Constitutive modeling of viscoelastic solids at large strains based on the theory of evolving natural configurations
Year: 2025
Type: preprint
Abstract: The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a Kelvin-Voigt model and their associated standard solids, viz., a Zener and a Poynting-Thompson solids respectively, have been modeled within a Lagrangian framework. We show that while a strain-space formulation of the evolving natural configurations is useful in modeling Maxwell-type materials, a stress-space formulation that incorporates a rate of dissipation function in terms of the relevant configurational forces is required for modeling the Kelvin-Voigt type materials. Furthermore, we also show that the basic Maxwell and Kelvin-Voigt models can be obtained as limiting cases from the derived standard solid models. Integration algorithms for the proposed models have been developed and numerical solutions for a relevant boundary value problem are obtained. The response of the developed models have been compared and benchmarked with experimental data. Specifically, the response of the novel Poynting-Thompson model is studied in details. This model shows a very good match with the existing experimental data obtained from a uniaxial stretching of polymers over a large extent of strain. The relaxation behavior and rate effects for the developed models have been studied.
Source: arXiv (Cornell University)
Authors: Singh, Tarun, Paul, Sandipan
Institution: Indian Institute of Technology Roorkee
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979375648
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