Overall elastic properties of a material containing inhomogeneities of concave shape

Finite Element Modeling of Porous Microstructures With Random Holes of Different-Shapes and -Sizes to Predict Their Effective Elastic Behavior

“…These materials have different pore shapes and sizes, overlapping patterns(distribution modes). Hence, this study aims to elaborate a computational strategy to generate porous models close to the real microstructures, which can lead to a more accurate estimate of the effective elastic moduli of porous materials [15][16][17][18], by taking account of the variation of pore sizes, shapes and the statistics information obtained experimentally.…”

“…The finite element method (FEM) is a possible approach to quantitatively evaluate the material properties influenced by defects, like holes, cracks and many other imperfections, in the materials and the large structures in view of its low cost and relatively high efficiency [11,12]. Many pioneering studies concerning this topic [1][2][3][4][5][13][14][15][16][17][18] have been conducted by now, and one critical step is to reconstruct a proper microstructure model of the porous materials. A straightforward way is adopting a commercial package, say Minics or others, to reproduce the true microstructures of porous materials at a specific scale by using the tomographic images generated by the atom-probe tomography [19], electron microscopy [20], X-ray tomography [21], or focused-ion-beam-nonatomography [22].…”

“…[28][29][30]. Recently, the influence of some more complex and irregular shapes of pores are considered in generating the porous models [15,16,18,[31][32][33][34][35], and some particular schemes, say hole forming agent method and space-holder technique, are developed simultaneously to reconstruct the porous model more efficiently. In Ref.…”

“…[23], a robust numerical approach is developed for generating 3D representative volume element models of bicontinuous nanoporous microstructures using Cahn's method [36] to generate the Gaussian random field and the sinusoidal wave of fixed wavelength but random in direction and phase. To be noted microstructures of porous materials of practical existence consist of randomly distributed pores of various sizes and different shapes and particularly, the distribution mode of these pores also obviously affects the overall elasticity of materials [13][14][15][16][17][18]31,35]. Hence, this paper aims to elaborate a novel computational strategy for generating porous microstructures accounting for the actual statistical pore-size, -shape and distribution-mode information simultaneously framed within the finite element method.…”

“…Hence, this paper aims to elaborate a novel computational strategy for generating porous microstructures accounting for the actual statistical pore-size, -shape and distribution-mode information simultaneously framed within the finite element method. To alleviate the difficulty in discretizing irregularly-shaped pores of various eccentricities from the CAD model and facilitate the pores of different arrangements generation, a generalized explicit mathematical description to characterize the actual pore shapes, which covers the models applied in the open literature [13,14,17,18,27] as special cases, is introduced, and an element-based algorithm is developed to produce porous microstructures of actual porous materials. This paper is organized as follows.…”