Crack growth in thin shells using the time-dependent energy limiter-based gradient damage model with SMITC4+ shell elements

This work introduces a novel computational model designed to simulate dynamic brittle fracture and crack growth in thin shell structures. This framework integrates an advanced implicit gradient damage model, which employs an energy limiter concept to ensure mesh insensitivity and prevent spurious damage, with a simplified MITC4+ shell finite element formulation to mitigate numerical locking issues in thin-shell analysis. The study details the governing equations, finite element implementation, and an efficient explicit dynamic solver with mass lumping. Numerical examples, including dynamic shear, tension, and compression tests on flat and curved shells, validate the model’s accuracy and robustness by comparing its predictions of crack paths, energy dissipation, and crack-tip velocities against experimental data and other numerical benchmarks. The authors conclude that this combined approach is highly effective for analyzing complex dynamic fracture in lightweight structural components like those used in aerospace and automotive industries. • We present an implicit nonlocal damage model with a critical energy threshold for fracture in shells. • The framework uses the SMITC4+ shell elements for spatial discretization without shear and membrane locking. • The model uses a physically meaningful characteristic length, reducing mesh sensitivity. • The framework is capable of capturing arbitrary and complex crack paths with branching without a crack-tracking algorithm. • Numerical performance reveals the effectiveness and accuracy of the developed approach for cracks in shells.