A Direct Approach to the Polar Representation of Plane Tensors

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2024-08-30 DOI:10.1007/s10659-024-10085-6

Marco Picchi Scardaoni

引用次数: 0

Abstract

We show we can derive the so called polar representation of 2D symmetric second and fourth order real tensors essentially just relying on the spectral theorem for unitary tensors in the complex field. The use of a coordinate-free approach allows us to clearly and methodically detect rotation-invariant quantities and to readily (and directly) deduce the representation theorems.

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平面张量极性表示的直接方法

我们的研究表明，只需依靠复数场中单元张量的谱定理，我们就能推导出二维对称二阶和四阶实张量的所谓极性表示。通过使用无坐标方法，我们可以清晰、有条不紊地检测旋转不变量，并轻松（直接）推导出表示定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.

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