Abstract
The quadratic variants of the generalized midpoint rule and return map algorithm for the J2 von Mises metal plasticity model are examined for the accuracy of deviatoric stress integration of the constitutive equation. The accuracy of stress integration using a strain rate vector for arbitrary direction is presented in terms of an iso-error map for comparison with the exact solution. Accuracy and stability issues of the quadratic integration method are discussed using a two-dimensional metal panel problem with a single slit-like defect in the center. The scale factor and shape factor were introduced to a quadratic integration rule for assuming a returning directional tensor from a trial stress onto the final yield surface. Luckily enough, the perfectly plastic model is the only case where the analytical solution is possible. Thus, solution accuracies were compared with those of the exact solutions. Since the standard scale factor ranges from 0 to 1, which is similar to the linear α -method, the penalty scale factors that are greater than 1 were mainly explored to examine the solution accuracies and computational efficiency. A higher value of scale factor above five shows a better computational efficiency but a decreased solution accuracy, especially in the higher plastification zone. A well-balanced scale factor for both computational efficiency and solution accuracy was found to be between one and five. The trade-off scale factor was proposed to be five. The proper shape factor was also proposed to be {1,1,4}/6 among the different combinations of weight distribution over a time interval. This proposed scale factor and shape factor is also valid for relatively long time periods.
Highlights
Calculation of crack extension and the behavior of the fracture process zone ahead of the current real void in ductile materials strongly depends on the computational method used for stress analysis
Krieg et al [2] explored the accuracies of several solution methods, including the tangent stiffness, secant stiffness, and radial return method compared to the exact solutions obtained from the elastic perfectly plastic model
Mises metal plasticity model are examined for the accuracy of deviatoric stress integration of the constitutive equation
Summary
Calculation of crack extension and the behavior of the fracture process zone ahead of the current real void (or crack) in ductile materials (such as metals) strongly depends on the computational method used for stress analysis. Krieg et al [2] explored the accuracies of several solution methods, including the tangent stiffness, secant stiffness, and radial return method compared to the exact solutions obtained from the elastic perfectly plastic model. The first two schemes used a generalized midpoint integration rule with return mapping procedure enforced by yield conditions The latter two schemes were two-stage algorithms developed by dividing each time step into two subintervals, in which equations were solved in turn. These approaches essentially rely on sub-steps in a time interval They develop an extensive comparison based on pointwise mixed stress-strain loading histories, iso-error maps and initial boundary value problem. They investigated the existence of solution, accuracy, stability and the algorithm behavior for long time steps. It is instructional to examine the solution using the perfectly plastic model, which only has the analytical solution available
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
