一般化CSDAを用いた大変形弾塑性モデルの実装

抄録

A method is proposed to easily and accurately calculate incremental variational formulations (IVFs) that describe the behavior of inelastic materials. The IVF requires first- and second-order numerical differentiation to obtain the internal variables by the Newton-Raphson method. In addition, first- and second-order numerical differentiation is also required to obtain stresses and consistent tangent modulai. Therefore, in this paper, we investigate the implementation of generalized CSDA (Complex-Step Derivative Approximation), which is highly accurate and easy to implement, for these differential operations. To confirm the validity of the proposed method, we applied it to an analytical example of a large elasto-plastic model. As a result, the proposed method was able to capture the behavior of the elasto-plastic model with high accuracy, and the accuracy was equivalent to that of the Hyper Dual Number (HDN) reference solution. Furthermore, the convergence of the nodal force residuals was also good, indicating that the analysis was performed with high accuracy.