Efficient nonlinear homogenization of bones using a cluster‐based model order reduction technique

Abstract

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 , while maintaining a sufficient accuracy level.