This paper presents a three-dimensional thermo-elastoplastic computational model for the analysis of phase change problems involving the mushy zone. The model utilizes a novel meshless radial basis reproducing kernel particle approach, incorporating a high-order kernel that integrates Gaussian and cosine functions. An energy balance equation for the entire domain is formulated using the effective heat capacity method, based on the enthalpy formulation. The governing equations are discretized using the Galerkin weak form to compute thermal residual stresses, with essential boundary conditions enforced through the penalty method. Plastic deformation is characterized using the von Mises criterion with isotropic hardening, and the strain term resulting from temperature-dependent material properties is incorporated into the incremental solution process. Determination of the plastic strain increment is based on the Prandtl–Reuss flow rule. The accuracy and efficiency of the proposed meshless approach were rigorously evaluated through numerical examples encompassing two- and three-dimensional problems. The computational results were compared against available analytical and validated numerical solutions. This comprehensive assessment substantiated the robustness and precision of the developed technique. The case studies presented elucidate the capacity of the novel meshless model to effectively predict temperature distributions and residual stress fields within mushy zone phase change phenomena, accommodating both regular and irregular geometries under various boundary conditions. Notably, the model demonstrated consistent stability and high accuracy across the spectrum of simulated scenarios, thus underscoring its potential as a valuable tool for investigating complex phase change processes.
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