A finite element procedure for plane strain metal flow within specified plastic boundaries (Q1085669)

A new set of two governing equations are developed for analyzing two- dimensional plane strain plasticity problems. Two sets of stress components are introduced - one set satisfying the equilibrium equations and the second ensuring that the yield criterion is satisfied. The differences between these two sets of stress components constitute the approximation errors. Using the method of least squares a simple triangular finite element method is developed by means of which the differences between the two sets of stress components are minimized. The formulation and the element developed are verified by analyzing three metal forming examples. Results computed with the proposed method correlate well with the exact solution of one example, and with the classical slip-line fields solutions of the other two examples.