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Symmetry and bifurcation in three-dimensional elasticity. II. (English) Zbl 0536.73010

[For part I see ibid. 80, 295-331 (1982; Zbl 0509.73018).]
Under the physical assumptions that the undeformed state of a body is stress free (i.e., the manifold has an embedding in \({\mathbb{R}}^ 3\) on which the stress function is zero), and that a certain condition is imposed on the energy (the system is strongly elliptic and its linearized theory satisfies the stability condition), the authors continue their investigation on the number of solutions to the partial differential equations of elastostatics and the stability of such solutions, along with their bifurcation diagrams. The treatment is heavily mathematical, but a few examples are given; it is a pity that so few attempts have been made to state or, more dangerously, to paraphrase the mathematical results in the language of engineering. Once again the authors have given a tour de force in their application of mathematics to continuum mechanics.
Reviewer: J.J.Cross

MSC:

74B20 Nonlinear elasticity
74G60 Bifurcation and buckling
35B32 Bifurcations in context of PDEs
74G99 Equilibrium (steady-state) problems in solid mechanics
74H99 Dynamical problems in solid mechanics
35B35 Stability in context of PDEs
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