Damage models based on representation of the non-local residual

A representation of the non-local residual is issued in the form of theorem. This representation makes the non-local residual satisfy the zero mean condition automatically. On the basis of this representation, a new theoretical framework and method to establish the non-local damage model are put forth. In this framework, the non-locality of damage and inelastic deformation is characterized by the non-local residual, and it need not introduce the non-local constitutive variables in the Helmholtz free energy and the dissipation potential. According to the new method, non-local quasi-brittle damage model and non-local viscoplastic damage model are established. The constitutive equations and evolution equations of damage are consistently derived from the thermodynamics principles.