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<p>In many engineering applications, materials are subjected to high loading rates and severe deformation, where the coupled effects of temperature and mechanical response become significant. This study presents an element-free Galerkin meshless method for modeling the thermo-viscoplastic behavior of materials under dynamic loading conditions. The formulation is derived based on first-order conservation laws for linear momentum, deformation gradient tensor, volume map, area map, and entropy, within a total Lagrangian framework. A variational multiscale stabilization approach is employed to ensure numerical robustness. The Johnson-Cook model is incorporated to capture strain rate sensitivity in plastic deformation. The method is validated through plasticity benchmark problems, including the modeling of Taylor impact test, necking bar, and equal channel angular pressing process. Furthermore, the temperature-dependent phase transformation behavior of shape memory alloys is simulated under dynamic loading. Results demonstrate the capability of the proposed method to accurately capture the complex interplay between thermal and mechanical effects in highly nonlinear scenarios.</p>

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An element-free Galerkin approach for rate- and temperature-dependent behavior of inelastic solids

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Hojjat Badnava,
  • Sayed Hassan Nourbakhsh,
  • Mahmoud Pezeshki

摘要

In many engineering applications, materials are subjected to high loading rates and severe deformation, where the coupled effects of temperature and mechanical response become significant. This study presents an element-free Galerkin meshless method for modeling the thermo-viscoplastic behavior of materials under dynamic loading conditions. The formulation is derived based on first-order conservation laws for linear momentum, deformation gradient tensor, volume map, area map, and entropy, within a total Lagrangian framework. A variational multiscale stabilization approach is employed to ensure numerical robustness. The Johnson-Cook model is incorporated to capture strain rate sensitivity in plastic deformation. The method is validated through plasticity benchmark problems, including the modeling of Taylor impact test, necking bar, and equal channel angular pressing process. Furthermore, the temperature-dependent phase transformation behavior of shape memory alloys is simulated under dynamic loading. Results demonstrate the capability of the proposed method to accurately capture the complex interplay between thermal and mechanical effects in highly nonlinear scenarios.