It is well argued that stability-initiated failure dominates, especially in older bone, because of the instability of single trabeculae which is prone to inelastic buckling at stresses far less than expected for strength-based failure. It is also well known that when several horizontal struts have disappeared, trabecula fails due to compression-buckling load. In this contribution, our main goal is to improve, from theoretical point of view, the mechanistic understanding of bone buckling failure which is known to be at the core of important clinical problems. For that and with respect to previous works, an attempt is made in order to establish a simplified adaptive-beam buckling model, formulated within the context of the nonlocal adaptive continuum mechanics, from which numerical computations were performed in order to get a better knowledge about bone-column buckling mechanism affected by both bone density and bone density gradient distributions restricted to Euler–Bernoulli beam theory. An attempt is made to compare the experimental data with the response of our simplified model. For that, controlled buckling tests of single trabeculae were carried out from three medial tibia end sections (knee joint).

中文翻译：

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非局部连续体自适应弹性骨柱屈曲模型

有充分理由认为，稳定性引发的失效占主导地位，尤其是在较旧的骨骼中，因为单个小梁的不稳定性在远低于基于强度的失效预期的应力下容易发生非弹性屈曲。众所周知，当几个水平支柱消失时，小梁由于压缩屈曲载荷而失效。在这项贡献中，我们的主要目标是从理论的角度改进对已知是重要临床问题核心的骨屈曲失败的机制理解。为此，对于以前的工作，尝试建立一个简化的自适应梁屈曲模型，在非局部自适应连续体力学的背景下制定，从中进行了数值计算，以便更好地了解受限制于欧拉-伯努利梁理论的骨密度和骨密度梯度分布影响的骨柱屈曲机制。尝试将实验数据与我们简化模型的响应进行比较。为此，从三个内侧胫骨末端部分（膝关节）进行了单个小梁的受控屈曲测试。