Mengoni M, Ponthot J P
a Department of Aerospace and Mechanical Engineering, MN2L , University of Liege (ULg) , Liège , Belgium.
Comput Methods Biomech Biomed Engin. 2015;18(12):1367-76. doi: 10.1080/10255842.2014.903933. Epub 2014 Apr 4.
The purpose of this work was to propose an enhancement of Doblaré and García's internal bone remodelling model based on the continuum damage mechanics (CDM) theory. In their paper, they stated that the evolution of the internal variables of the bone microstructure, and its incidence on the modification of the elastic constitutive parameters, may be formulated following the principles of CDM, although no actual damage was considered. The resorption and apposition criteria (similar to the damage criterion) were expressed in terms of a mechanical stimulus. However, the resorption criterion is lacking a dimensional consistency with the remodelling rate. We propose here an enhancement to this resorption criterion, insuring the dimensional consistency while retaining the physical properties of the original remodelling model. We then analyse the change in the resorption criterion hypersurface in the stress space for a two-dimensional (2D) analysis. We finally apply the new formulation to analyse the structural evolution of a 2D femur. This analysis gives results consistent with the original model but with a faster and more stable convergence rate.
这项工作的目的是基于连续损伤力学（CDM）理论，对多布莱雷（Doblaré）和加西亚（García）的内部骨重塑模型进行改进。在他们的论文中，他们指出，尽管未考虑实际损伤，但骨微观结构内部变量的演变及其对弹性本构参数修改的影响，可以按照CDM的原理来表述。吸收和沉积标准（类似于损伤标准）是根据机械刺激来表达的。然而，吸收标准与重塑速率缺乏量纲一致性。我们在此提出对该吸收标准的改进，确保量纲一致性，同时保留原始重塑模型的物理特性。然后，我们针对二维（2D）分析，分析应力空间中吸收标准超曲面的变化。最后，我们应用新公式来分析二维股骨的结构演变。该分析给出的结果与原始模型一致，但收敛速度更快且更稳定。
