Residual stresses in metal deposition modeling: Discretizations of higher order

This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This application demands for the solution of a coupled thermo-elasto-plastic problem on transient meshes within which history variables need to be managed dynamically on non-boundary conforming discretizations. To this end, we propose to combine the multi-level hp-method and the finite cell method. The former was specifically designed to treat high-order finite element discretizations on transient meshes, while the latter offers a remedy to retain high-order convergence rates also in cases where the physical boundary does not coincide with the boundary of the discretization. We investigate the performance of the method at two analytical and one experimental benchmark.