A Modified Peridynamics Formulation for Corrosion Modelling Overcoming Surface Effects in Electrochemical Systems

  • Chattopadhyay, Saswata (Robert Bosch GmbH, TU Hamburg)
  • Shojaei, Arman (Helmholtz-Zentrum Hereon)
  • Fuchs, Alexander (Robert Bosch GmbH)
  • Bauer-Trossmann, Kathrin (Robert Bosch GmbH)
  • Cyron, Christian (TU Hamburg, Helmholtz-Zentrum Hereon)

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While classical methods like the Finite Element Method (FEM) are widely used, their local nature limits the ability to model nonlocal processes like corrosion. Peridynamics (PD), a nonlocal reformulation of continuum mechanics, offers a compelling alternative by using integral equations to naturally handle discontinuities. However, a persistent challenge in PD is the surface effect, where truncated particle interactions near boundaries cause accuracy loss and numerical artifacts such as artificial material softening. Current state-of-the-art approaches for corrosion modeling address this by adding extra fictitious boundary nodes [1]. To overcome this limitation, we modify standard PD operators using a moment-based optimization scheme introduced in [2]. This approach derives a spatially varying weight function that enforces consistency conditions, ensuring the nonlocal operator accurately reproduces polynomial fields while maintaining the physics of the problem through constraints. We implement this framework for the first time in multiphysics problems, specifically for the diffusion and Nernst-Planck-Poisson (NPP) equations. The method is validated on a pure diffusion problem, demonstrating significantly higher accuracy and faster convergence to analytical solutions compared to existing PD surface correction methods. We then extend the nonlocal NPP formulation from [3] by incorporating the moment-based optimization scheme, applying it to 1D and 2D electrochemical corrosion problems. This approach eliminates the need for fictitious boundary nodes while enhancing both computational efficiency and solution accuracy.