Some estimates for the oscillation of the deformation gradient

Mošová, Vratislava. "Some estimates for the oscillation of the deformation gradient." Applications of Mathematics 45.6 (2000): 401-410. <http://eudml.org/doc/33068>.

@article{Mošová2000,
abstract = {As a measure of deformation we can take the difference $D\vec\{\phi \}-R$, where $D\vec\{\phi \}$ is the deformation gradient of the mapping $\vec\{\phi \}$ and $R$ is the deformation gradient of the mapping $\vec\{\gamma \}$, which represents some proper rigid motion. In this article, the norm $\Vert D\vec\{\phi \}-R\Vert _\{L^p(\Omega )\}$ is estimated by means of the scalar measure $e(\vec\{\phi \})$ of nonlinear strain. First, the estimates are given for a deformation $\vec\{\phi \}\in W^\{1,p\}(\Omega )$ satisfying the condition $\vec\{\phi \}\big |_\{\partial \Omega \} = \vec\{\hspace\{0.7pt\}\mathop \{\mathrm \{id\}\}\}$. Then we deduce the estimate in the case that $\vec\{\phi \}(x)$ is a bi-Lipschitzian deformation and $\vec\{\phi \}\big |_\{\partial \Omega \} \ne \vec\{\hspace\{0.7pt\}\mathop \{\mathrm \{id\}\}\}$.},
author = {Mošová, Vratislava},
journal = {Applications of Mathematics},
keywords = {hyperelastic material; deformation gradient; strain tensor; matrix and spectral norms; bi-Lipschitzian map; hyperelastic material; deformation gradient; strain tensor; scalar measure; nonlinear strain; bi-Lipschitzian mapping},
language = {eng},
number = {6},
pages = {401-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some estimates for the oscillation of the deformation gradient},
url = {http://eudml.org/doc/33068},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Mošová, Vratislava
TI - Some estimates for the oscillation of the deformation gradient
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 6
SP - 401
EP - 410
AB - As a measure of deformation we can take the difference $D\vec{\phi }-R$, where $D\vec{\phi }$ is the deformation gradient of the mapping $\vec{\phi }$ and $R$ is the deformation gradient of the mapping $\vec{\gamma }$, which represents some proper rigid motion. In this article, the norm $\Vert D\vec{\phi }-R\Vert _{L^p(\Omega )}$ is estimated by means of the scalar measure $e(\vec{\phi })$ of nonlinear strain. First, the estimates are given for a deformation $\vec{\phi }\in W^{1,p}(\Omega )$ satisfying the condition $\vec{\phi }\big |_{\partial \Omega } = \vec{\hspace{0.7pt}\mathop {\mathrm {id}}}$. Then we deduce the estimate in the case that $\vec{\phi }(x)$ is a bi-Lipschitzian deformation and $\vec{\phi }\big |_{\partial \Omega } \ne \vec{\hspace{0.7pt}\mathop {\mathrm {id}}}$.
LA - eng
KW - hyperelastic material; deformation gradient; strain tensor; matrix and spectral norms; bi-Lipschitzian map; hyperelastic material; deformation gradient; strain tensor; scalar measure; nonlinear strain; bi-Lipschitzian mapping
UR - http://eudml.org/doc/33068
ER -