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.

中文翻译：

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使用基于集群的模型降阶技术对骨骼进行有效的非线性均质化

我们提出了一种用于骨骼有效非线性均质化的降阶模型，考虑了强度差异效应，并包含一些众所周知的塑性模型（如 von Mises 或 Drucker-Prager）作为特例。降阶均质化是通过使用基于聚类的模型降阶技术来完成的，称为基于聚类的非均匀变换场分析。对于离线阶段，对细观塑性应变场进行时空分解，同时采用聚类分析对细观 RVE 模型进行空间分解。另外还引入了体积偏量分裂来捕获介观塑性应变场的丰富特征。对于在线分析，降阶模型是在统一的最小化问题中制定的，该模型与多种材料模型兼容。皮质骨和小梁骨都被考虑用于数值实验。与传统的基于有限元的 RVE 计算相比，开发的降阶模型呈现出相当大的加速度，超出了${10}^3$，同时保持足够的准确度水平。