Average-chain behavior of isotropic incompressible polymers obtained from macroscopic experimental data. A simple structure-based WYPiWYG model in Julia language

Abstract

Elastomeric materials and soft biological tissues are made up of synthetic and protein fibers, respectively. The uncoiling of these fibers during loading produces a non-linear elastic macroscopic behavior in the regime of finite strains. Many hyperelastic models have been developed to reproduce this behavior assuming the existence of a strain energy function. In structure-based models, the analytical energy function is obtained from the stored energy of all the material constituents. This stored energy is given frequently by the entropy of the chain network obtained from Langevin statistical treatment of the possible configurations adopted by the chains, and a representative cell for their spatial distribution. One of the most used models is the eight chain model, being its salient feature that it reproduces the overall response of isotropic hyperelastic materials with only two material parameters obtained from a tensile test. On the other hand, in WYPiWYG hyperelasticity the stored energies are numerical instead of analytical and capture, to any precision, the experimental tests on the material. However, due to their phenomenological nature, their determination requires more tests. In this work, we develop a microstructure-based WYPiWYG hyperelastic model in which the average chain behavior is obtained from macroscopic tests through a simple automatic inverse procedure. We show that, without assuming a probability distribution function nor any particular chain arrangement, we obtain, at the same computational cost, better predictions than the 8-chain model. Code of the model and of the examples in the Julia programming language are included.