Convergence analysis for mesh-free discretization of irreversible-damage peridynamic models

Establish a rigorous convergence analysis for the mesh-free discretization of the peridynamic models with irreversible damage developed in COSKUN2025106302 and bromley2026blendedapproachevolvingphase, including the one-point quadrature used in practical implementations.

Background

The paper surveys convergence results for several non-linear peridynamic models, noting that existing analyses either concern models without irreversible damage or use different discretization approaches. It identifies the models developed in COSKUN2025106302 and bromley2026blendedapproachevolvingphase as incorporating irreversible damage while also accounting for compression and additional constitutive effects such as hysteresis.

Unlike the model analyzed in the present paper, for which convergence of the mesh-free discretization with one-point quadrature is proved, the corresponding rigorous numerical analysis for these broader irreversible-damage models remains unresolved.

References

A rigorous analysis of the corresponding mesh-free discretization is, however, to the best of our knowledge, still open.

— On the Convergence of the Mesh-Free Discretization of a Non-Linear Bond-Based Peridynamic Model with a Bond-Breakage Criterion  (2610.13355 - Pflug et al., 9 Oct 2026) in Section 1, Introduction