Numerical modeling of void migration in solids due to temperature gradient using the boundary element method

Voids (a land of flaw) are not desired in the products of many industrial and manufacturing processes. In this article, we seek effective ways to remove the void by modeling the void migration and predicting the intermediate and the final shape of the cavity. The boundary element method (BEM) is applied to the quasi-steady state void migration process governed by Laplace’s equation. The conduction solution depends on the void shape, and the void shape depends on the conduction solution. Hence this is a conjugate problem. The analytical formulation and the numerical approach are outlined. The Overhauser spline elements are used in the BEM to ensure continuous first-order derivatives on the void boundary. Given the material properties, geometry of the physical model, and boundary conditions, this computer model can predict detailed information such as flux, velocity and direction of void motion, and temperature at any stage of the void migration. Different strategies for void removal are investigated.