Abstract:
Failure phenomenon is conventionally treated by two mathematically grounded theories; fracture mechanics and damage mechanics. In fracture mechanics, the stress field in the vicinity of discretely modelled cracks in a continuum is investigated whereas, in damage mechanics, damage is interpreted as a thermodynamic state of solid, affecting its properties. This paper presents failure analysis in a unified manner, based on the state based philosophy. With this philosophy, failure is considered as the change of state of the entity between its two end states. The damage parameters are explicitly defined in terms of the state variable (which is the calibrated index of damage) using the recently developed state and phenomenon functions. Consequently, all types of damage are treated in unified and simple formulations. The work is validated with the help of examples from fracture mechanics, pushover analysis and fragility analysis of structures.