A finite element model for thermomechanical stress-strain fields in transversely isotropic strain-limiting materials

Authors

• Saugata Ghosh, The University of Texas Rio Grande Valley
• Dambaru Bhatta, The University of Texas Rio Grande Valley
• S. M. Mallikarjunaiah, Texas A & M University - Corpus Christi

Document Type

Article

Publication Date

11-2026

Abstract

This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress concentrations. We address the challenge of unphysical strain singularities at crack tips by employing a strain-limiting theory of elasticity. This theory is characterized by an algebraically nonlinear constitutive relationship between stress and strain, which intrinsically enforces a limit on the norm of the strain tensor. This approach allows the development of very large stresses, as expected near a crack tip, while ensuring that the corresponding strains remain physically bounded. A loosely coupled system of linear and nonlinear partial differential equations governing the response of a thermo-mechanical transversely isotropic solid is formulated. We develop a robust numerical solution based on the finite element method, utilizing a conforming finite element discretization within a continuous Galerkin framework to solve the two-dimensional boundary value problem. The model is applied to analyze the stress and strain fields near an edge crack under severe thermo-mechanical loading. Our numerical results reveal a significant departure from classical predictions: while stress concentrates intensely at the crack tip, the strain grows at a substantially slower rate and remains bounded throughout the domain. This work validates the efficacy of the strain-limiting model in regularizing thermo-elastic crack-tip fields and establishes a reliable computational foundation for the predictive modeling of thermally driven crack initiation and evolution in advanced anisotropic materials.

Comments

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Recommended Citation

Ghosh, Saugata, Dambaru Bhatta, and S. M. Mallikarjunaiah. "A finite element model for thermomechanical stress-strain fields in transversely isotropic strain-limiting materials." Communications in Nonlinear Science and Numerical Simulation (2026): 110469. https://doi.org/10.1016/j.cnsns.2026.110469

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Communications in Nonlinear Science and Numerical Simulation

DOI

10.1016/j.cnsns.2026.110469