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# Normality Structures With Homogeneous Kinetic Rate Laws

[+] Author and Article Information
Q. Yang1

Department of Hydraulic Engineering,  Tsinghua University, Beijing 100084, P. R. China. yangq@tsinghua.edu.cn

L. G. Tham

Rick Engineering Research Center,  The University of Hong Kong, Hong Kong, China

G. Swoboda

Faculty of Civil Engineering and Architecture,  The University of Innsbruck, Innsbruck, Austria

In this paper, Einstein’s summation convention is adopted for repeated indexes. However, if an index range is listed like $α$ in Eq. 9, the index is considered as a free index without the summation convention.

1

Author to whom correspondence should be addressed. Telephone: 8610-62794874; Fax: 8610-62782159.

J. Appl. Mech 72(3), 322-329 (Jul 21, 2004) (8 pages) doi:10.1115/1.1867991 History: Received August 13, 2002; Revised July 21, 2004

## Abstract

In this paper, a homogeneous type of kinetic rate laws of local internal variables and its corresponding macroscopic behaviors, are explored within the framework of “normality structures” by Rice. Rice’s kinetic rate laws of local internal variables, with each rate being stress dependent only via its conjugate thermodynamic force, are corner stones of the normality structure. It is revealed in this paper that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally if each rate is a homogeneous function of degree $q$ in its conjugate force. Furthermore, the nonlinear phenomenological coefficient matrix is identical to the Hessian matrix of the flow potential function in conjugate forces only scaled by $q$. It is further shown that the refined version of Griffith criterion proposed by Rice, $(G−2γ)ȧ⩾0$, can be derived from the normality structure with the homogeneous rate laws. Finally, some issues related to damage evolution laws have been discussed based on the remarkable properties.

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