Stroh formalism for various types of materials and deformations

IF 1.5 4区 工程技术 Q3 MECHANICS Journal of Mechanics Pub Date : 2022-01-01 DOI:10.1093/jom/ufac031
C. Hwu, W. Becker
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引用次数: 1

Abstract

The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.
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强大的形式主义,各种类型的材料和变形
Stroh形式是一种复杂的变量公式,最初是为了解决二维线性各向异性弹性问题而发展起来的。通过分离位移沿厚度方向线性变化的第三变量,证明了该方法适用于拉伸-弯曲耦合变形问题。Radon变换将三维实体映射到二维平面,可以应用于三维变形。根据弹粘弹性对应原理,在拉普拉斯域中对粘弹性材料也是有效的。通过扩展矩阵维数,可以推广到压电、压磁、磁电弹性等耦合场材料。通过在材料常数上引入一个小的扰动,它也可以应用于各向同性材料等简并材料。因此,本文将几种不同类型的材料(各向异性弹性、压电、压磁、磁-电弹性、粘弹性)和变形(二维、耦合拉伸-弯曲、三维)的Stroh形式组织在一起,并以相同的数学形式表示。
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 Mechanics
Journal of Mechanics 物理-力学
CiteScore
3.20
自引率
11.80%
发文量
20
审稿时长
6 months
期刊介绍: The objective of the Journal of Mechanics is to provide an international forum to foster exchange of ideas among mechanics communities in different parts of world. The Journal of Mechanics publishes original research in all fields of theoretical and applied mechanics. The Journal especially welcomes papers that are related to recent technological advances. The contributions, which may be analytical, experimental or numerical, should be of significance to the progress of mechanics. Papers which are merely illustrations of established principles and procedures will generally not be accepted. Reports that are of technical interest are published as short articles. Review articles are published only by invitation.
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