Meshless methods with application to metal forming

In recent years, a new family of computational methods has emerged. The so-called meshless or mesh-free methods have been investigated and used by many researchers for treating a large variety of engineering problems, involving usually large displacements as encountered for example in forming process simulations. The main advantage of meshless methods is the fact that the interpolation accuracy is not significantly affected by the nodal distribution. Nevertheless, a troublesome task in these techniques is the imposition of essential boundary conditions, as in general the Kronecker delta property is not satisfied. Despite of several techniques have been proposed to overcome this problem, an appealing alternative technique which allows to circumvent this difficulty lies in the use of the natural neighbor interpolation (NEM). This paper focuses on the description and analysis of the natural element method, and its application for simulating some forming processes involving large displacements as well as fixed or moving discontinuities.