Elastic properties of solid material with various arrangements of spherical voids

Abstract

In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure) or randomly, and may overlap in order to produce connected voids. In that way, the entire range of void fraction between 0.00 and 0.95 is covered, including closed-cell and open-cell structures. For each arrangement of voids and for different void fractions the full stiffness tensor is computed. From this, the Young's modulus and Poisson ratios are derived for different orientations. Special care is taken of assessing and reducing the numerical uncertainty of the method. In that way, a reliable quantitative comparison of different void structures is carried out. Among other things, this work shows that the Young's modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane, even though these structures are very similar. For a given void fraction SC offers the highest and the lowest Young's modulus depending on the direction. For BCC at a critical void fraction a switch of the elastic behaviour is found, as regards the direction in which the Young's modulus is maximised. For certain crystalline void arrangements and certain directions Poisson ratios between 0 and 1 were found, including values that exceed the bounds for isotropic materials. For subsequent investigations the full stiffness tensor for a range of void arrangements and void fractions are provided in the supplemental material.

A DEM method for simulating rubber tyres

“…The Young's modulus and Poisson's ratio of granular materials are known to be influenced by different packings with various void fractions and void overlapping (Fleischmann et al 2013;Heitkam et al 2016). Each packing is associated with a certain coordination number and atomic packing factor (APF).…”

Effects of Void Array Orientation on Compressive Properties of Cellular Structures

“…This close agreement in calculated shear modulus for the two differing orientations confirms that, for the FEA analysis, the elastic properties of the simple cubic pore array show cubic symmetry in agreement with results from unit cell-based FEA results. [9] If the shear modulus had been calculated solely from the {100} orientation results assuming isotropic properties the resulting values would be 12.5 and 11.9 GPa for the partial cylinder and single layer models, respectively, -more than twice the values calculated assuming cubic symmetry. [a] Key: E -Young's modulus, Rp0.2 (MPa) -0.2% offset yield strength, y -Poisson's ratio.…”

“…Cellular materials with a cubic symmetry -such as those described above -are expected, therefore, to require three properties to fully describe their elastic behavior. [8,9] In addition to the intrinsic structural symmetry, isotropy can be affected by the layer-by-layer nature of the additive manufacturing process. Anisotropic microstructures, pore morphologies and distributions, strength, and toughness have been widely reported in the literature for powder-bed fusion parts.…”

Aluminum Matrix Composites with Weak Particle Matrix Interfaces: Effective Elastic Properties Investigated Using Micromechanical Modeling

“…These models are able to describe mechanical fields resulting from particle-matrix interactions during mechanical or thermal loading. The unit cell approach was used to investigate the effective properties of porous materials [ 11 ] and various composites [ 12 , 13 , 14 , 15 , 16 ]. In [ 12 ], the unit cell approach was used to demonstrate that the reinforcing particle arrangement in the unit cell did not significantly influence the computed effective elastic properties of an Al–SiC composite.…”