EUROPEAN CONGRESS AND EXHIBITION ON ADVANCED MATERIALS AND PROCESSES - EUROMAT 2021

Enhancing trust in in silico approaches is a fundamental challenge. The uncertainties associated with simulations and mathematical models limit the degree of confidence in their outcomes. Thus, quantifying these uncertainties will play an important role in empowering this approach, in particular when considering models of material systems that will be implanted into the body. The ability of magnesium (Mg) and its alloys to degrade under physiological conditions creates a new class of biodegradable implants that can replace the classical non-biodegradable bone implants. However, this is not a straightforward process due to the challenges of controlling the degradation process within the biological environments. To accelerate the development process of Mg-based biodegradable implants, computational models can be used if they are reliably predicting the material behaviour.
Here, a physical model of the degradation of pure Mg based on the Nernst-Planck equation is developed and implemented in COMSOL Multiphysics. The model includes the chemical and electrochemical interactions between the different ionic species present during in vitro degradation in simulated body fluid under physiological conditions.
One of the main challenges of this model is to accurately estimate its parameters; such as reaction rate constants, porosity and diffusion coefficients. The model parameters are optimized under uncertainty by applying the Gaussian process regression algorithm, also known as Kriging. The Kriging algorithm estimates the parameters of the model within a confidence interval, which quantifies the uncertainties associated with each of these parameters. Further sensitivity analysis is performed to evaluate the contributions of each single input parameter over the outcomes of the model. All uncertainty quantification tests are performed in UQLab, a MATLAB-based Uncertainty Quantification framework. We will present the effect of quantifying the uncertainties over the current model outputs and the enhanced degree of agreement with in-house validation data.