Modeling of trabecular bone transition into plastic deformation stage under uniaxial compression

Abstract

This article deals with the nonlinear behavior of trabecular bone tissue under uniaxial compression. The model of this behavior is a stress-strain curve with an ascending branch, a peak point, and a descending branch. The known stress-strain model predicts the behavior of trabecular bone tissue at the pre-peak and partially at the post-peak stage of deformation. The model does not take into account the transition of trabecular bone into the plastic stage of deformation and the appearance of residual deformations, which (depending on the scale) may be physiologically unacceptable. The aim of this work is to predict the transition point of trabecular bone into the plastic state. The article proposes and implements an approach based on the joint application of the stress-strain model and the differential energy criterion of brittle fracture. This study contributes to the development of new models, the use of which improves the possibilities of analyzing the mechanical behavior of trabecular bone tissue under mechanical impact, which is important for the practice of load rationing in traumatology and sports medicine. The small amount of initial data is a positive quality of the proposed approach to modeling the transition of trabecular bone into the plastic state. Given the small volume of studies using the proposed approach, it is necessary to continue research in this direction, despite the good agreement of the modeling results with the experimental data known from the literature.