On the hyperbolicity of the governing equations for the linearization of a class of implicit constitutive relations

IF 1.9 4区工程技术 Q3 MECHANICS

Mechanics Research Communications Pub Date : 2024-05-01 DOI:10.1016/j.mechrescom.2024.104291

D. Sfyris , R. Bustamante , K.R. Rajagopal

引用次数: 0

Abstract

For a relatively new class of linearization of implicit constitutive relations, wherein the linearized strain tensor is assumed to be a function of the Cauchy stress tensor, we write the balance of linear momentum and the time differentiated constitutive relation as a first order system, and we examine conditions for the hyperbolicity of such a system; this procedure is carried out for one and three dimensions. For the one dimensional case we use the characteristic polynomial and find conditions so that our system is hyperbolic. For three dimensions we find conditions so that our system can be put in a symmetric hyperbolic form.

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论一类隐式构成关系线性化控制方程的双曲性

对于一类相对较新的线性化隐式构成关系（其中线性化应变张量被假定为柯西应力张量的函数），我们将线性动量平衡和时间微分构成关系写成一阶系统，并研究了这种系统的双曲性条件；这一过程适用于一维和三维情况。在一维情况下，我们使用特征多项式，找到系统双曲的条件。对于三维空间，我们要找到使我们的系统能够以对称双曲形式存在的条件。

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

Mechanics Research Communications 物理-力学

CiteScore

4.10

自引率

4.20%

发文量

114

审稿时长

9 months

期刊介绍： Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.