Wiggly strain localizations in peridynamic bars with non-convex potential

Aguiar, Adair Roberto; Royer-Carfagni, Gianni; Seitenfuss, Alan B.

doi:10.1016/j.ijsolstr.2017.12.023

Cited by 6 publications

(3 citation statements)

References 37 publications

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“…This behavior is consistent with the results of Mengesha and Du [20]. Aguiar, Royer-Carfagni, and Seitenfuss [1] analyzed a nonconvex peridynamic material with two stable branches that produces equilibrium deformations with a repeating pattern of localizations. These localizations are strongly affected by the way boundary conditions are applied in a bar of finite length.…”

Section: Nonconvex Micropotentialssupporting

confidence: 89%

“…In this sense, the present method applies to large displacements. Previous studies within peridynamics of structures like phase boundaries and fractures, whose evolution is strongly influenced by material instability, allow for large displacement, for example [1,4,17]. The applicable concept of material stability in these studies is energy minimization.…”

Section: Discussionmentioning

confidence: 99%

“…Since the homogeneous deformation by itself is in equilibrium, and since by assumptionũ is small, the equation of motion (1) with the linearized material model (10) becomes:…”

Section: Bond-based Peridynamic Theorymentioning

confidence: 99%

See 2 more Smart Citations

Kinetics of Failure in an Elastic Peridynamic Material

Silling

2020

J Peridyn Nonlocal Model

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The dynamic behavior of an elastic peridynamic material with a nonconvex bond potential is studied. In spite of the material's inherently unstable nature, initial value problems can be solved using essentially the same techniques as with conventional materials, both analytically and numerically. In a suitably constructed material model, small perturbations grow exponentially over time until the material fails. The time for this growth is computed explicitly for a stretching bar that passes from the stable to the unstable phase of the material model. This time to failure represents an incubation time for the nucleation of a crack. The finiteness of the failure time in effect creates a rate dependence in the failure properties of the material. Thus, the unstable nature of the elastic material leads to a rate effect even though it does not contain any terms that explicitly include a strain rate dependence.

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Section: Nonconvex Micropotentialssupporting

confidence: 89%

Section: Discussionmentioning

confidence: 99%