Sensitivity analysis of transient metal forming with incompressible linear elements

On the basis of a recently developed method which allows the use of linear elements for metal forming simulation within the flow approach, sensitivity analysis is carried out. Aiming at large, industrial problems, attention is focused on the explicit version, which is considered more effective for such problems, although implicit time integration is possible as well. By time step splitting a stabilization sub-matrix is obtained, which allows the use of equal interpolation for velocity and pressure. Specifically, linear triangles and tetrahedra have been used, which are easily generated by automatic meshers. Sensitivity analysis is carried out by the Direct Differentiation Method, with which similar analyses have been performed by the author for the flow approach within a direct solution scheme.