A thermodynamically consistent tensorial framework for elastoplastic damage mechanics via direct construction of damaged stiffness tensor

This study presents a general thermodynamically consistentcontinuum elastoplastic damage mechanics theory within a unified tensorial framework. Classical hypotheses in damage mechanics, including the strain equivalence hypothesis and the energy equivalence hypothesis, are critically re-examined. It is demonstrated that the strain equivalence hypothesis provides a more physically consistent foundation when the bulk strain energy, rather than the strain energy density, is appropriately interpreted with explicit consideration of the constituent volume fractions. In contrast to conventional formulations that introduce damage effects through predefined effective stress measures, the proposed framework first constructs the damaged stiffness tensor directly through a symmetric fourth-order stiffness loss tensor , from which the corresponding effective stress is subsequently derived in a mathematically consistent manner. This construction guarantees preservation of both major and minor symmetries of the damaged stiffness tensor in anisotropic damage, while providing a constrained and physically interpretable definition of the effective stress . Furthermore, the stiffness loss tensor is shown to possess a rigorous micromechanical interpretation through the crack-induced compliance tensor, thereby establishing a direct connection between microstructural damage mechanisms and macroscopic constitutive behavior. A general Helmholtz free energy potential, together with coupled damage and plasticity evolution laws, is employed to develop a fully thermodynamically admissible constitutive framework. The proposed formulation establishes a mathematically rigorous and physically interpretable constitutive foundation for anisotropic elastoplastic damage mechanics and provides a general theoretical framework for the future development of material-specific constitutive models, computational implementations, and engineering applications involving coupled damage–plasticity behavior.