JOURNAL OF MATERIALS SCIENCE 31 (1996) 1107-1113 Well tailored compressive stress-strain relations for elastomeric foams in uni-axial stress compression G. BEN-DOR, G. CEDERBAUM, G. MAZOR, O. IGRA Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel Well tailored compressive stress-strain relations for elastomeric open and closed cell foams under a uni-axial stress compression were developed. These sets are aimed at replacing those presented by Gibson and Ashby (1988) 1-11 since they are mismatched and cannot be used. The proposed set of compressible stress-strain relations for elastomeric open cell foams was compared with experimental results. Good agreement was seen. 1. Introduction In order to simulate phenomena in which flexible foams are compressed as a result of the action of external loads, e.g. shock waves, there is a need to know the compressive stress-strain relations of the foams under consideration. As shown by Gibson and Ashby [1] and by Ben-Dor and co-workers [2], the compressive stress-strain relations of cellular materials, in general, and foams in particular, depend on the following major factors: 1. the type of foam; 9 elastomeric foams 9 elastic-plastic foams 9 elastic-brittle foams 2. the internal structure of the foam; 9 open cell 9 closed cell 3. the mode of compression; 9 uni-axial stress mode 9 bi-axial stress mode 9 uni-axial strain mode The general shapes of the various stress-strain relations are similar. They all show linear elastic behaviour at low strains, followed by a long collapse regime in which the stress rises slightly, truncated by a regime of densification in which the stress rises steeply. The main difference between the above mentioned three types of foams is in the mechanical behaviour in their collapse regime. In elastomeric foams the collapse is due to elastic buckling of the cell walls, in elastic plastic foams the collapse arises from plastic yielding of the cell walls and in elastic-brittle foams the collapse is due to brittle crushing of the cell walls. A comprehensive and generally accepted book, in which the mechanical properties, in general, and the stress-strain relations, in particular, are derived and 0022 2461 9 1996 Chapman & Hall given for a variety of cellular materials, has been published by Gibson and Ashby [1-]. Chapter 5 of their book is devoted to foams. In section 5.5 they summarize the mechanical behaviour of foams and provide some experimental and theoretical stress-strain maps. Unfortunately, however, when attempting to use their correlations in our numerical simulations, we realized that they are very problematic, and cannot be used. Consequently, it is the aim of this study to develop a correct set of compressive stress-strain relations. 2. Theoretical background Let us consider, for example, the compressive stress-strain correlations for elastomeric open cell foams under a uni-axial stress mode of compression as proposed by Gibson and Ashby [1] in their equations (5.55a and b). In general they divide the stress-strain plane into two domains, the linear-elastic and the post buckling domains (for more details see [1] pp. 161-162). In the linear elastic domain (0 ~ e ~<ael) cr = E*~ (1) where E* is the effective modulus of elasticity of the cellular material. When treating the post-buckling domain they claim that experimental results are "best described in two segments", which they refer to as a plateau and a densification regime. For these regimes they suggested the following two correlations: in the plateau regime (tel ~ ~ ~ F~2) = E*8el (2) in the densification regime (~z ~<e < aD) 1( ; cy = E* eel E D -- E (3) 1107