On Microscopic Thermodynamic Mechanisms of Damage Evolution Laws

Abstract

Most existing phenomenological damage evolution laws can be covered by phenomenological equations or linear irreversible thermodynamics. In this paper, general microscopic thermodynamic mechanisms leading to nonlinear phenomenological equations are explored within the framework of ‘normality structures’ by Rice (Rice, J.R. (1971). Inelastic Constitutive Relations for Solids: An Internal Variable Theory and its Application to Metal Plasticity, Journal of the Mechanics and Physics of Solids, 19: 433-455, Rice, J.R. (1975). Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms, In: Argon, A.S. (ed.), Constitutive Equations in Plasticity, MIT Press, Cambridge, MA, pp. 23-79.) at the level of microstructural rearrangements. Rice’s kinetic rate laws of local internal variables, with each rate being stress dependent only via its conjugate thermodynamic force, are cornerstones of the normality structure. It is revealed in this paper that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally from the normality structures 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 scaled by q. Finally, as an application and demonstration, some fundamental issues on damage evolution laws for microcracked solids have been addressed based on the revealed remarkable properties. It is shown that the deduced flow potential functions of microcracked solids can be expressed in the forms of well-established Hill (Hill, R. (1950). The Mathematical Theory of Plasticity, Clarendon Press, Oxford.) anisotropic yield function and Karafillis and Boyce (Karafillis, A.P. and Boyce, D.B. (1993). A General Anisotropic Yield Criterion Using Bounds and a Transformation Weighting Tensor, Journal of the Mechanics and Physics of Solids, 46: 85-113.) isotropic yield surface.