A micro-mechanically-based constitutive model for hyperelastic rubber-like materials considering the topological constraints

Abstract

Hyperelastic rubber-like materials are described by their nonlinear elastic behavior subjected to large deformations. The one-dimensional strain energy function for polymeric material was introduced in Mahnken and Mirzapour (2022). This follow-up contribution presents a three-dimensional statistical micro-mechanical-based constitutive model incorporating the topological constraint’s effects. The micro strain energy corresponding to the stored energy in a single polymer chain is mainly entropic and calculated from the entropic part of the Helmholtz free energy based on the Boltzmann equation. Then, the macro strain energy corresponding to the polymer networks is obtained by homogenizing the micro strain energy over the unit volume. At the same time, it can be decomposed into cross-linked and entangled strain energies. The current model is developed on the different angles of the polymer chain. The random nature of the polymer chain’s angles is defined by proper probability distribution functions (PDFs) representing different angles’ distribution. I incorporate the entangled chains based on the statistical degree of freedom introduced as polymer angles. Numerical examples to calibrate and verify the proposed model illustrate the capability of the current proposed model to reproduce the highly nonlinear behavior of rubber-like materials under different loading conditions.