A Hereditary Integral, Transient Network Approach to Modeling Permanent Set and Viscoelastic Response in Polymers

TL;DR

This paper introduces an efficient numerical framework for modeling the viscoelastic and permanent deformation behaviors of polymers using a hereditary integral approach based on transient network theory, applicable to various material models.

Contribution

It develops a recurrence-based numerical method for transient network models, enabling efficient simulation of polymer viscoelasticity and permanent set under complex loading histories.

Findings

Successfully models rate-dependent responses.

Handles residual strains in polymers.

Applicable to multiple material models.

Abstract

An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with different natural equilibrium states. Chains continually detach from previously formed networks and reattach to new networks in a state of zero stress. The free energy of these networks is given in terms of the deformation gradient relative to the configuration at which the network was born. A decomposition of the kernel for various free energies allows for a recurrence relationship to be established, bypassing the need to integrate over all time history. The technique is established for both highly compressible and nearly incompressible materials through the use of neo-Hookean, Blatz-Ko, Yeoh, and Ogden-Hill material models. Multiple examples are presented showing the ability to handle rate-dependent response and residual strains under complex loading histories.