Issue 53

Z. Li et alii, Frattura ed Integrità Strutturale, 53 (2020) 446-456; DOI: 10.3221/IGF-ESIS.53.35 448 G ENERAL IDEA FOR THE COUPLED ELASTOPLASTIC DAMAGE MODEL ased on our theoretical analysis and experimental investigations, a coupled elastoplastic damage model is established to describe the mechanical behaviors of semi-brittle geomaterials. As mentioned earlier, an anisotropic damage model can be used to describe the degradation process that is induced by the microcracks found in semi-brittle geomaterials. Generally, small strain assumption is adopted, and the total strain tensor can be decomposed into an elastic part, e ε and a plastic part, p ε [7,12, 27-28] e p = ε ε + ε (1) In an isothermal process without viscous dissipation, Helmholtz free energy is dependent on three state variables: ( , , ) e p    = D  (2) where ε denotes the elastic strain tensor, p  represents the scalar-valued internal variables of plasticity, and D refers to the tensor-valued internal variables of damage. Assuming that a thermodynamic potential exists in the damaged elastoplastic geomaterials, plastic deformation and plastic hardening both occur within the damage process. Helmholtz free energy can be resolved into elastic and plastic components: ( , , ) ( , ) ( , ) e p p p       = = + D D D ε ε (3) where 0 ( , ) (1 ( ) p p p p tr      = − D D) , ( ) ( ) ( ) 0 0 0 0 2 ( ) m m m p p p p p p p p p p B           = − + − + − , 0 p  is the initial plastic yielding threshold, m p  is the ultimate value of hardening function, B is a model’s parameter controlling plastic hardening rate, and  is the model’s parameter coupling of damage evolution and plastic flow. To insure that the second law of thermodynamics is justified, the Clausius – Duhem's inequality principle indicates that the reduced dissipation inequality contains: : 0    −  σ (4) The evaluation of the inequality involves the time derivative of the Helmholtz free energy: ( , , ) : : e e P p p p p             = + + +     D D D D D ε ε ε (5) Substitution in the reduced dissipation inequality results in: : : : : 0 e e e P p p p               − + − − −           p e e ε D D D D ε ε   (6) where the additive decomposition is utilized in consideration of the elastic and plastic strain contributions. The thermodynamic conjugate forces for plasticity and damage are, respectively: P p p R    = −  (7)   = −  Y D (8) B