Dataset for: An explicit microFE approach to investigate the post-yield behaviour of trabecular bone under large deformations

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic and yield material properties, which are typically determined by implicit μFE analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.均质化有限元（Homogenised finite element, FE）分析能够预测骨质疏松相关骨折，且可在临床场景中发挥实用价值。有限元分析的预测结果取决于表观、非均质、各向异性的弹性与屈服材料特性，这类特性通常通过骨小梁的微观有限元（μFE）隐式分析得到。本研究旨在探索一种显式微观有限元方法，用以确定骨小梁在弹性与屈服特性之外的表观屈服后行为。骨组织的材料行为采用弹塑性本构描述，其冯·米塞斯（von Mises）屈服准则辅以平面帽型硬化，以适配正静水压力条件，区分拉伸与压缩状态下的屈服后行为。研究校准了拉伸与压缩两种工况下的极限应变，用于触发单元删除并复现骨小梁的损伤过程。为评估网格的影响，本研究开展了收敛性分析。针对三个体积分数依次递增的人体骨小梁样本，施加了采用周期性兼容混合均匀边界条件的13种载荷工况，同时探究了大应变条件下的致密化效应。收敛性分析结果显示，表观极限应力与应变强烈依赖于单元尺寸。研究团队在归一化应力空间中成功拟合得到骨小梁的表观二次强度曲面，致密化效应的复现结果与既往实验结果吻合良好。本研究证实了显式有限元建模方法与单元删除技术在通过微观有限元分析复现骨小梁损伤过程中的应用潜力。不过，在兼顾实际计算时长的前提下，妥善处理网格敏感性仍是一项颇具挑战性的工作。