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The generalised Hamilton-Jacobi inequality and the stability of equilibria in nonlinear elasticity. (English) Zbl 0709.73014
The author presents general techniques for demonstrating the stability of solutions of the equilibrium equations of nonlinear elasticity under the constitutive assumption of polyconvexity. This approach extends and unifies ideas from the classical field theory of the calculus of variations and shows that a sufficient condition for stability is that there exists a solution to a certain generalized Hamilton-Jacobi differential inequality. Application to a large class of polyconvex stored energy functions is also shown in this paper.
Reviewer: S.Zheng

MSC:
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
49J40 Variational inequalities
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