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A field theory approach to stability of radial equilibria in nonlinear elasticity. (English) Zbl 0612.73013
The mechanical problem under consideration is an isotropic nonlinearly elastic sphere subject to a homogeneous surface traction. For small tractions the sphere is in a state of hydrostatic tension, and the displacement is proportional to the distance from the center of the sphere. If a critical surface forms at the center. The paper is devoted to the study of the stability and uniqueness of the deformation. It is based on the field theory of the calculus of variations. The results are interesting to mathematicians working in nonlinear elasticity.
Reviewer: U.Gamer

MSC:
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
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References:
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