Accounting for incompressibility in reproducing kernel particle meshless approximations - Joyot, Pierre; Trunzler, Jean; Chinesta, Francisco (European Journal of Computational Mechanics, 2006)
Meshless approximations seem to be an appealing choice for simulating forming processes involving large transformations because they allows alleviating the mesh constraints. However, because the novelty of these techniques a lot of questions are today unresolved. One of these open problems is the treatment of incompressibility which as well known impose some restrictions on the choice of the approximation spaces. The accurate treatment of incompressibility is a key point in the simulation of forming processes because the plastic flow can be in fact considered as incompressible. This paper introduces the problematic as well as some possibilities for taking into account the incompressibility in the context of mixed formulations, making special emphasis in a kind of Hermite approximations.