A formulation for finite element simulation of highly nonlinear problems including friction and contact with arbitrarily shaped rigid surfaces is proposed (CFS approach), prompted by difficulties in robust and accurate simulations of industrial forming processes. Nonlinearities are caused by large strains, plastic flow, and complex boundary conditions with frictional contact. In Part I the theoretical basis is described and the appropriate numerical algorithm is derived. The complete set of the governing relations, comprising equilibrium and interfacial equations, is appropriately linearized; resulting in a consistent tangent operator of the Newton-Raphson algorithm. In Part II, as a numerical verification, plane-strain sheet-forming processes are analyzed using a rigid-viscoplastic material model. Results are presented and discussed for test problems and for complex simulation of reverse drawing by concave tools.

A simple finite element approach to problems of dynamic structural instability under step loading is discussed. The method proposed is believed to yield important information about the structural behaviour in the non‐linear range. Incorporation of the method into existing finite element codes is straightforward.

Results of a comprehensive study on deep drawing are presented. The numerical results are based on finite element procedure developed for simulation of arbitrarily shaped, 3-D forming operations. The elastic-plastic material description with Hill’s anisotropic model is employed allowing for elastic effects, unloading, and multistage processes. By applying a proper computational model of large strain and large rotation plasticity, reliable results were obtained even using relatively simple material and friction laws. Predicted values of the press force, strain distributions, and flange reduction are compared with the corresponding results from axisymmetric deep draw experiments for a wide range of materials used in real forming applications including a deep drawing quality steel, brass, high strength steel, stainless steel, and aluminum. The parametric study shows the sensitivity of the solution on material parameter variations. Presented results can be considered as a set of benchmark problems.

Severe-plastic deformation processes are receiving increasing attention as methods to develop ultrafine-grain microstructures at the nanoscale. One such process, equal-channel angular extrusion (ECAE), offers the ability to manufacture bulk products from a wide range of metals and alloys. Despite the apparent simplicity of ECAE, however, metal fl ow and texture evolution are complex. The application of process, crystal-plasticity, and workability models to describe deformation and the evolution of microstructure, texture, and defects during ECAE is summarized in this article.

Using the method derived in Part I, plane-strain sheet-forming processes are analyzed and discussed. Stretch and deep draw forming by cylindrical and flat-bottom punches are presented and compared to closed-form solutions and existing numerical results. The performance of the new algorithm is successfully tested on a complex set of concave, irregular tools by simulating redrawing and reverse drawing with two-sided draw-in and various drawbead forces. The results demonstrate good robustness, accuracy, and efficiency even in the presence of large relative movements between contact surfaces. A quadratic rate of asymptotic convergence is documented for the consistent algorithm and comparison is made to the “linearized” theory which exhibits only linear rate of convergence and reduced numerical stability.