A constitutive framework of plastically deformed damaged continuum and a formulation using theendochronic concept

The concepts of continuum damage mechanics "CDM# are discussed and a constitutive framework of CDM is proposed for in_nitesimal deformation based on the internal variables approach[ The framework involves transforming the actual damaged continuum into an equivalent _ctitious undamaged continuum[ A distinction is made between the state of damage and the damage measure[ The development makes use of the concept of {damage force|[ The negative of the damage force is related to the energy required to restore the _ctitious undamaged continuum to its undamaged state after each step of deformation and damage[ A set of equation and constraint governs the deformation of the _ctitious continuum\ while another set of equation and constraint governs the damage behavior[ The coupling between the deformation and damage processes is provided for by the damage restoring force concept[ Within the proposed constitutive framework\ the endochronic concept has been used to derive explicit constitutive equations[ The proposed model has been shown to describe the three!dimensional state of deformation of a cylindrical concrete specimen subjected to uniaxial compression