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Novel Homogenized 3D Brick Element for Multiscale Modeling Using Mechanics of Structure Genome
Abstract
Traditional multiscale analysis homogenizes a heterogeneous body to be an equivalent homogeneous body with the effective material stiffness matrix or compliance matrix computed from a representative volume element (RVE). Traditional multiscale analysis assumes that there is a clear scale separation between the microstructure and the macroscopic structure so that the microstructure can be considered as a point in the macroscopic analysis. This is only true if the microstructure repeats many times around one point within the macroscopic structure. However, in most real applications, such repeated microstructure does not exist. In this paper, we will develop a novel homogenized 3D element using the mechanics of structure genome (MSG) by homogenizing a heterogeneous body discretized by many elements into a single 8-node or 20-node brick element. The theory would generate an effective element stiffness matrix, which can be used as input for a 3D brick element developed using the Abaqus user element subroutine (UEL). After computing the macroscopic behavior using the UEL elements, the local displacements, stresses, and strains can be computed through a dehomogenization process based on MSG. To verify the developed theory, we created three different examples to demonstrate its application and accuracy in comparison to other alternative approaches.
DOI
10.12783/asc35/34865
10.12783/asc35/34865