異方性地盤材料の構成モデルの陰解法有限要素解析への適用

Implicit numerical algorithm using return-mapping method has been proven to provide an excellent performance when integrating a nonlinear isotropic elastoplasticity; i.e., a pressure-dependent model, in particular, where only a few scalar equations are required to formulate whole governing equations (Aravas, 1987). The simplicity lies in the fact that return directions to yield surface are coaxial with updated stresses in principle stress space. Accordingly, an explicit form of a consistent tangent operator in regard to a modified Cam-clay was derived by Borja et al. (1990), giving by-passed steps needed for evaluating a costly inversion of material stiffness tensor. However, the similar procedure is not conveniently applicable to an anisotropic model mainly because return directions to anisotropic yield surface are not coaxial with updated state of stresses. Luccioni et al. (2000) employed a return-mapping technique to an anisotropic Bear-Clay model and concluded that the formulation of governing equations under a return-mapping scheme is complicated and relatively cumbersome due to the complexity of anisotropy; therefore, the method loses a performance and appears impractical to initial boundary value problems. In this study, a return-mapping regularization applicable to anisotropic models was developed following a typical procedure but a newly-developed process corresponding to invariant-based tensor basis was applied to solve a concerned limitation. An implementation of implicit finite element method and numerical illustration were presented to demonstrate a computational performance under the proposed procedure. The performance of the proposed procedure is evaluated through numerical simulations of compression test under plane strain conditions. The resulting solutions can reach a convergence with considerably accuracy even by a relatively large strain.