TY - JOUR

T1 - The scaled boundary finite element method for computational homogenization of heterogeneous media

AU - Talebi, Hossein

AU - Silani, Mohammad

AU - Klusemann, Benjamin

PY - 2019/4/6

Y1 - 2019/4/6

N2 - Materials exhibit macroscopic properties that are dependent on the underlying components at lower scales. Computational homogenization using the finite element method (FEM) is often used to determine the effective mechanical properties based on the microstructure. However, the use of FEM might suffer from several difficulties such as mesh generation, application of periodic boundary conditions or computations in presence of material interfaces, and further discontinuities. In this paper, we present an alternative approach for computational homogenization of heterogeneous structures based on the scaled boundary finite element method (SBFEM). Based on quadtrees, we are applying a simple meshing strategy to create polygonal elements for arbitrary complex microstructures by using a relatively small number of elements. We show on selected numerical examples that the proposed computational homogenization technique represents a suitable alternative to classical FEM approaches capable of avoiding some of the mentioned difficulties while accurately and effectively calculating the macroscopic mechanical properties. An example of a two-scale semiconcurrent coupling between FEM and SBFEM is presented, illustrating the complementarity of both approaches.

AB - Materials exhibit macroscopic properties that are dependent on the underlying components at lower scales. Computational homogenization using the finite element method (FEM) is often used to determine the effective mechanical properties based on the microstructure. However, the use of FEM might suffer from several difficulties such as mesh generation, application of periodic boundary conditions or computations in presence of material interfaces, and further discontinuities. In this paper, we present an alternative approach for computational homogenization of heterogeneous structures based on the scaled boundary finite element method (SBFEM). Based on quadtrees, we are applying a simple meshing strategy to create polygonal elements for arbitrary complex microstructures by using a relatively small number of elements. We show on selected numerical examples that the proposed computational homogenization technique represents a suitable alternative to classical FEM approaches capable of avoiding some of the mentioned difficulties while accurately and effectively calculating the macroscopic mechanical properties. An example of a two-scale semiconcurrent coupling between FEM and SBFEM is presented, illustrating the complementarity of both approaches.

KW - computational homogenization

KW - effective properties

KW - microstructure

KW - polygonal elements

KW - SBFEM

KW - Engineering

UR - http://www.scopus.com/inward/record.url?scp=85059486457&partnerID=8YFLogxK

U2 - 10.1002/nme.6002

DO - 10.1002/nme.6002

M3 - Journal articles

AN - SCOPUS:85059486457

VL - 118

SP - 1

EP - 17

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 1

ER -