Inelastic constitutive relations for foamed materials: A statistical approach and its application to open-cell melamine

The aim of this study is to characterize the viscoelastic behavior at finite strain of a melamine foam submitted to multiple loading paths of uniaxial compression. The constitutive law is obtained by specializing a previously proposed model arising from an irreversible thermodynamic approach for several types of material (e.g. polymer, metal alloys) to include the essential microscopic features of this open-cell foam. The model is based on the central concept of relaxed state, which is defined as a thermodynamic state of metastable equilibrium including the strain history effect. In the case of the present material, it is shown that the corresponding relaxed stress may thus be formulated using the tools of statistical mechanics: namely, the Shannon entropy 〈S〉 is extremized under adequate geometric constraints. Thus, the Lagrange multipliers associated with these requirements are defined as forces conjugated to the degrees of freedom of the geometrical transformation. By comparing the predictions from the proposed inelastic constitutive model with experimental data for uniaxial compression interrupted by loading–unloading sequences, we conclude that the constitutive relations predict the mechanical behavior of the melamine foam.