Applicability of Kroon network theory for biaxial mechanics in rubber through multiscale approach

In this paper, we address the problem of the multiscale prediction of the multiaxial hyperelastic behavior of rubber. Our goal is to test the predictive capabilities of a hyperelastic model grounded in the principles of continuum mechanics, bridging the gap between continuum-level mechanics and molecular-level descriptions. This constitutive model posits that macroscopic behavior results from the non-affine deformation of the molecular network, influenced by topological constraints. We employ molecular dynamics methods to measure the mechanical behavior of a rubber network structure under various deformation modes. The study includes an analysis of the molecular network deformation during the straining process, shedding light on the deformation mechanisms at the molecular level. By examining how the total network stress in our specifically designed molecular structure responds to biaxial strain ratios, we are able to assess the effectiveness of the hyperelastic constitutive model.