Abstract

The paper presents an overview of the advances in recent years on the finite element method (FEM) and on particle-based methods for the simulation of industrial metal forming processes. More specifically, we present the evolution of the FEM in the field from the early plastic/viscoplastic flow approaches to the new stabilized FEM for analysis of multiphysics bulk forming processes. Also the paper describes the state of the art in the new rotation-free shell elements for simulation of sheet stamping processes. Finally, we present the so-called Particle Finite Element Method (PFEM), as a component of a family of new computational techniques integrating particle-based methods and mesh-based procedures. The PFEM is particularly suited for large deformation problems in solids and fluids involving nonlinear mechanical and geometrical effects, fluid-structure interactions and frictional contact situations. Applications of the FEM and the PFEM to several metal and material forming processes are presented.

Abstract

In this paper some results of a wide experimental program are presented and compared with some finite element solution of sheet metal forming problems using a viscous shell formulation.

Abstract

An important concern in sheet stamping is the risk of obtaining brittle final products that can be affected by fracture. Monte Carlo simulations presented herein show that this is governed by two main factors, namely static and dynamic friction coefficients. Whereas the latter correlates in a non-linear manner with minimum and maximum end thickness, the relationship of these design parameters to the former exhibits a bifurcation that is typical of highly non-linear phenomena, in which there is a sensitivity to small perturbations of the input values (chaos). In order to estimate the reliability of the process (i.e., the probability of obtaining brittle products due to low minimum and maximum thicknesses) with a reduced number of Monte Carlo runs, it is proposed to assimilate the problem to a pattern recognition task, due to the existence of two classes, namely robust and brittle. Among many pattern recognition algorithms that are useful to this end, use is made of support vector machines, as this incorporates the powerful tool of class margins that allow a drastic reduction of the number of simulations.

Abstract

The finite element method is the reference technique in the simulation of metal forming and provides excellent results with both Eulerian and Lagrangian implementations. The latter approach is more natural and direct but the large deformations involved in such processes require remeshing-rezoning algorithms that increase the computational times and reduce the quality of the results. Meshfree methods can better handle large deformations and have shown encouraging results. However, viscoplastic flows are nearly incompressible, which poses a challenge to meshfree methods. In this paper we propose a simple model of viscoplasticity, where both the pressure and velocity fields are discretized with maximum entropy approximants. The inf-sup condition is circumvented with a numerically consistent stabilized formulation that involves the gradient of the pressure. The performance of the method is studied in some benchmark problems including metal forming and orthogonal cutting.

Abstract