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Zbl 1002.74011
Mošová, Vratislava
Some estimates for the oscillation of the deformation gradient. (English)
[J] Appl. Math., Praha 45, No.6, 401-410 (2000). ISSN 0862-7940; ISSN 1572-9109/e

The author generalizes the estimate of deformation gradient $D \vec \phi $ due to {\it R. V. Kohn} [Arch. Ration. Mech. Anal. 78, 131-172 (1982; Zbl 0491.73023)] to the case when $p \neq 2$. The norm $\parallel D \vec \phi - R \parallel _{L^p(\Omega)}$ is estimated by means of scalar measure $e(\vec \phi)$ of nonlinear strain (here $R$ is the gradient of a mapping $\vec \gamma $ corresponding to some rigid motion, $\vec \phi : \Omega \to\bbfR^n$ is the deformation.) First, the estimate is given for a deformation $\vec \phi \in W^{1,p}(\Omega)$ satisfying the condition $\vec \phi |_{\partial \Omega } = id$. After this, the estimate is derived for general bi-Lipschitzian mapping $\vec \phi $.
[Oldřich John (Praha)]

MSC 2000:: *74B20 Nonlinear elasticity
35Q72 Other PDE from mechanics

Keywords: hyperelastic material; deformation gradient; strain tensor; scalar measure; nonlinear strain; bi-Lipschitzian mapping

Citations: Zbl 0491.73023

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