Application of an enhanced homogenization technique to the structural multiscale analysis of a femur bone

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 beyond10 3 , while maintaining a sufficient accuracy level.

A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method

Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach - the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.