A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part I: Theory

► A systematic thermodynamic framework for rate- and time-dependent materials. ► Coupled viscoelasticity, viscoplasticity, viscodamage, and micro-damage healing. ► A micro-force balance is derived for each nonlinear behavior is formulated. ► Only two functions are needed; the free energy and rate of dissipation functions. ► Non-associative plasticity is obtained from the principle of virtual power. A general thermodynamic-based framework for deriving coupled temperature-dependent viscoelasticity, viscoplasticity, viscodamage, and micro-damage healing constitutive models for constitutive modeling of time- and rate-dependent materials is presented. Principle of virtual power, Clausius–Duhem inequality, and the principle of maximum rate of dissipation are used to construct this general thermodynamic framework. A micro-damage healing natural configuration is introduced to enhance the continuum damage mechanics theories in modeling the healing phenomenon. This healing configuration can be considered as the extension of the well-known Kachanov’s effective (undamaged) configuration (Kachanov, 1958). The viscoplasticity loading condition is defined from the microforce balance derived directly from the principle of virtual power. Moreover, for the first time, viscoelasticity, viscodamage, and micro-damage healing microforce balances are derived directly from the principle of virtual power. It is also shown that the generalized non-associative plasticity/viscoplasticity theories can be a direct consequence of postulating the principle of virtual power. The emphasis in this paper is placed on the decomposition of thermodynamic conjugate forces into energetic and dissipative components. It is shown that this decomposition is necessary for accurate estimation of the rate of energy dissipation. The energetic components are related to the Helmholtz free energy, whereas the dissipative components are related to the rate of energy dissipation. This thermodynamic framework is used for deriving more comprehensive viscoelastic, viscoplastic, and viscodamage, and micro-damage healing constitutive models.