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Abstract This paper provides a comprehensive derivation and application of the nonlocal Nernst-Planck-Poisson (NNPP) system for accurate modeling of electrochemical corrosion with a focus on the biodegradation of magnesium-based implant materials under physiological conditions. The NNPP system extends and generalizes the peridynamic bi-material corrosion model by considering the transport of multiple ionic species due to electromigration. As in the peridynamic corrosion model, the NNPP system naturally accounts for moving boundaries due to the electrochemical dissolution of solid metallic materials in a liquid electrolyte as part of the dissolution process. In addition, we use the concept of a diffusive corrosion layer, which serves as an interface for constitutive corrosion modeling and provides an accurate representation of the kinetics with respect to the corrosion system under consideration. Through the NNPP model, we propose a corrosion modeling approach that incorporates diffusion, electromigration and reaction conditions in a single nonlocal framework. The validity of the NNPP-based corrosion model is illustrated by numerical simulations, including a one-dimensional example of pencil electrode corrosion and a three-dimensional simulation of a Mg-10Gd alloy bone implant screw decomposing in simulated body fluid. The numerical simulations correctly reproduce the corrosion patterns in agreement with macroscopic experimental corrosion data. Using numerical models of corrosion based on the NNPP system, a nonlocal approach to corrosion analysis is proposed, which reduces the gap between experimental observations and computational predictions, particularly in the development of biodegradable implant materials. 

Abstract We present an ordinary state-based peridynamic model in 2D and 3D consistent with rate-independent J2 plasticity with associated flow rule. The new contribution is the capability of the elastoplastic law to describe isotropic, kinematic and mixed hardening. The hardening formulations follow those available in the literature for classical elastoplasticity. The comparison between the results obtained with the peridynamic model and those obtained with a commercial FEM software shows that the two approaches are in good agreement. The extent of the plastic regions and von Mises stress computed with the new model for 2D and 3D examples match well those obtained with FEM-based solutions using ANSYS. 

We derive numerical stability conditions and analyze convergence to analytical nonlocal solutions of 1D peridynamic models for transient diffusion with and without a moving interface. In heat transfer or oxidation, for example, one often encounters initial conditions that are discontinuous, as in thermal shock or sudden exposure to oxygen. We study the numerical error in these models with continuous and discontinuous initial conditions and determine that the initial discontinuities lead to lower convergence rates, but this issue is present at early times only. Except for the early times, the convergence rates of models with continuous and discontinuous initial conditions are the same. In problems with moving interfaces, we show that the numerical solution captures the exact interface location well, in time. These results can be used in simulating a variety of reaction-diffusion type problems, such as the oxidation-induced damage in zirconium carbide at high temperatures.