Fourth-order tensors - tensor differentiation with applications to continuum mechanics. Part II: Tensor analysis on manifolds

Kintzel O

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Fourth-order tensors - tensor differentiation with applications to continuum mechanics. Part II: Tensor analysis on manifolds

机译：四阶张量-张量微分及其在连续力学中的应用。第二部分：流形上的张量分析

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In Part H of this contribution the theory of fourth-order tensors and tensor differentiation introduced in Part I will be applied to finite deformation problems using a mathematical framework which is mainly borrowed from tensor analysis on manifolds. The main aspects are the explicit consideration of component variance, the introduction of different configurations and its associated metric tensors. Some relevant problems of continuum mechanics like the construction of tangent operators are discussed. Special attention is given to the conjugated formulation of the corresponding tangent operator in terms of the left CAUCHY-GREEN-tensor. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.

机译：在本部分的H部分中，第一部分中介绍的四阶张量和张量微分理论将使用主要从流形上的张量分析中借鉴的数学框架应用于有限变形问题。主要方面是组件差异的明确考虑，不同配置的引入及其相关的度量张量。讨论了诸如切线算子的构造等连续力学的一些相关问题。根据左CAUCHY-GREEN张量，特别注意相应切线算符的共轭公式。（c）2006 WILEY-VCH Verlag GmbH＆Co. KGaA。温海姆。

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2006年第4期|共23页
作者
Kintzel O;
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正文语种 eng
中图分类应用数学;
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fourth-order tensors; tensor differentiation; tangent operators; anisotropic hyperelasticity; NONLINEAR SOLID MECHANICS; DOYLE-ERICKSEN FORMULA; MATHEMATICAL ASPECTS; DUAL VARIABLES; FINITE; IMPLEMENTATION; ELASTICITY; ALGEBRA;

机译：四阶张量;张量微分;切线算子;各向异性超弹性;非线性固体力学;道尔-艾里克森公式;数学方面;对偶变量;有限;实现;弹性;代数;

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Fourth-order tensors - tensor differentiation with applications to continuum mechanics. Part II: Tensor analysis on manifolds

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