We propose a three-dimensional macroscopic continuum model designed to predict the remodeling phenomenon of bone tissue. In the proposed model, we focus on the evolution of two crucial stiffness parameters: the bulk and shear moduli. These parameters independently adapt to the mechanical demands to which bone tissue is subjected, mainly to withstand hydrostatic and deviatoric deformations. These mechanical stimulations influence the activity of bone cells, leading to changes in bone structure and strength and, in turn, the above-mentioned moduli. The formulation is simplified, serving as an initial step towards a more comprehensive modeling approach. The evolution of these stiffness parameters is proposed based on an energetic argument to describe the functional adaptation process. Numerical experiments, conducted on a cylindrical specimen resembling a femur, demonstrate the feasibility of modeling the bone remodeling process with distinct evolutions for multiple material parameters, in contrast to the conventional approach that permits only one-parameter evolution.

我们提出了一个三维宏观连续体模型，旨在预测骨组织的重塑现象。在所提出的模型中，我们关注两个关键刚度参数的演变：体积模量和剪切模量。这些参数独立适应骨组织所承受的机械要求，主要是为了承受静水变形和偏变形。这些机械刺激会影响骨细胞的活性，导致骨骼结构和强度的变化，进而导致上述模量的变化。该公式经过简化，是迈向更全面建模方法的第一步。这些刚度参数的演变是基于一个能量论点提出的，以描述函数适应过程。对类似于股骨的圆柱形标本进行的数值实验证明了对多个材料参数具有不同演变的骨骼重塑过程进行建模的可行性，相比之下，传统方法只允许单参数演变。