Some remarks on implicit integration of modified cam-clay model

The application of MCC material model in computational procedures requires the integration of stresses in Gauss points of integration based on known size of deformation increments in these points. This problem is known from the application of other elasto-plastic models and often is considered as crucial in solution of system of non-linear equations. Inappropriate integration of stress field may bad to very awkward situations, where drift of stress-field from the yield condition with false unbalanced forces is the one with far reaching consequences. Implicit integration of stress field from the known size of deformation increment is a concept that heavily relies on Euler's method of differential equations' integration. Its application increases not only the robustness of the numerical scheme, but also its accuracy. In this article it is shown that the implicit integration of stress field in MCC material can be reduced to evaluation of a single governing parameter, current preconsolidation pressure. This parameter is found as a solution of a single non-linear equation. This equation follows from the fulfilment of the yield condition at the end of iteration in increment, and the size of plastic deformations. The solution of non-linear equation with a single unknown, current preconsolidation pressure, can be found using standard, web known numerical procedures such as: bisection method, method of successive iterations, Newton method, etc. Upon completion of this procedure, update of stress field in increment's iteration is a straightforward, routine procedure.