Hyperbolic Eulerian Gradient Damage Modeling of Dynamic Brittle Fracture at Finite Strain
Please login to view abstract download link
We propose a hyperbolic Eulerian formulation of gradient damage for brittle solids undergoing large deformations. The model extends a previously developed infinitesimal-strain hyperbolic gradient-damage framework to the fully nonlinear finite-strain regime in the Eulerian setting. The formulation is derived within an extended Lagrangian framework, ensuring thermodynamic consistency while coupling finite-deformation hyperelasticity with a gradient-regularized scalar damage model. The governing equations form a first-order system of hyperbolic equations with local source terms, which is well suited for explicit time integration. A hyperbolicity analysis carried out for a class of separable stored energies leads to sufficient conditions that guarantee the well-posedness of the resulting system. The proposed framework enables the use of explicit finite-volume schemes on fixed grids, making it particularly attractive for dynamic fracture problems involving large strains, rotations, and fragment dispersion. Numerical simulations are presented to illustrate the capabilities of the model in dynamic fracture configurations, highlighting its ability to capture wave propagation, damage evolution, and fragmentation phenomena in an Eulerian setting.
