Document Type

Article

Publication Date

2-1-2025

Abstract

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 a solution in the L2 norm at the rate C1Δt+C2h2/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.

Publication Source (Journal or Book title)

Computer Methods in Applied Mechanics and Engineering

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