Non Local Mechanics in the Time and Space Domain-Fracture Propagation via a Peridynamics Formulation: A Stochastic\Deterministic Perspective

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Non Local Mechanics in the Time and Space Domain-Fracture Propagation via a Peridynamics Formulation: A Stochastic\Deterministic Perspective by Georgios I. Evangelatos Novel numerical methods for treating fractional differential and integrodifferential equations arising in non local mechanics formulations are proposed. For fractional differential equations arising in modeling oscillatory systems incorporating viscoelastic elements governed by fractional derivatives, the devised scheme is based on the Grunwald-Letnikov fractional derivative representation, dual time meshing technique and Taylor expansion. The proposed algorithm transforms the governing fractional differential equation into a second order differential equation with appropriate effective coefficients. The enhanced efficiency of the scheme hinges upon circumventing the calculation of the non local fractional derivative operator. Several examples of application are provided. Further, the concept of non locality, specificall

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