A 3D RVE-based computational homogenization approach for predicting the effective fourth-order elasticity tensor of periodic porous materials

Abstract

In the present contribution, a computational homogenization framework is explored for predicting the effective fourth-order elasticity tensor of periodic porous materials. To improve the accuracy of the computational approach, an extrapolation strategy based on a posteriori error estimation is employed to estimate the effective elastic properties from the numerical results computed by the computational homogenization procedure. The computational strategy is implemented in ANSYS software using the Ansys Parametric Design Language, where new routines are created to provide an easy-to-use tool. In particular, the influence of void morphology in periodic porous materials is assessed. Three morphologies for the representative volume element are defined in the three-dimensional numerical analyses conducted by finite element simulations: (i) cube with a unidirectional void of circular cross-section, (ii) cube with a unidirectional void of square cross-section, and (iii) cube with a unidirectional void of octagonal cross-section. Different porosity values are simulated for the periodic porous material, and approximate parametric expressions are proposed to calculate the effective constitutive components in terms of void morphology and porosity. One concludes that void morphology has a strong influence on some components of the fourth-order elasticity tensor. Regarding the comparison between periodic materials with circular and square cross-section voids, significant differences are observed for the components associated with shear response in the plane cutting the void cross-section. Periodic materials with octagonal and circular cross-section voids have similar effective results. Overall, the computational approach is an interesting tool to design non-homogeneous materials, accounting for accuracy to predict effective properties.