Speaker
Description
Osteoporosis is the most common bone disease worldwide. The disease is characterized by a loss in bone density, which reduces the bone stiffness over time and thus increases the likelihood of fractures. In past contributions (e.g., [1-3]), we introduced a multiscale material model of cancellous bone considering mechanical, electric and magnetic effects. An important application of this model is the simulation of early detection of osteoporosis via sonography, which may be a viable future diagnostics tool. In this talk, we present important developments in our modeling approaches. First, we introduce a dimensionless (scaled) formulation of the underlying PDE system to generalize the problem and to enhance its numerical stability. Furthermore, we derive a simplified, decoupled model from the original equations and discuss its advantages and disadvantages in comparison to the fully coupled model. To solve the new model, we then apply the finite element (FE) fast Fourier transform (FFT) method, which has been used in the past to solve a variety of multiscale problems [4]. We show numerical results and discuss results regarding accuracy, applicability and computational costs.
References:
[1] Blaszczyk, M., Hackl, K., “Multiscale modeling of cancellous bone considering full coupling of mechanical, electric and magnetic effects”, Biomech. Model. Mechanobiol., (2021).
[2] Stieve, V., Blaszczyk, M., Hackl, K., “Inverse modeling of cancellous bone using artificial neural networks”, Z. Angew. Math. Mech., (2022).
[3] Blaszczyk, M., Hackl, K., “On the effects of a surrounding medium and phase split in coupled bone simulations”, Z. Angew. Math. Mech., (2024).
[4] Gierden, C., Kochmann, J., Waimann, J., Svendsen, B., Reese, S., “A review of FE-FFT-based two-scale methods for computational modeling of microstructure evolution and macroscopic material behavior”, Arch. Comput. Methods. Eng., (2022).
