A multiscale predictor/corrector scheme for efficient elastoplastic voxel finite element analysis, with application to CT-based bone strength prediction

Voxel finite elements combined with plasticity have been shown to accurately predict the evolution of bone failure, but involve a prohibitive computational cost when applied to high-resolution CT scans of a complete bone. We present a simple multiscale predictor/corrector scheme that uses elasticity and the finite cell method on a coarse-scale mesh, complemented by plasticity and fine-scale voxel finite elements in regions where failure occurs. The core components of our method are top-down displacement and bottom-up stress projectors for the exchange of information between coarse and fine scales. Our choice of projectors eliminates communication of fine-scale voxel elements beyond boundaries of coarse-scale cells, which enables the solution in terms of a series of small uncoupled systems at a fraction of the computing power and memory required by the fully coupled fine-scale system. At the same time, we illustrate that the multiscale approach yields the same accuracy as the full-resolution voxel finite element method, if we appropriately balance the approximation power of coarse-scale and fine-scale meshes. We demonstrate the advantages of our method for the load capacity analysis of a patient-specific vertebra.