応用力学論文集
平面ひずみ圧縮を受ける乗算分解型超弾性-塑性材料の拡散型分岐条件に関する理論解法と数値解法との比較
佐藤 啓介山川 優樹堤 成一郎
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8 巻 (2005) p. 519-530

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This paper investigates bifurcation behavior of an elasto-plastic material under plane strain deformation. A simple and isotropic material in finite strains based on the multiplicative decomposition of the deformation gradient and Hencky's hyperelastic model is employed, and the expressions of instantaneous modulus of the material in rate form are explicitly derived. We present a theoretical approach for bifurcation analysis, and calculate bifurcation stresses of diffuse modes. The analysis reveals that elastic nonlinearity due to the hyperelastic constitutive model significantly changes general characteristics of the governing partial differential equation, and, moreover, this change influences occurrence of bifurcation. Finally, we conduct numerical bifurcation analysis based on FEM. Comparison between the theoretical and numerical results shows that the numerical approach provides good accuracy for estimate of the bifurcation stress.

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