cases of the corresponding procedures for two-phase composites with interphase stresses if the stiffness moduli of nanoinclusions are negligibly small. The specific realization of these approaches is made in the finite element package ANSYS. An algorithm for automatic determination of interphase boundaries and location of shell elements on them, which works for different sizes of representative volumes, built in the form of a cubic lattice of hexahedral finite elements, is described. The efficiency of the algorithm has been tested using the models of porous material of hexagonal system at different values of surface moduli, porosity and number of pores. Simulations have revealed the influence of the area of the value of interphase boundaries on the effective moduli of the porous material with nanosized structure.