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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >THE APPLICATION OF TENSOR ALGEBRA ON MANIFOLDS TO NONLINEAR CONTINUUM MECHANICS - INVITED SURVEY ARTICLE
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THE APPLICATION OF TENSOR ALGEBRA ON MANIFOLDS TO NONLINEAR CONTINUUM MECHANICS - INVITED SURVEY ARTICLE

机译：流形上的张量代数在非线性连续力学的检验文章中的应用。

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Some properties of the tensor algebra on manifolds are discussed with respect to the classical tensor algebra of continuum um mechanics, Basic definitions and relations of linear maps are briefly recalled and applied to tensor spaces, where special attention is focused to the definition of dual and transposed maps. As application to nonlinear continuum mechanics, algebraic pull-back and push-forward maps, and Lie-like time derivatives associated with linear maps are defined and used to build up commutative schemes for deformation measures. objective deformation rates, stresses, and frame-invariant forms of the stress power. The transition to the classical formulation of tensor algebra by identifying vector spaces and their duals is examined. It is shown how this concept enables a straightforward derivation of the Doyle-Ericksen formula and its possible variants. [References: 62]
机译：讨论了流形上张量代数的一些性质，涉及连续力学的经典张量代数。简要回顾了线性映射的基本定义和关系，并将其应用于张量空间，其中特别注意对偶和转置的定义。地图。作为非线性连续体力学的应用，定义了代数后推和前推映射以及与线性映射相关的类李时间导数，并将其用于建立变形测度的交换方案。客观变形率，应力和应力强度的框架不变形式。通过识别向量空间及其对偶来检查张量代数到经典形式的过渡。说明了此概念如何直接推导Doyle-Ericksen公式及其可能的变体。 [参考：62]

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