Papers › Nodal finite element approximation of peridynamics
Nodal finite element approximation of peridynamics
Prashant K. Jha, Patrick Diehl, Robert Lipton
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This work considers the nodal finite element approximation of peridynamics, in which the nodal displacements satisfy the peridynamics equation at each mesh node. For the nonlinear bond-based peridynamics model, it is shown that, under the suitable assumptions on an exact solution, the discretized solution associated with the central-in-time and nodal finite element discretization converges to the exact solution in L² norm at the rate C₁ Δt + C₂ h²/ϵ². Here, Δt, h, and ϵ are time step size, mesh size, and the size of the horizon or nonlocal length scale, respectively. Constants C₁ and C₂ are independent of h and Δt and depend on norms of the solution and nonlocal length scale. Several numerical examples involving pre-crack, void, and notch are considered, and the efficacy of the proposed nodal finite element discretization is analyzed.
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