动态轴向载荷下皮质骨的切向应力

J. Choi, C. Dharan
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引用次数: 0

摘要

皮质骨是一种复杂的分层复合层状结构,通常由矿物相(羟基磷灰石钙)、有机相(胶原蛋白)和液体组成[1]。在骨的分析中,液相通常被忽略,这一假设对于稳态或准静态载荷是合理的。然而,当皮质骨在轴向动态加载时,受约束流体的存在会在切向产生随时间变化的应力。由于切向应力垂直于骨的弱横向,它可以在这个方向上造成损伤。轴向循环压缩加载会导致切向循环拉伸加载,最终导致疲劳损伤。在对高强度运动赛马的研究中,这种损伤实际上已经被观察到,损伤表现为垂直于切向的微裂纹,其断裂面沿轴向分布[2]。在这项工作中,皮质骨被建模为由充满液体的可渗透复合材料组成的双相材料。所考虑的几何结构是由充满流体的多个同心渗透性薄片组成的空心圆柱体(图1)。当该结构在轴向受压时,会产生拉切向应力,该应力随时间衰减。衰减率是渗透率和径向位置的函数。渗透率越大,衰减速度越快。切向应力在内半径处达到峰值,并随着径向位置的增加而减小(图2)。切向应力在内半径处达到峰值的时间也更早。在骨受到切向应力的时间较长的情况下,骨的外表面的衰变速度比内表面慢得多(图2)。这种将骨视为受动态载荷影响的双相结构的观点,可能为在体内观察到的受循环和冲击载荷影响的骨的一些损伤模式提供了理论依据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tangential Stress in Cortical Bone Subjected to Dynamic Axial Loading
Cortical bone is a complex hierarchical composite lamallae structure consisting, in general, of a mineral phase (calcium hydroxyapatite), an organic phase (collagen) and fluid [1]. In the analysis of bone, the liquid phase is usually neglected, an assumption that is reasonable for steady state or quasi-static loading. However, when cortical bone is loaded dynamically in the axial direction, the presence of the constrained fluid generates time-dependent stresses in the tangential direction. Since the tangential stress acts perpendicular to the weak transverse direction of the bone, it can create damage in this direction. Cyclic axial compressive loading will result in cyclic tensile loading in the tangential direction which can eventually result in fatigue damage. Such damage has actually been observed in studies conducted on heavily exercised race horses where damage was observed in the form of micro cracks oriented perpendicular to the tangential direction and whose fracture planes lie along the axial direction [2]. In this work, cortical bone is modeled as a biphasic material consisting of a permeable composite material filled with fluid. The geometry considered is that of a hollow cylinder made up of multiple concentric permeable lamellae filled with fluid (Fig. 1). When this structure is loaded axially in compression, a tensile tangential stress is developed which decays with time. The decay rate is a function of permeability and radial position. The greater the permeability, the faster the decay rate. The tangential stress peaks at the inner radius and decreases with radial position (Fig. 2). The tangential stress also peaks earlier at the inner radius. The rate of decay is slower at the outside surface where the bone is subjected to the tangential stress for a much longer time than at the inner surface (Fig. 2). This view of bone as a biphasic structure subjected to dynamic loading may provide a rationale for some of the damage modes observed in vivo in bones subjected to cyclic and impact loading.
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