Evaluation of the FMBEM efficiency in the analysis of porous structures

Abstract

Purpose The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time. Design/methodology/approach The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered. Findings FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver. Research limitations/implications The present results are limited to linear elasticity. Originality/value This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

Inverse Identification of Elastic Properties of Constituents of Discontinuously Reinforced Composites

“…There are several common features in engineering materials that may cause additional issues connected with the inverse identification procedure: (a) reinforcing fibers may have anisotropic properties, (b) porosity present in the material is not constant and increases with increasing volume fraction of the reinforcement, (c) orientation distribution of the reinforcement is not strictly random but depends on manufacturing process and may vary from unidirectional to random, and (d) the interface between the matrix and the reinforcement is imperfect. Moreover, the directions for future research are connected with improving the efficiency of micromechanical models for non-spheroidal inclusions, for example, by applying boundary element methods [48,49], instead of FEM, during the numerical solution of equivalent inclusion problem or developing metamodels instead of using time-consuming micromechanical models.…”

Determination of Local Strain Distribution at the Level of the Constituents of Particle Reinforced Composite: An Experimental and Numerical Study

“…Therefore, very often, the RVE is considered as a model for simplifying the geometrical features of the real microstructure to provide a reasonable computation time [ 5 , 6 ]. Various numerical methods can be used for the analysis of the RVE, like, for instance, the boundary element method (BEM) [ 7 , 8 , 9 , 10 ], or the fast Fourier transform-based method (FFT) [ 11 , 12 , 13 ]. However, the most frequently used is the finite element method (FEM), which has become a standard approach.…”

Evolutionary identification of microstructure parameters in the thermoelastic porous material

“…An analytical method can be applied only to simple models. Numerical homogenization (Buyrachenko, 2007;Fish, 2006;Zhodi and Wriggers, 2008) using the boundary element method (BEM) (Ptaszny and Hatłas, 2018) or the finite element method (FEM) (Qiang et al, 2018) on the other hand is a very efficient and popular method. The identification problem may deal with searching of desired material properties, shape or position of inclusions or voids in the structure.…”