On finding equilibria for isotropic hyperelastic materials.

*(English)*Zbl 0721.73003In 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.

This work is interesting and may find some application in the approximate solution of hyperelastic, isotropic elastic bodies.

Reviewer: H.Demiray (İstanbul)

##### 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 |

##### Keywords:

potential energy function; minimizing solutions; equilibrium solutions; quasiconvexity; growth conditions; sequentially weak lower semicontinuous; Euler equation; iterative scheme##### Software:

LINPACK
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\textit{J. G. Dix} and \textit{T. W. McCabe}, Nonlinear Anal., Theory Methods Appl. 15, No. 5, 437--444 (1990; Zbl 0721.73003)

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##### References:

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