One-dimensional dynamic fragmentation with the cohesive Lipschitz (CLIP) approach

Abstract Dynamic fragmentation of brittle materials involves complex crack nucleation, propagation, and interaction under high-rate loading. Traditional cohesive zone models (CZM) accurately capture discrete cracks, but suffer from mesh dependency and constrained crack paths, whereas continuous damage models offer mesh independence at the expense of sharp-crack representation. This paper presents the Cohesive Lipschitz (CLIP) model, which unifies interface-based cohesive damage with a Lipschitz-projected bulk damage field to enforce spatial regularization. Analytical equivalence with a linear CZM yields closed-form degradation and dissipation functions, and a regularization parameter governs energy redistribution between cohesive interfaces and diffuse zones. Quasi-static validation confirms exact reproduction of CZM behavior under tensile loading. An explicit dynamic finite-element implementation simulates one-dimensional fragmentation of alumina across a wide range of strain rates. The CLIP model successfully predicts the transition from sparse to fine fragmentation, producing fragment statistics in agreement with established theoretical and numerical studies, thereby demonstrating robust fracture predictions with computational efficiency and a clear physical interpretation.