A diffused material interface based homogenization method for periodic composites

In this article, we propose a novel semi-analytical method to model complicated material interfaces by using a Gaussian kernel function and the resulting error function (erf) available in the symbolic toolbox of MATLAB. The proposed method provides an analytical expression for the smoothened material properties via a diffused representation of material interfaces that eliminates the requirement to track material interfaces explicitly while implementing the finite element method. In this article, we have demonstrated the proposed diffused representation approach for the homogenization of composites with periodic microstructures. We have studied the influence of varying shapes and sizes of inclusion on the overall effective material properties and the elastic response of the homogenized composites. However, the method is very generic and can be applied to obtain an analytical expression for smoothened material properties for any complicated material interface that may be useful to design high-performance topologically interlocked composites.