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

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Higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances, both material and geometrical non-linearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. The present study addresses the performance of surface-cracked inelastic 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 point 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 means of a Mindlin shell finite element. The cracked parts are accounted for by means of inelastic line spring elements. The three-dimensional models employ eight-noded solid elements. These models also account for ductile crack growth due to void coalescence by means of a modified Gurson–Tvergaard constitutive model, hence providing detailed solutions that the two-dimensional simulations can be tested against. Using this, the accuracy of the two-dimensional approach is checked thoroughly. The analyses show that the two-dimensional 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 occurs before final failure, the line spring ligaments have to be updated due to crack growth.
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Keywords: cracked shells; ductile fracture; line springs; non-linear geometry; plasticity; shell finite elements; solid finite elements

Document Type: Research Article

Affiliations: Div. Applied Mechanics, The Norwegian University of Science and Technology, N-7034, Trondheim, Norway, 1SINTEF Materials Technology, N-7034 Trondheim, Norway

Publication date: 2000-03-01

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