Numerical methods in metalforming

At the very heart of metal forming analysis is the theory of plasticity. A brief description of this theory is given. The infinitesimal theory of plasticity, simplified by discarding the elastic part of deformation (also known as the flow theory) has produced several approximate methods of analysis that have proved very useful in metal forming. The basic assumptions are presented that lead to the uniform deformation method, the slab method, the upper-bound method and the slip-line field method. The availability of computers with relatively inexpensive, large amounts of number-crunching capabilities fostered the development of the finite element method. Originally used in structural analysis, it rapidly expanded into other fields, and has been applied to metal forming analysis since the early seventies. This is the area in which most of the recent work in this field has been done. The first one is based on the rigid plastic approach (the flow theory) for which the infinitesimal theory of plasticity has been sufficient. It leads to relatively simple formulations which have allowed its users to attack the difficult problems specific to metal forming applications. The second one is based on the more complete elasto-plastic approach which almost always requires a large deformation theory of plasticity. The formulations are more complicated and have followed, if not actually led to, development in the theory itself. This reports ends with an introduction to the fundamental concepts of the finite element method.