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

Abstract

International audienceIn 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 a-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

A stabilized formulation with maximum entropy meshfree approximants for viscoplastic flow simulation in metal forming

“…Therefore using the alpha-shape criterion the mesh has to be modified removing the triangles whose circum-radius is bigger than a given value. This approach has been already successfully applied in other reference works such as [46], where its application is discussed in detail. Once the mesh is obtained the integration is realized with standard Gauss quadrature methods within the triangles.…”

“…Although in some studies the strong form of the problem is treated with collocation techniques [38][39][40], in the majority of the literature a Galerkin approximation based on the weak form is preferred. We refer to [41][42][43] where the RKPM is applied together with elastoplastic material models and to [44][45][46][47] where the NEM is employed and a viscoplastic behaviour of the material is assumed. A detailed analysis on the application of meshless methods to metal forming is provided in [48].…”

A comparative study on the performance of meshless approximations and their integration

“…Afterwards, the concept of α-shapes ensures that concave boundaries can be represented without defining that concave boundary explicitly. A description of the method for solid mechanics can be found in Alfaro et al [1]. For the SCNI integration, a set of cells is made with a technique as used by Chen et al [14].…”

Modélisation et résolution du problème de contact mécanique et son application dans un contexte multi-physiques /

“…Les méthodes sans maillages, telles que celles basées sur la partition de l'unité ( [25]), ou encore celles des éléments naturels ( [26,27,28,29,30,31,32] n. Afin de connaître l'état de déformation dans ie voisinage de n'importe quelle particule, à l'instant t, la transformation étudiée est supposée être différentiable sur Q a .…”