A Strain Energy Density Potential for Non-Crystalline Solids Using Molecular Interactions

Non-crystalline solids have important applications in engineering and science. To predict the stress-strain behaviour of these materials, this work constructs an efficient strain energy density function using the concepts of molecular interactions. Considering hard contact between molecules, strain energy density of materials is defined in terms of packing fraction (volume occupied by the molecules per unit volume of the material) in deformed configurations. The packing fraction is represented in terms of strain invariants of right Cauchy-Green deformation tensor. Constitutive model obtained from the present strain energy density function is applied for predicting finite deformations of the materials like uniaxial extension, equibiaxial extension, and pure dilation. We observe that increasing reference packing fraction increases the Cauchy stress components. Results obtained from the present theoretical model is compared with experimental results of flexible polyurethane foam materials. We obtain good agreement with the experimental results. The present strain energy density function can be applied for predicting deformation as well as stress-strain behaviour of any other micro/nano components used in engineering systems.