Normality Structures With Homogeneous Kinetic Rate Laws

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.