Development of an ABAQUS™ plug-in to evaluate the fourth-order elasticity tensor of a periodic material via homogenization by the asymptotic expansion method

Abstract This paper presents the development of an ABAQUS™ plug-in for estimation of the effective properties of heterogeneous three-dimensional periodic media using the asymptotic homogenization method (AHM). The developed plug-in is user-friendly and requires only basic skills in ABAQUS™. All aspects of the plug-in development are presented, including the solutions found to implement this approach within the finite element package in ABAQUS™. The application of the load cases is performed by using a Uexpan subroutine written in the Fortran language. The application of periodic boundary conditions, as well as the post-processing, are made in Python script. All codes are connected by an ABAQUS™ plug-in and can be called directly by the graphical user interface (GUI) of the software. In order to use the plug-in, the user must only generate the geometry, define the properties of the materials, and mesh the model. The remaining calculations are done automatically. Several case studies are presented and compared with the results found in the literature. Additionally, several element types were evaluated in order to test the versatility of the implemented method. The results show an excellent agreement with the results found in the literature. All of the implemented codes are provided as supplementary material to this paper.