13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- energy F, and specific entropy . The energy balance and the entropy can be written as r q : 1 e F T T ik ik , (4) r 0 T q , where 1 2 3x , x , x , the superposed dot stands for the material time derivative. We assume the following kinematical relationship for the material under study T T ~ ~ ~ ~ ~p p e , (5) where e ik is the elastic strain tensor, p ~ is the plastic strain tensor (related to the defect motion), ~ is the thermal expansion coefficient tensor, and T is the reference temperature. To introduce the list of independent variables for the free energy F ~ ,T, ~p e the equations (4) give ~ : ~ ~p 0 1 F : ~p T T q p ~p , (6) p e cT q r Q Q , (7) where e T eQ TF : ~ e - heat production due to thermoelastic effect; ~ F : ~p ~ 1 ~ : 1 Q TF : ~p p p Tp p - represents the inelastic part to the heat production; TT c TF - the specific heat capacity. To assume the linear links between thermodynamic forces and the thermodynamics fluxes, we obtain the constitutive equations ~p p ~ ~ p l F F ~ l F e p e p , (8) e p e p ~ ~p p ~ ~p l F F l F , (9) where the function pF follows from the presentation of free energy given by the statistical model of solid with mesodefects.
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