Computational modeling of skeletal tissue seeks to predict the structural adaptation of bone in response to mechanical loading. The theory of continuum damage-repair, a mathematical description of structural adaptation based on principles of damage mechanics, continues to be developed and utilized for the prediction of long-term peri-implant outcomes. Despite its technical soundness, CDR does not account for the accumulation of mechanical damage and irreversible deformation. In this work, a nonlinear mathematical model of independent damage accumulation and plastic deformation is developed in terms of the CDR formulation. The proposed model incorporates empirical correlations from uniaxial experiments. Supporting elements of the model are derived, including damage and yielding criteria, corresponding consistency conditions, and the basic, necessary forms for integration during loading. Positivity of mechanical dissipation due to damage is proved, while strain-based, associative plastic flow and linear hardening describe post-yield behavior. Calibration of model parameters to the empirical correlations from which the model was derived is then accomplished. Results of numerical experiments on a point-wise specimen show that damage and plasticity inhibit bone formation by dissipation of energy available to biological processes, leading to material failure that would otherwise be predicted to experience a net gain of bone.

中文翻译：

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模拟骨重建中的渐进性损伤累积解释了过载引起的骨吸收的热力学基础

骨骼组织的计算建模旨在预测骨骼对机械载荷的结构适应性。连续损伤修复理论是一种基于损伤力学原理的结构适应的数学描述，继续被开发并用于预测长期种植体周围结果。尽管技术上很合理，CDR 并没有考虑到机械损伤和不可逆变形的累积。在这项工作中，根据CDR公式开发了独立的损伤累积和塑性变形的非线性数学模型。所提出的模型结合了来自单轴实验的经验相关性。推导出模型的支撑要素，包括损伤和屈服准则、相应的一致性条件以及基本、加载过程中集成的必要形式。证明了由于损坏引起的机械耗散的积极性，而基于应变的关联塑性流动和线性硬化描述了屈服后行为。然后完成将模型参数校准到从中导出模型的经验相关性。逐点样本的数值实验结果表明，损伤和可塑性通过耗散生物过程可用的能量来抑制骨形成，导致材料失效，否则预计会出现骨的净增益。然后完成将模型参数校准到从中导出模型的经验相关性。逐点样本的数值实验结果表明，损伤和可塑性通过耗散生物过程可用的能量来抑制骨形成，导致材料失效，否则预计会出现骨的净增益。然后完成将模型参数校准到从中导出模型的经验相关性。逐点样本的数值实验结果表明，损伤和可塑性通过耗散生物过程可用的能量来抑制骨形成，导致材料失效，否则预计会出现骨的净增益。