A model for hyperelastic rubber-like materials based on micro-mechanical elements

Abstract

In this work, we propose a microstructurally motivated hyperelastic model to describe the behavior of rubber-like materials. At the scale of the Representative Volume Element (RVE), we assume that, for each macromolecular chain, the segments of the chains are deformable and that there is a bending energy between two consecutive segments. We propose to model each macromolecular chain using micro-mechanical elements: elastic bars to represent the segments between cross-linking points and elastic spire to illustrate the flexibility of rotations around the cross-linking points. We thus suggest to model the behavior of the macrochain, using a quadratic spring like potential for a linear behavior of the chain segments, associated with a nonlinear elastic sigmoidal behavior at the connection points between Kuhn segments. Numerical simulation, on different RVEs, show that the proposed modeling represent the response of hyperelastic rubber-like materials in uniaxial extension, simple shear, pure shear and biaxial extension. In order to validate the proposed model, the results obtained in the case of four RVEs will be compared with the experimental data of Treloar (1944). These comparisons show that the proposed model is able to reproduce the experimental behavior of rubber-like materials.