Conforming to interface structured adaptive mesh refinement: New technique for the automated modeling of materials with complex microstructures

Abstract

This manuscript introduces a new method named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) for the automated finite element modeling of problems with complex morphologies. The CISAMR transforms a simple structured mesh of quadrilateral elements into a conforming hybrid mesh composed of quadrilateral and triangular elements with low aspect ratios using a non-iterative algorithm. The automated construction of the mesh begins with implementing a customized Structured Adaptive Mesh Refinement (SAMR) algorithm to achieve the desired element size along materials interfaces. A new r-adaptivity algorithm is then employed to move selected nodes of nonconforming elements to intersection points of their edges with the interface, followed by the diagonal sub-triangulation of all elements deformed during this process into conforming sub-triangles. CISAMR does not require relocating the nodes of the background mesh or creating any new node away from materials interfaces after the completion of the SAMR phase. Further, this method can easily handle special cases such as intersecting boundaries/interfaces, while ensuring that aspect ratios of resulting sub-elements are lower than three. A comprehensive discussion is provided on different aspects of the implementation of CISAMR, followed by several example problems to show its application for modeling materials with complex microstructures.