Abstract
In this work, we have developed a nonlocal geometrically-exact shell theory and its computational formulation, which can model fracture and crack growth in shell structures under finite deformations. We have derived the local form of the nonlocal balance laws for a nonlocal continuum, which are instrumental in developing the nonlocal stress-resultant based geometrically-exact shell theory. This approach is particularly efficient for modeling material damage and structural failure process with strong discontinuities. A meshfree Galerkin weak formulation is developed for the nonlocal geometrically-exact shell theory by using nonlocal differential operators. Several numerical examples, including finite deformation and fractures, are conducted to verify the effectiveness of the present method. The numerical results demonstrate that the proposed nonlocal shell theory is an accurate and robust method to model the failure of shell structures.
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