A Hybrid Lagrangian–Eulerian Formulation of Thin-Shell Fracture

The hybrid Lagrangian/Eulerian formulation of continuum shells is highly effective for producing challenging simulations of thin materials like cloth with bending resistance and frictional contact. However, existing formulations are restricted to materials that do not undergo tearing nor fracture due to the difficulties associated with incorporating strong discontinuities of field quantities like velocity via basis enrichment while maintaining $$ continuity or $$ regularity. We propose an extension of this formulation to simulate dynamic tearing and fracturing of thin shells using Kirchhoff–Love continuum theory. Damage, which manifests as cracks or tears, is propagated by tracking the evolution of a time-dependent phase-field in the co-dimensional manifold, where a moving least-squares (MLS) approximation then captures the strong discontinuities of interpolated field quantities near the crack. Our approach is capable of simulating challenging scenarios of this tearing and fracture, all-the-while harnessing the existing benefits of the hybrid Lagrangian/Eulerian formulation to expand the domain of possible effects. The method is also amenable to user-guided control, which serves to influence the propagation of cracks or tears such that they follow prescribed paths during simulation.