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

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Abstract:

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.

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: March 1, 2000

bsc/ffems/2000/00000023/00000003/art00273
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