Kinetics of Failure in an Elastic Peridynamic Material

Abstract

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.

An incremental bond‐based peridynamic method for elastoplastic problems

“…[23][24][25] With the improvement of the BB-PD theory, many studies on viscoelasticity and plasticity have been reported. [26][27][28][29][30] These works have laid the foundation for the research of elastoplastic problems in the BB-PD framework. However, there are still some issues to be solved.…”

The Calderón Problem for the Fractional Wave Equation: Uniqueness and Optimal Stability

“…The fractional wave equation can be regarded as a special case of the peridynamics which models the nonlocal elasticity theory, see e.g. [Sil16].…”