Study on Accuracy of Finite-Element Solutions in Elastoplastic Large Deformation : Effects of Shape Function and Numerical Integration, and Application of Mixed Method

We discuss the accuracy of finite-element solutions for metals possessing dominant plasticity, resulting in an incompressible response in a large deformation field. It is known that poor numerical solutions are obtained for the constrained problem due to incompressibility of deformed metals, but they can be improved by selecting an appropriate shape function and numerical integration technique, as well as by applying the mixed method derived from Lagrangian multipliers. Many studies have been made for rigid-plastic finite-element solutions so far, but large-deformation elastoplastic structural analysis is rarely discussed in the literature. In this work, we discuss the advantages of such techniques in large-deformation analysis using the Jaumann stress rate and isotropic hardening hypoelasticity model.