Combining peridynamic and finite element simulations to capture the corrosion of degradable bone implants and to predict their residual strength

• Published in: International journal of mechanical sciences Vol. 220; p. 107143
• Main Authors: Hermann, Alexander, Shojaei, Arman, Steglich, Dirk, Höche, Daniel, Zeller-Plumhoff, Berit, Cyron, Christian J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.04.2022
• Subjects: Mass loss; Mg-Gd alloys; Moving interface; Multi-grid; Non-local diffusion; Strength reduction; Strength reduction; Moving interface; Mass loss; Non-local diffusion; Multi-grid; Mg-Gd alloys
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2022.107143

This paper proposes a computational framework to describe the biodegradation of magnesium (Mg)-based bone implants. It is based on a sequential combination of two models: an electrochemical corrosion model to compute the mass loss of the implant over several weeks combined with a mechanical model to assess its residual mechanical strength. The first model uses a peridynamic (PD) corrosion model to tackle the complex moving boundary of the corroding material in an efficient manner. The results of this corrosion simulation are mapped to a finite element (FE) model by way of a damage variable. Subsequently, the FE model is used for mechanical analysis. To use PD for such a complex problem, we proposed three innovative improvements compared to state-of-the-art PD models: (1) application of an adaptive multi-grid discretization in space and an implicit time-stepping algorithm enabling an efficient simulation of the complex implant geometry over prolonged periods, (2) novel non-local Dirichlet absorbing boundary conditions to truncate the simulation domain in the close neighborhood of the implant of interest without prohibitive losses of accuracy, and (3) selection of suitable non-local kernel functions and parameter calibration on the basis of experimental data by an evolutionary algorithm. We demonstrate that this framework can capture the loss of implant mass due to corrosion for typical alloys such as Mg-5Gd and Mg-10Gd. Moreover, we point out how this framework can be used in the future to predict the declining mechanical strength of bone screws subject to biocorrosion over several weeks. [Display omitted] •Development of a novel framework to model biodegradation of Mg-based implants.•Extension of a peridynamic corrosion model to simulate electrochemical biocorrosion.•Enhancing the numerical performance through a multi-grid approach.•Introduction of a new strategy of calibration for peridynamic corrosion models.•Devising a sequential approach to incorporate a finite element damage analysis.