Technology Category
Machine Learning: Kernel MethodsCognitive Modeling & Cognitive Systems: (Computational) Cognitive ArchitecturesPlanning, Routing, and Scheduling: Temporal Planning
A Hereditary Integral, Transient Network Approach to Modeling Permanent Set and Viscoelastic Response in Polymers
🤖 AI Summary
Addressing the challenge of coupled modeling of polymer viscoelasticity and permanent deformation (i.e., residual strain), this work proposes a transient network theory framework based on genetic integrals. The approach explicitly captures nonlinear, rate-dependent, and irreversible responses under complex loading histories by assigning polymer chains to multiple equilibrium networks and introducing a zero-stress reattachment mechanism. A novel recursive algorithm is developed to decompose the free-energy kernel function, circumventing full-history integration and thereby significantly enhancing computational efficiency—while remaining universally applicable to both compressible and nearly incompressible materials. Integrated with classical constitutive models—including neo-Hookean, Blatz–Ko, Yeoh, and Ogden–Hill—the method accurately predicts residual strain and rate-dependent behavior across diverse polymer loading paths. Numerical experiments confirm its robust stability and broad model-agnostic applicability.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Modeling viscoelasticity and permanent set in polymers
Handling rate-dependent response under complex loading
Predicting residual strains using transient network theory
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hereditary integral transient network theory
Recurrence relationship bypasses time integration
Supports compressible and incompressible material models
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