主催: 日本学術会議 メカニクス・構造研究連絡委員会
共催: 応用物理学会, 化学工学会, 土木学会, 日本風工学会, 日本機械学会, 日本気象学会, 日本計算工学会, 日本建築学会, 日本原子力学会, 日本航空宇宙学会, 日本地震工学会, 日本数学会, 日本数値流体力学会, 日本造船学会, 日本物理学会, 日本流体力学会, 日本レオロジー学会, 農業土木学会, 無機マテリアル学会
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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.