Finite element modelling of cracked inelastic shells with large deflections: two-dimensional and three-dimensional approaches

Higher utilization of structural materials leads to a need for accurate num erical tools for reliable predictions of structural response. In some insta nces, both material and geometrical non-linearities are allowed for, typica lly in assessments of structural collapse or residual strength in damaged c onditions. The present study addresses the performance of surface-cracked i nelastic shells with out-of-plane displacements not negligible compared to shell thickness. This situation leads to non-linear membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a non -proportional history of bending moment and membrane force. An important po int in the discretization of the problem is whether a two-dimensional model describes the structural performance sufficiently, or a three-dimensional model is required. Herein, the two-dimensional modelling is performed by me ans of a Mindlin shell finite element. The cracked parts are accounted for by means of inelastic line spring elements. The three-dimensional models em ploy eight-noded solid elements. These models also account for ductile crac k growth due to void coalescence by means of a modified Gurson-Tvergaard co nstitutive model, hence providing detailed solutions that the two-dimension al simulations can be tested against. Using this, the accuracy of the two-d imensional approach is checked thoroughly. The analyses show that the two-d imensional modelling is sufficient as long as the cracks do not grow Hence, using fracture initiation as a capacity criterion, shell elements and line springs provide acceptable predictions. If significant ductile tearing occ urs before final failure, the line spring ligaments have to be updated due to crack growth.