We investigate the error incurred in replacing a nonlinear nonlocal bondbased peridynamic model with linearized peridynamics or classic localelastodynamics away from the fracture set. The nonlinear nonlocal model ischaracterized by a double well potential. We establish a convergence rate fordifferentiable solutions of nonlinear nonlocal peridynamics to the solution ofclassical linear elastodynamics. The convergence rate is shown to be linear inthe length scale of non locality and uniform in time. The linear rate alsoholds for the convergence of solutions of the linearized peridynamic model tothe classical elastodynamics solution. The consistency error of numericalapproximation for peridynamics is shown to explicitly depend on the ratio ofmesh size and peridynamic horizon. For central difference schemes in time andlinear interpolation in space the stability condition for linearizedperidynamics is shown to be given by a generalization of the CFL condition.Numerical results are presented to illustrate how nonlinear and linearizedperidynamics converge to classical elastodynamics.
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