RESUMO
We present a reduced order model for efficient nonlinear homogenization of bones, accounting for strength difference effects and containing some well-known plasticity models (like von Mises or Drucker-Prager) as special cases. The reduced order homogenization is done by using a cluster-based model order reduction technique, called cluster-based nonuniform transformation field analysis. For an offline phase, a space-time decomposition is performed on the mesoscopic plastic strain fields, while a clustering analysis is employed for a spatial decomposition of the mesoscale RVE model. A volumetric-deviatoric split is additionally introduced to capture the enriched characteristics of the mesoscopic plastic strain fields. For an online analysis, the reduced order model is formulated in a unified minimization problem, which is compatible with a large variety of material models. Both cortical and trabecular bones are considered for numerical experiments. Compared to conventional FE-based RVE computations, the developed reduced order model renders a considerable acceleration rate beyond 10 3 , while maintaining a sufficient accuracy level.
