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

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.

Microstructural Modeling and Strengthening Mechanism of TiB/Ti-6Al-4V Discontinuously-Reinforced Titanium Matrix Composite.

A novel modeling method was proposed to provide an improved representation of the actual microstructure of TiB/Ti-6Al-4V discontinuously-reinforced titanium matrix composite (DRTMC). Based on the Thiessen polygon structure, the representative volume element (RVE) containing the complex microstructures of the DRTMC was first generated. Thereafter, by using multiple user-defined subroutines in the commercial finite element software ABAQUS, the application of asymmetric mesh periodic boundary conditions on the RVE was realized, and the equivalent elastic modulus of the DRTMC was determined according to the homogenization method. Through error analyses on the experimental and calculated results regarding the equivalent elastic parameters of the DRTMC, the rationality of generating the DRTMC finite element model by using the present method was validated. Finally, simulations based on four types of network-like models revealed that the present simplifications to the particle shape of the reinforcement phase had less of an influence on the overall composite strength. Moreover, the present study demonstrates that the DRTMC enhancement is mainly attributed to the matrix strengthening, rather than the load-transferring mechanism. The strengthening influences of the distribution forms of the reinforcement phases, including their distribution density and orientation, were studied further. It was found that both the higher distribution density and limited distribution orientation of the particles would increase the probability of overlapping and merging between particles, and; therefore, higher strength could be yielded when the volume fraction of the reinforcement phase reached a certain threshold. Owing to the versatility of the developed methods and programs, this work can provide a useful reference for the characterization of the mechanical properties of other composites types.