有限変形における非圧縮性材料と残差仕事の変分原理

抄録

The present paper proposes variational principles in finite deformation for a metal alloy showing predominant plastic flow or nearly incompressible material in elastic range, in order to improve the accuracy of numerical analysis. The variational theorems are presented in total Lagrangian formulation in terms of second Piola-Kirchhoff symmetric stress tensor, which can be easily reduced in an updated Lagrangian one. Attention is also focused on the unified derivation of mixed variational principles for residual work related to unbalanced forces which have not been studied previously.