A novel algorithm to resolve lack of convergence and checkerboard instability in bone adaptation simulations using non-local averaging.
José Luis Calvo-Gallego, Peter Pivonka, José Manuel García-Aznar, Javier Martínez-Reina
International Journal for Numerical Methods in Biomedical Engineering | Published : 2021
Checkerboard is a typical instability in finite element (FE) simulations of bone adaptation and topology optimization in general. It consists in a patchwork pattern with elements of alternating stiffness, producing lack of convergence and instabilities in the predicted bone density. Averaging techniques have been proposed to solve this problem. One of the most acknowledged techniques (node based formulation) has severe drawbacks such as: high sensitivity to mesh density and type of element integration (full vs reduced) and, more importantly, oscillatory solutions also leading to lack of convergence. We propose a new solution consisting in a non-local smoothing technique. It defines, as the m..View full abstract