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Peridynamics for
antiplane shear and torsional deformations
Selda Oterkus and Erdogan Madenci |
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Vol. 10 (2015), No. 2, 167–193
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Abstract |
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A rod or beam is one of the most widely used members in engineering construction. Such members must be properly designed to resist the applied loads. When subjected to antiplane (longitudinal) shear and torsional loading, homogeneous, isotropic, and elastic materials are governed by the Laplace equation in two dimensions under the assumptions of classical continuum mechanics, and are considerably easier to solve than their three-dimensional counterparts. However, when using the finite element method in conjunction with linear elastic fracture mechanics, crack nucleation and its growth still pose computational challenges, even under such simple loading conditions. This difficulty is mainly due to the mathematical structure of its governing equations, which are based on the local classical continuum theory. However, the nonlocal peridynamic theory is free of these challenges because its governing equations do not contain any spatial derivatives of the displacement components, and thus are valid everywhere in the material. This study presents the peridynamic equation of motion for antiplane shear and torsional deformations, as well as the peridynamic material parameters. After establishing the validity of this equation, solutions for specific components that are weakened by deep edge cracks and internal cracks are presented. |
Keywords
peridynamics, nonlocal, antiplane shear, torsion, fracture
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Milestones
Received: 3 February 2015
Revised: 19 May 2015
Accepted: 9 June 2015
Published: 5 August 2015
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Authors |
| Selda Oterkus | |
| Department of Aerospace and
Mechanical Engineering The University of Arizona 1130 N Mountain Tucson, AZ 85721-0119 United States |
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| Erdogan Madenci | |
| Department of Aerospace and
Mechanical Engineering The University of Arizona 1130 N Mountain Tucson, AZ 85721-0119 United States |
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