Three-dimensional simulation of aluminium extrusion by the α-shape based natural element method

In this work we study the possible advantages of an updated Lagrangian perspective in the numerical simulation of aluminium extrusion. For this purpose, we have employed a well established meshless technique known as Natural Element Method (NEM). This technique presents some advantages over finite element simulations, such as no remeshing requirements and the accuracy of the approximation even with highly distorted triangles or tetrahedra. It is employed in conjunction with the notion of α-shapes of the cloud of nodes in order to extract the geometry of the extrudate as it evolves. This state-of-the-art geometrical concept allows us to avoid complex geometrical checks of self-contact on the boundary of the domain. Aluminium is modelled as a rigid-plastic material, governed by a Sellars–Tegart-type law. The paper includes some examples that illustrate the potential of the method.