On the constitutive modelling of elasto-plastic self-healing materials

Abstract

A novel three-dimensional elasto-plastic damage-healing (EPDH) model, based on continuum damage mechanics, is proposed capturing the self-healing phenomenon occurring in plastically deforming materials. A novel secondary damage variable, with separate evolution law, is introduced removing an assumption in the existing literature that the healed area cannot undergo damage again or healed area undergoes damage only once. The implicit damage-healing formulation, based on the irreversible thermodynamics, is developed detailing evolution equations of all internal variables. A novel pressure-dependent yield surface (qualitatively behaving like Gurson model) is developed by damage-healing equivalent stress modifying von Mises yield surface. The physical interpretation of damage and healing energy release rates are presented to elucidate their impact on the energy dissipation within the system. The proposed formulation is numerically implemented by return mapping approach employing elastic strain equivalence hypothesis. The applicability of newly proposed EPDH + secondary damage framework is successfully demonstrated considering different strain histories. The secondary damage variable is finally found crucial while obtaining the physically realistic stress–strain response of self-healing materials leading to complete failure upon exhaustion of healing capabilities.