Correction of hydrostatic pressure obtained by the finite element flow formulation using moving least squares method

In the analyses of metal forming processes by the flow formulation, deviatoric components of stress are calculated. However the total components of stress must also be known. Hence it is necessary to evaluate the hydrostatic stress, as well. One of the major drawbacks of the flow formulation is that in this method the hydrostatic pressure cannot be accurately evaluated. In this paper, hydrostatic stress is obtained by satisfying the equilibrium equations for the current distribution of deviatoric stresses. The divergence of the deviatoric stresses are approximated by the moving least squares method. In the present work for the first time, the equilibrium equation is approximated in a least square sense, by its minimisation with respect to hydrostatic pressure. Determination of the approximated pressure field is achieved, using the conventional finite element approach. This approach is first satisfactorily verified, using a cantilever beam with known analytical stress field. Finally this method is applied to a typical 2D axisymmetric bulk metal forming process. Approximated pressure field has been compared with available solutions. The results of the present approach are very encouraging.