Constitutive modelling for understanding stress-stretch behaviour of Lennard-Jones non-crystalline molecular Solid

Abstract Non-crystalline molecular solid materials have many scientific and engineering applications. This study develops a constitutive equation for understanding stress-stretch behaviour of non-crystalline molecular solid using Lennard-Jones (LJ) intermolecular interaction. The strain energy derived from Lennard-Jones interactions between molecules. Based on the excluded volume (spherical volume occupied by the molecules maintaining centre to centre distance with a reference molecule) and density of the molecules, strain energy density is developed. In order to relate the molecular approach with continuum approximation, the excluded volume and density are expressed as a function of strain invariants of right Cauchy-Green deformation tensor. Finally, the constitutive equation in the form of Cauchy stress tensor is developed using the present strain energy density function. The present constitutive model is used to study finite deformations of the molecular solid like uniaxial extension. We compare our theoretical results with the experimental data of flexible polyurethane foams and obtain very good agreements. The current constitutive model can predict the deformation of micro/nano engineering system components.