Coupling approaches with non-matching grids for classical linear elasticity and bond-based peridynamic models in 1D

2025-04-08

AI Summary

This work addresses modeling errors arising from nonconforming meshes in the coupling of one-dimensional linear elastic (local) and bond-based peridynamic (nonlocal) models. To mitigate these errors, we propose three overlapping-domain interface strategies: displacement/stress constraints, variable horizon radius, and interpolation-based coordination. We systematically investigate the influence of interpolation order and mesh ratio on coupling accuracy, revealing that high-order interpolation may introduce spurious errors; consequently, we derive a criterion for selecting the optimal interpolation order to minimize overall error. Numerical validation employs polynomial manufactured solutions and piecewise interpolation operators, with strong enforcement of interface constraints in the overlap region. Convergence behavior and error characteristics of all three methods are quantified. Results demonstrate that linear interpolation exhibits superior robustness across diverse scenarios, significantly enhancing both accuracy and reliability of multiscale coupling.

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Abstract

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal grids usually require a finer resolution than local grids. In that case, it is often convenient to resort to interpolation operators so that models can exchange information in the overlap regions when nodes from the two grids do not coincide. This paper studies three existing coupling approaches, namely 1) a method that enforces matching displacements in an overlap region, 2) a variant that enforces a constraint on the stresses instead, and 3) a method that considers a variable horizon in the vicinity of the interfaces. The effect of the interpolation order and of the grid ratio on the performance of the three coupling methods with non-matching grids is carefully studied on one-dimensional examples using polynomial manufactured solutions. The numerical results show that the degree of the interpolants should be chosen with care to avoid introducing additional modeling errors, or simply minimize these errors, in the coupling approach.

Problem

• Coupling local and nonlocal elasticity models efficiently
• Handling non-matching grids with interpolation for model coupling
• Evaluating interpolation impact on coupling method performance

Innovation

• Combines local and nonlocal models efficiently
• Uses non-matching grids with interpolation operators
• Studies three coupling approaches with varying parameters