We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton–Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

中文翻译：

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用于骨小梁骨折模拟和实验验证的网格独立损伤模型

我们在这项研究中提出了一种二维本构模型，用于结合连续损伤和嵌入强不连续性的小梁骨。该模型能够描述小梁骨组织的三个失效阶段，这里将其视为一种准脆性材料，假定应变和旋转很小，并且没有粘性、热或其他非机械效应。本模型的有限元实现使用恒应变三角形 (CST) 元素。位移跳跃向量通过局部（有限元）级的返回映射算法隐式求解，而全局平衡方程则通过牛顿-拉夫森方法处理。对所提出的骨小梁骨折模型的性能、准确性和适用性进行了评估，并根据实验测量进行了验证。