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On finding equilibria for isotropic hyperelastic materials. (English) Zbl 0721.73003
In this work the authors studied the equilibrium solutions for isotroic hyperelastic materials. For this, they first obtained a potential energy function and showed that the minimizing solutions of this potential are also the equilibrium solutions. They also showed that under the assumptions of quasiconvexity and certain growth conditions, the potential function is sequentially weak lower semicontinuous and thus, it has minimizers. They proved that the Euler equation of the potential energy function has a unique solution. An iterative scheme is also suggested in the paper.
This work is interesting and may find some application in the approximate solution of hyperelastic, isotropic elastic bodies.

MSC:
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
Software:
LINPACK
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References:
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