期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 114, 期 13, 页码 1389-1410出版社
WILEY
DOI: 10.1002/nme.5791
关键词
finite element approximation; nonlocal mechanics; numerical analysis; peridynamic modeling
资金
- US Army Research Laboratory
- US Army Research Office [W911NF1610456]
- U.S. Department of Defense (DOD) [W911NF1610456] Funding Source: U.S. Department of Defense (DOD)
We quantify the numerical error and modeling error associated with replacing a nonlinear nonlocal bond-based peridynamic model with a local elasticity model or a linearized peridynamic model away from the fracture set. The nonlocal model treated here is characterized by a double-well potential and is a smooth version of the peridynamic model introduced in the work of Silling. The nonlinear peridynamic evolutions are shown to converge to the solution of linear elastodynamics at a rate linear with respect to the length scale epsilon of nonlocal interaction. This rate also holds for the convergence of solutions of the linearized peridynamic model to the solution of the local elastodynamic model. For local linear Lagrange interpolation, the consistency error for the numerical approximation is found to depend on the ratio between mesh size h and epsilon. More generally, for local Lagrange interpolation of order p1, the consistency error is of order h(p)/epsilon. A new stability theory for the time discretization is provided and an explicit generalization of the CFL condition on the time step and its relation to mesh size h is given. Numerical simulations are provided illustrating the consistency error associated with the convergence of nonlinear and linearized peridynamics to linear elastodynamics.
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