Second gradient substitution model for high contrast bi-phase structure

Abstract

Lightweight structures with soft inclusion material, such as hollow core slabs, foam sandwich wall, pervious pavement ... are widely used in construction engineering for sustainable goals. Voids and soft inclusion can be modeled as a very soft material, while the main material is modeled with its original rigidity, which is so much higher than inclusion's one. In consequence, highly contrast bi-phase structure attracts the interests of scientists and engineers. One important demand is how to build a homogeneous equivalent model to replace the multi-phase structure which requires much resources and time to perform structure analysis. Various homogenization schemes have succeeded in establishing a homogeneous substitution model for composite materials which fulfill the scale separation condition (characteristic length of heterogeneity is very small in comparison to structure dimensions). Herein, elastic stiffness matrix of a homogeneous model which replaces a bi-phase material is computed by a higher-order homogenization scheme. A non-homogeneous boundary condition (a polynomial inspired from Taylor series expansion) is used in computation. Homogeneous substitution model constructed from this computation process, can give engineers a fast and effective tool to predict the behavior of bi-phase structure. Instead of a classical Cauchy continuum, second gradient model is selected as a potential candidate for substituting the composite material behavior because of the separation scale (volume ratio of inclusion to matrix phase reaches unit).
 Keywords:
 generalized continuum; second-gradient medium; higher-order homogenization; non-homogeneous boundary conditions; representative volume element.