An improved model to describe the repeated loading-unloading in compression of cellular materials

Cellular materials, often referred as foams or structural foams when used for energy absorption, are largely used to protect people and goods in the case of shocks and impacts. The detailed knowledge of their behavior is fundamental to design components for this aim. Peroni et al. (2008)-(2009) proposed a model able to describe the mechanical compression behavior of some polymeric material. Such model, based on the work by Rusch (1970), described the stress-strain curve as a sum of two contributions, the first for the elastic part and the second for the densification. More recently Avalle and Belingardi (2018) presented a more general model where the stress is calculated as a sum of three terms, one for the elasto-plastic phase, the second for the plateau, and a third for the densification. The model could include effects like density and strain-rate. However, those models allow to describe only the monotonic compression behavior: in several situations repeated impacts can happen with unloading followed by further reloading. Unfortunately unloading cannot be described by a linear relation between stress and strain (as is usually considered for metals). Unloading follows a non-linear law with a variable relation between stress and strain in the successive cycles: this requires a particularly complex model. In this work, a new model able to effectively reproduce the compression behavior of some polymeric cellular materials is presented. The model is validated and tuned on the basis of experimental tests with specimen subject to complex cycles of repeated loading and unloading. The model describes both the loading from different levels of residual compression and unloading from any value of compression level. The application to several materials justifies the generality of the method.