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

Abstract

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.