An analysis of metal forming processes using large deformation elastic-plastic formulations

A concise survey of the literature related to the large deformation elasto-plasticity problems including unilateral contact and friction is presented together with an extension of the friction law for large deformation analysis. Starting from the principle of virtual work, the so-called total Lagrangian and updated Lagrangian formulations are derived based on some fundamental assumptions in linearizing the nonlinear equations. By introducing the Zaremba-Jaumann (co-rotational) increment to the Cauchy stress tensor, the classical Prandtl-Reuss equations are generalized for describing the elastic-plastic material behavior. To allow a proper consideration of the contact conditions in the incremental analysis, a general friction law with an associated isotropic Coulomb sliding rule is obtained by the similarity between dry friction and plasticity. Finite element discretizations and approximations are applied to the resulting formulation of the updated Lagrangian approach. Four example problems are solved to test the formulations developed in this paper. The emphasis is made toward the numerical accuracy of the finite element solutions.

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