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

International audienceIn this paper we review some recent results in the field of numerical simulation of extrusion and other forming processes obtained by the authors by using a meshless approach, together with a wide review of the existing bibliography on the topic. Three main alternatives exist in the literature, namely (updated) Lagrangian, Eulerian and arbitrary Lagrangian-Eulerian (ALE) methods. A review of the most important characteristics of each of these three approaches is here presented and their possible advantages are pointed out. Finally, an updated Lagrangian approach over a meshless approximation, based on a class of methods globally coined as natural element methods (also as natural neighbour Galerkin methods) is analysed and its relative advantages studied. Some numerical examples are included that clearly show the potential capabilities of the proposed method

In this work a pancreatic surgery simulator is developed that provides the user with haptic feedback. The simulator is based on the use of model order reduction techniques, particularly Proper Generalized Decomposition methods. The just developed simulator presents some notable advancements with respect to existing works in the literature, such as the consideration of non-linear hyperelasticity for the constitutive modeling of soft tissues, an accurate description of contact between organs and momentum and energy conserving time integration schemes. Pancreas, liver, gall bladder, and duodenum are modeled in the simulator, thus providing with a very realistic and immersive perception to the user.

In this paper two different formulations for the numerical simulation of laser surface coating processes are presented and analysed. Both are based on the use of natural neighbour interpolation, but one employs a Galerkin approach and takes temperature as the primary variable while the second one is based on the use of finite differences and enthalpy as primary variable. The main practical difference is thus the description of the interphase of the melted zone during the process. While in the first method the interphase is described by a set of nodes that evolve in time, in the second one it is located somewhere between a string of nodes. Both formulations are described and compared, showing their potential benefits for the simulation of the before mentioned process.