Three-dimensional image-based numerical homogenisation using octree meshes. (September 2020)

• Record Type: Journal Article
• Authors: Saputra, Albert A.; Eisenträger, Sascha; Gravenkamp, Hauke; Song, Chongmin
• Is Part Of: Computers & structures. Volume 237(2020)
• Publication Date: 2020-09
• Subjects: Image-based analysis -- Octree mesh -- Representative volume element (RVE) -- Effective material properties -- Periodic boundary conditions -- Scaled boundary finite element method (SBFEM); Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2020.106263
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: Automatic image-based octree meshes for efficient modelling of composites. Extension of scaled boundary finite element method (SBFEM) for homogenisation in 3D. Use of piece-wise polynomial functions on the surface of a polyhedral element. Implementation of periodic boundary conditions in SBFE analysis. Computation of homogenised material properties for piezoelectric composites. Abstract: The determination of effective material properties of composites based on a three-dimensional representative volume element (RVE) is considered in this paper. The material variation in the RVE is defined based on the colour intensity in each voxel of an image which can be obtained from imaging techniques such as X-ray computed tomography (XCT) scans. The RVE is converted into a numerical model using hierarchical meshing based on octree decompositions. Each octree cell in the mesh is modelled as a scaled boundary polyhedral element, which only requires a surface discretisation on the polyhedron's boundary. The problem of hanging (incompatible) nodes – typically encountered when using the finite element method in conjunction with octree meshes – is circumvented by employing special transition elements. Two different types of boundary conditions (BCs) are used to obtain the homogenised material properties of various samples. The numerical results confirm that periodic BCs provide a better agreement with previously published results. The reason is attributed to the fact that the model based on the periodic BCs is not over-constrained as is the case for uniform displacement BCs.