Branecka Natalia, Yildizdag Mustafa Erden, Ciallella Alessandro, Giorgio Ivan
Faculty of Mechanical and Industrial Engineering, Warsaw University of Technology, 00-661 Warsaw, Poland.
International Research Center for the Mathematics and Mechanics of Complex Systems, University of L'Aquila, 67100 L'Aquila, Italy.
Biomimetics (Basel). 2022 May 6;7(2):59. doi: 10.3390/biomimetics7020059.
A macroscopic continuum model intended to provide predictions for the remodeling process occurring in bone tissue is proposed. Specifically, we consider a formulation in which two characteristic stiffnesses, namely the bulk and shear moduli, evolve independently to adapt the hydrostatic and deviatoric response of the bone tissue to environmental changes. The formulation is deliberately simplified, aiming at constituting a preliminary step toward a more comprehensive modeling approach. The evolutive process for describing the functional adaptation of the two stiffnesses is proposed based on an energetic argument. Numerical experiments reveal that it is possible to model the bone remodeling process with a different evolution for more than one material parameter, as usually done. Moreover, the results motivate further investigations into the subject.
提出了一个宏观连续介质模型,旨在为骨组织中发生的重塑过程提供预测。具体而言,我们考虑一种公式化表述,其中两个特征刚度,即体积模量和剪切模量,独立演化,以使骨组织的静水和偏量响应适应环境变化。该公式化表述经过刻意简化,旨在朝着更全面的建模方法迈出初步步骤。基于能量论据提出了描述两种刚度功能适应性的演化过程。数值实验表明,与通常做法一样,用不止一个材料参数的不同演化来模拟骨重塑过程是可能的。此外,这些结果促使对该主题进行进一步研究。