Accurate Absorbing Boundary Conditions in Peridynamics: Part II – Elastic Waves
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In this contribution, we propose a novel method for the construction of accurate absorbing boundary conditions (ABCs) for elastic wave propagation in unbounded domains. Our approach is based on deriving a semi-analytical solution of the exterior region of the peridynamic governing equation, which is composed of a finite series of plane waves, referred to as fundamental solutions or modes, that satisfy the peridynamic dispersion relations. The modes are adjusted to effectively transmit energy from the interior to the exterior region. The unknown coefficients of the series are determined through nodal displacement and velocity field information at a layer of points adjacent to the absorbing boundary, through a collocation procedure at subregions (clouds) around each absorbing point. This method offers several advantages, particularly its ease of implementation, since the ABCs are of Dirichlet-type and the construction is in the time and space domains, thus eliminating the need for Fourier or Laplace transforms, which are challenging to perform on nonlocal models. The proposed method is evaluated through several numerical examples to assess the numerical stability over time as well as the level of accuracy. We further demonstrate the applicability in scenarios involving highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.
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