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The elastica and the problem of the pure bending for a non-convex stored energy function. (English) Zbl 0481.73018


MSC:

74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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[1] Euler, Leonhard, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, additamentum I de curvis elastics. Lausanne and Geneve. Opera Omnia I 24 (1744) 231–297.
[2] Crandall, Stephen H., Norman C. Dahl and Thomas J. Lardner, An Introduction to the Mechanics of Solids, second ed. with SI units. McGraw-Hill 1978. · Zbl 0433.73001
[3] Ericksen, J. L., Equilibrium of bars. Journal of Elasticity 5 (1975) 191–201. · Zbl 0324.73067
[4] James, Richard D., Co-existent phases in the one dimensional static theory of elastic bars. Arch. Rational Mech. Anal. 72 (1979) 99–140. · Zbl 0429.73001
[5] Dunn, J. E., R. L. Fosdick and R. Stone, On minimizing states and their stability in elastic bars. In preparation.
[6] Dunn, J. Ernest, and Roger L., Fosdick, The morphology and stability of material phases. Arch. Rational Mech. Anal. 74 (1980) 1–99. · Zbl 0434.73120
[7] Knowles, James K., On the dissipation associated with equilibrium shocks in finite elasticity. Journal of Elasticity 9 (1979) 131–158. · Zbl 0407.73037
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