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A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

This paper focuses on the design of a superconducting quadrupole prototype. This structure includes many frictional contact zones, and the loading conditions are complex (mechanical, thermal and magnetic). A dedicated computational strategy, based on both a decomposition of the structure and an iterative resolution scheme, has been applied to solve this problem. A simplified approach is used to take complex loading conditions into account. The initial set of results, which are presented herein, demonstrates the interest of this approach with respect to classical finite element methods. This study was conducted within the framework of a joint research contract between the CEA (DSM/DPANIA/STCM) and LMT‐Cachan.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.