On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity

Merodio J; Ogden RW

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On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity

机译：关于有限弹性的材料和空间设置中的强椭圆性的等价性

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摘要

It is known from Shield's theorem that the equilibrium equations for the inverse deformation in finite elasticity are equivalent to those for the primary deformation. We review this result for compressible elastic solids and then use it to provide a simple proof that strong ellipticity in the material setting is equivalent to that in the spatial setting. The result is then extended to incompressible materials.

机译：从希尔德定理可知，有限弹性反变形的平衡方程与一次变形的平衡方程等效。我们审查了可压缩弹性固体的结果，然后用它来提供简单的证明，即材料设置中的强椭圆率等于空间设置中的强椭圆率。然后将结果扩展到不可压缩的材料。

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《ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees》 |2006年第6期|共6页
作者
Merodio J; Ogden RW;
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正文语种 eng
中图分类应用数学;
关键词
nonlinear elasticity; finite elasticity; large deformations; strong ellipticity;

机译：非线性弹性;有限弹性;大变形;强椭圆率;

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1. On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity [J] . Merodio J, Ogden RW ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees . 2006,第6期

机译：关于有限弹性的材料和空间设置中的强椭圆性的等价性
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On the equivalence of strong ellipticity in the material and spatial settings of finite elasticity

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