非线性连续统力学应变率和应力率的近期探讨

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Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics

摘要: 本文对连续统力学的两个基本概念——应变率和应力率——进行了若干考虑,并提出一些结果.首先对应变和应力概念作了一个扼要的系统回顾.第二节用绝对符号法给出一个至今尚属未知的右伸长张量时间变化率的显表达式.尔后,本工作提议区分定义客观性应力率的两种途径.按照第二种途径分析了若干特例之后,作者提出一个称为广义Jaumann导数的作为客观性应力率.它包含了大部分现有的应力率定义,以及Hill的结果.

Abstract: Presenting some recent considerations and results, the present paper deals with two basic concepts of the continuum mechanics, strain- and stress-rates. Upon a brief systematic survey of concepts of strain and stress, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation. This paper then suggests to distinguish two ways of defining objective stress-rates, Following the second procedure, after analyzing several particular cases, the author proposes a generalized daumann flux, which contains the majority of the existing definitions for stress-rate and the Hill's result as well.

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