Implicit multiscale finite element analysis of polymer physics-based multiscale constitutive model for elastomers

Abstract

This paper proposes a multiscale visco-hyperelastic constitutive model that can predict the material behavior bridging molecular properties to response at the continuum level and its integration within implicit finite element analysis. The proposed model incorporates all parameters having actual physical meaning obtained from molecular simulations based on the tube theory. Despite the advantages that the constitutive equation was determined from molecular network characteristics, applications of the model have been restricted to the simple shape of Finite Element (FE) models with a few cases of specific deformations, owing to its complexity and absence of the implicit formulation. Therefore, the application of the model to the 3D implicit FE analysis with a tangent stiffness was proposed by applying numerical differentiation with the complex step derivative approximation (CSDA) method. Combined with the Neo-Hookean hyperelasticity model, the results from the example analysis applied to the tensile specimen model were examined to manifest the visco-hyperelastic characteristics of elastomers under cyclic loading, stability of the analysis, and further discussion on the visco-hyperelastic constitutive model were proposed.