Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics

Abstract Unified descriptions of the constitutive and evolution equations of elastic-brittle damage materials are developed on the basis of irreversible thermodynamic theory for constitutive equations. The Helmholtz free energy is assumed to be a function of elastic strain tensor and second rank symmetric damage tensor. In order to take account of the effects of unilateral condition of damage due to the opening and closure of microcracks, modified elastic strain tensor is introduced into the Helmholtz free energy. A damage dissipation potential related to the entropy production rate is expressed in terms of damage conjugate force. The constitutive and the damage evolution equations derived by these potentials were applied to an elastic-brittle damage material. The anisotropic elastic-brittle damage behavior of high-strength concrete under uniaxial, proportional and nonproportional combined loading was analysed to elucidate the utility and the limitations of the present theory. Finally, the initial damage surfaces in the axial-shear and biaxial stress spaces are calculated.

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