AN INTEGRATION ALGORITHM FOR DRUCKER-PRAGER ELASTIC-PLASTIC MODEL WITH NON-ASSOCIATED FLOW RULE AND ISOTROPIC HARDENING

We present an analytical solution for the integration of Drucker-Prager (DP) elastic-plastic model considering non-associated flow rule and isotropic hardening using the Generalized Midpoint Method (GMM). GMM is an implicit algorithm with good accuracy and stability, of which the Closest Point Project Method (CPPM) is a special case with first-order accuracy and unconditional stability. This GMM solution is an explicit function of the initial stress state and the strain increment due to the special characteristic of DP plastic potential function. Without any iterative process, the computational efficiency is greatly promoted and the convergence problem is naturally avoided. Numerical examples show the advantage in accuracy of GMM (ξ=1/2) against CPPM when the deviation angle between the initial and incremental stress is large, but this advantage vanishes as the loading process approximates proportional. The theoretical solution of thick walled cylinder using DP yield criterion is derived to evaluate the accuracy of numerical solutions. The deformation localization effect of thick walled cylinder is simulated using DP model with non-associated flow rule and isotropic linear hardening.