Multiscale computational modelling of closed cell metallic foams with detailed microstructural morphological control

Abstract

This contribution addresses the multiscale computational modelling of closed cell metallic foams by means of an integrated RVE (Representative Volume Element) generation and computation strategy. The microstructural geometry is computationally generated by controlling relevant fine scale features such as the distribution of cell sizes, the spatial organization of cell sizes and cell wall thicknesses and curvatures. The number of faces per cell and edges per face are also set to comply with the experimentally observed values. The computational generation of the RVE is built on three ingredients: (i) a random close inclusions packing algorithm based on random sequential addition assisted by neighbour distance control, (ii) a distance field-based shape tessellation (morphing) that allows reproducing cell wall curvatures and varying cell wall thicknesses from the inclusions packing, (iii) a close control of the shape of the cells. The RVE geometry is thus described using implicit functions, thereby allowing a seamless transition towards a recently developed mesh generation technique for heterogeneous microstructures represented by such implicit functions, enabling simulations in standard softwares. This controlled generation methodology is illustrated based on experimental data available in literature for morphological indicators relevant to the foam mechanical behaviour. A qualitative and quantitative agreement between FE results and experimental data is obtained for the mechanical response of a commercially available ALPORAS foam. The individual contribution of each microstructural feature (size distributions, wall thickness and curvatures) to the average behaviour of closed cell foams is assessed through FE computations on increasingly complex geometries.

Efficient computational modelling of closed cell metallic foams using a morphologically controlled shell geometry

“…The simulation of the mechanical behaviour of a closed cell metallic foam with a 3D finite element model under compression loading was shown to be very expensive computationally due to the large number of degrees of freedom (DOFs) induced by the complex geometry [31]. Among the available solutions to reduce this computation cost (e.g.…”

“…A closed cell 3D geometry can be defined implicitly with level sets functions as shown in [32] and exploited using 3D volumetric finite elements in [31]. The missing ingredients for a successful shell-based finite element modelling with respect to these earlier efforts is a robust procedure for the extraction of a surface geometry from this 3D data with a special care to preserving the embedded morphological features.…”

“…For the sake of completeness, the main steps of the generation of a 3D implicit geometry for a closed cell foam with microstructural morphological control are recalled here, see [31]. Complex geometries, such as closed cell foams, can be described in an implicit framework by using a combination of level set functions and signed distance fields [32].…”

“…• A level set-assisted random close packing algorithm based on a random sequential addition (DN-RSA) [34] • A distance field-based shape tessellation (morphing) [32] • A microstructural feature control procedure [31].…”

“…cell wall curvature with wriggles and corrugations, plateau borders) are usually lacking in most computational contributions. In a previous work [31], a methodology was developed to generate 3D foam geometries complying with real probabilistic foam data which naturally incorporates spatial thickness variations in the cell walls, as well as the plateau borders at the wall edges. Even though such 3D finite element models allow investigating the effect of microstructural features, they were observed to be computationally expensive, even when restricted to a loading of 5% macro strain and without considering contact conditions.…”