Strong-Form Collocation Method for Solidification and Mechanical Analysis of Polycrystalline Materials

Materials engineering problems related to polycrystalline solids often require the prediction of grain growth and the stress analysis of polycrystalline materials. This study presents the particle difference method (PDM) as a reliable computational method applicable to this class of engineering problems. The PDM is a meshfree collocation method that directly discretizes the strong form of the governing partial differential equations based on Taylor series approximation and the moving least-squares approach. The PDM was applied to polycrystalline solids in the context of two-dimensional grain growth solidification and stress analysis of the resulting polycrystalline morphology. First, the PDM was used to predict grain growth during the solidification process of polycrystalline materials using a multiphase field model. Then the resulting morphology of the polycrystalline solids was adopted for successive stress analysis of the polycrystalline solids. Results from these analyses were compared with the results from the conventional finite-element method to verify the accuracy and efficacy of the PDM.