Dynamic analysis of three-dimensional polycrystalline materials using the boundary element method

A new computational framework to analyse the microscale dynamic behaviour of three-dimensional polycrystalline materials with different lattice structures is presented. The absence of analytical solutions for these stochastic materials has been a challenge in validating the numerical results. In macroscale analysis, when the number of crystal aggregates in the microscale is large, polycrystalline aggregates exhibit an effective isotropic nature. To model the elastodynamic effects, random crystalline orientations and morphology configurations are used for each polycrystalline aggregate. The recently proposed fundamental solution based on double Fourier series for general anisotropy coupled to the dual-reciprocity boundary element method is used. A drastic reduction in the degrees of freedom is achieved owing to the nature of the boundary mesh. The stochastic time-dependent displacement wave under various boundary conditions is evaluated, and the validation is carried out using homogenisation over the grain surfaces. An assessment of the effective macroscopic properties of the available analytical isotropic models is proposed, wherein the convergence is evaluated using statistical samples. Numerical results are presented using a large number of simulations to obtain a good confidence interval.