Quasi-static compressive behavior and constitutive model of graded foams

Abstract Functional Graded Materials are widely developed in the past decades and graded foams are introduced recently because such graded foams can exhibit better energy absorption capacities than the uniform ones of the same weight. Meanwhile, very limited investigation on their constitutive model has been reported. Therefore, this study aims to investigate experimentally the quasi-static compressive behavior of graded foams and then establish a constitutive model based on the property of the homologous uniform foams. For this purpose, uniform foams with six different cell sizes and graded foams with twelve different gradient distributions are manufactured by using the additive manufacturing technique. Comparing with uniform foams, graded foams with similar relative density show a similar behavior in elastic and densification stages. The main difference lies in the fact that graded foams possess a hardening plateau stage rather than a constant one. Such hardening behavior is due to a successive collapse from the weakest region to the strongest region. In other words, graded foams exhibit successive plateau stresses of their component layers. Thus, the graded-foam property can be modeled using the mechanical properties of uniform-foam component layers. Indeed, we first determine the Gibson-Ashby relations for uniform foams from experimental data. Then, an elastic, plastic-hardening, locking model for graded foams is built from these uniform-foam Gibson-Ashby relations. This constitutive model can be used for predicting the quasi-static compressive responses of various graded foams, and verified by our experimental data and some published results. A finite element simulation is also conducted to verify the validity of this model. On the basis of this model, it is possible to tailor the mechanical properties of graded foams for various engineering applications without conducting experimental studies.