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The mechanical properties of closed-cell aluminium foams are governed by their geometrical and topological evolution during impact. Here we non-destructively investigate the deformation mechanisms of a closed-cell aluminium foam sample at the cell scale. The sample has been compressed with 21 interrupted drop-weight impacts at a nominal strain rate of 40 s−1 and the post-impacted sample has been imaged at four pertinent strain states with high-resolution X-ray micro-computed tomography (XCT). Moreover, a number of qualitative and quantitative structural analyses are carried out using advanced 3D image analyses to understand the effect of foam geometry/topology on its mechanical response. Our results show that the deforming microstructure creates strong correlations across a range of geometrical, topological and shape characteristics. Quantitative image analyses of the sample at four different strain states reveal that the regions with large void fractions predominantly undergo collapse and subsequently reduces the structural heterogeneity. Further, we show that the deformation mechanism leaves topological signatures in the evolving microstructure, which can be used to better understand the mechanical response of the sample at various stages of impact-deformation. We demonstrate here, for the first time, how the topological quantities can be used to explore the foam deformation mechanisms and to correlate the deformation with mechanical response during impact.

This work was funded in part by ARCgrant DP110102888 (to A.P.S. and V.R.),and ARC Future FellowshipsFT100100470 (A.P.S.) and FT140100604(V.R.). Financial support was alsoprovided by the member companiesof the ANU/UNSW DigicoreConsortium, who have alsocontributed samples for this study.

The mechanism of crystallisation in highly dissipative materials such as foams or granular materials is still widely unknown. In macroscopic granular materials high levels of energy need to be injected to overcome the natural propensity of these dissipative materials to form amorphous structures [1, 2]. The transition from disordered to ordered packings in such systems triggers a wide range of geometrical, topological and mechanical changes at multi length scales [3]. Formation of cavities and patterns by aggregates of grains and their evolution during this transition requires a complete topological description of the system. Here, crystallisation of three-dimensional packings of frictional spheres is studied at the grain scale with x-ray tomography. Using a novel and powerful topological tool, Persistent Homology, we describe the complete formation process of perfect tetrahedral and octahedral patterns: the two building blocks of FCC and HCP crystalline arrangements. Additionally we present possible and allowable deformations of these components that accurately reproduce the main topological features of the system. These results give new insights into the crystallisation of these highly dissipative materials.

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss=-1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE≈-0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.

Here we present an experimental and numerical investigation on the grain-scale geometrical and mechanical properties of partially crystallized structures made of macroscopic frictional grains. Crystallization is inevitable in arrangements of monosized hard spheres with packing densities exceeding Bernal's limiting density ϕ(Bernal)≈0.64. We study packings of monosized hard spheres whose density spans over a wide range (0.59

Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers.