Dynamic brittle fracture with a new energy limiter-based scalar damage model

We present a new scalar damage model for dynamic brittle fracture. In contrast to existing damage theories, the internal damage variable is alternatively derived based on energy limiter theory, directly tightening to its physical meaning. Finite element implementation for the developed approach at small strain towards localized brittle failure is given. We integrate the energy decomposition into the theory to eliminate nonphysical damaged phenomenon when cracks develop in compression domain, while the crack band theory is employed to treat mesh sensitivity. As a result, the current model does not involve any length scale parameter, and therefore nor diffusive equation of damage evolution characterizing the degradation of material stiffness is required. Two simple methods for estimating crack-tip velocity and dissipated energy are provided. Discrete forms of governing equation are solved by a simple staggered scheme in an effective manner. Several numerical examples for dynamic brittle fracture including crack branching are studied.