Accurate stress updating algorithm based on constant strain rate assumption
The calculation of the stresses for path-dependent materials possesses a delicate problem. Here the constitutive equations are reformulated using the assumption of constant strain rate within an increment. This assumption allows the constitutive laws to be rewritten as ordinary differential equations and thus a large set of tools is available to solve the constitutive equations. Within this concept, the possibility to form an algorithmic stiffness tensor is investigated and it turns out that the `true' tensor is expensive to calculate, but it is of interest that an inexpensive well behaving approximative algorithmic stiffness tensor can be formulated. To investigate the properties of the solution method, both with respect to stress calculation and convergence properties in a NewtonRaphson method, an elasto-plastic damage model based on von Mises plasticity is considered. An interesting observation is that, for the usual closest-point projection method, the damage evolution is very sensitive to the size of load step.
plasticity nonlinear mechanics numerical solution procedures