Total finite element tearing and interconnection method for computationally efficient micromechanical analysis

Abstract

Micromechanical analysis of a representative volume element (RVE) is commonly performed to estimate the material’s effective/homogenized properties in a multiscale analysis of deformation of materials. Typically numerical analysis techniques such as the finite element (FE) method are used for such an analysis. A highly refined FE mesh is required to capture microstructure features accurately for the analysis of RVE. However, this increases the number of degrees of freedom and affects computational time adversely. In this contribution a total finite element tearing and interconnection (TFETI) domain decomposition method based approach is presented for a computationally efficient micromechanical analysis. Two critical aspects of the micromechanical analysis, namely, a) computationally efficient solution of the boundary value problem and b) ease of computation of effective properties, are addressed in this work. This work focuses on the displacement driven micromechanical analysis where the boundary conditions are available in terms of displacements over the entire boundary. Two types of displacement boundary conditions, viz uniform or proportional displacements and periodic displacements corresponding to the state of uniaxial extension and simple shear are considered. The performance of the adapted TFETI with commonly used preconditioners, namely Dirichlet and lumped, for such displacement driven analysis is investigated. An efficient algorithm that exploits the structure of the TFETI method is proposed to calculate the effective properties. The proposed method’s efficacy is demonstrated by analyzing some representative model problems of composite materials. It is observed that the method’s performance depends on various problem parameters such as volume fraction, the shape of inclusion, the distance between the inclusions, and the contrast between the material properties of matrix and inclusion. The performance also depends on the numerical method parameters, such as the number of subdomains, shape of subdomains, and preconditioners. Therefore, a systematic study is carried out to study the influence of these parameters on the method’s performance.