A constitutive model for the compressive response of metallic closed-cell foams including micro-inertia effects

Romain Barthélémy,Steven Kerampran,François Vermeersch,Nicolas Jacques

doi:10.1051/epjconf/20159404014

Romain Barthélémy, Steven Kerampran + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/20159404014

Copy DOI

Abstract

Metallic foams have known a keen interest in the last decades. Their ability to undergo very large deformations while transmitting low stress levels make them capable of performing functions of protective layers against intense loadings and of energy absorbers, for instance. The behaviour of metal foams varies considerably between quasi-static and dynamic regimes. Those differences can be linked to the strain-rate sensitivity of the skeleton material and to micro-inertial effects (induced by the crushing of the foam cells). In the present work, a micromechanical model has been developed to take into account micro-inertia effects on the macroscopic behaviour of closed-cell foams under dynamic loading conditions. The proposed modelling is based on the dynamic homogenisation procedure introduced by Molinari and Mercier (J. Mech. Phys. Solids 49 (2001) 1497–1516). Within this framework, the macrostress is the sum of two terms. The first one is a static stress, that can be described with any existing model of metal foam. The second contribution is a dynamic stress related to micro-inertia effects. Considering an initially spherical shell as a Representative Volume Element (RVE) of the foam material, a closed-form expression of the dynamic stress was obtained. The proposed modelling was applied to shock propagation in aluminium foams (it should however be noted that the present theory is not restricted to uniaxial deformation but can be applied to arbitrary loadings). From experimental data of the literature, it is observed that incorporating micro-inertia effects allows one to achieve a better description of the foam shock response. This indicates that micro-inertia may have a significant influence on the dynamic behaviour of metallic foams.

Highlights

IntroductionCellular ones have known large developments in the last decades
Among recent materials, cellular ones have known large developments in the last decades
No lateral expansion of the specimen is observed during the shock compaction of the sample. This behaviour can be related to the results presented by Deshpande and Fleck [24], who observed that the plastic Poisson ratio of low-density metal foams is close to zero

Summary

Introduction

Cellular ones have known large developments in the last decades. They are found at natural state (wood, cancellous bones, sponges, cork...) or manmade (bread, foams...). Cellular solids are often classified according to their relative density (the ratio of the density of the foam sample to the one of its constitutive material). Cellular materials with high relative density are called “porous media” while “foam” corresponds to materials with a relative density lower than 0.3 [1]. The latter is the focus of this study. Foam skeletons can be made of different materials such as polymer, ceramic, glass or metal and present two types of structure (open-cell or closed-cell), see Fig. 1

Objectives

Results

Conclusion