Hosseini Hadi S, Horák Martin, Zysset Philippe K, Jirásek Milan
Faculty of Medicine, Institute for Surgical Technology and Biomechanics, University of Bern, Stauffacherstr. 78, Bern, CH-3014, Switzerland.
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Zikova 1903/4, Praha 6, 166 36, Czech Republic.
Int J Numer Method Biomed Eng. 2015 Nov;31(11). doi: 10.1002/cnm.2728. Epub 2015 Jun 14.
Investigation of trabecular bone strength and compaction is important for fracture risk prediction. At 1-2% compressive strain, trabecular bone undergoes strain softening, which may lead to numerical instabilities and mesh dependency in classical local damage-plastic models. The aim of this work is to improve our continuum damage-plastic model of bone by reducing the influence of finite element mesh size under large compression.
This spurious numerical phenomenon may be circumvented by incorporating the nonlocal effect of cumulated plastic strain into the constitutive law. To this end, an over-nonlocal implicit gradient model of bone is developed and implemented into the finite element software ABAQUS using a user element subroutine. The ability of the model to detect the regions of bone failure is tested against experimental stepwise loading data of 16 human trabecular bone biopsies.
The numerical outcomes of the nonlocal model revealed reduction of finite element mesh dependency compared with the local damage-plastic model. Furthermore, it helped reduce the computational costs of large-strain compression simulations.
To the best of our knowledge, the proposed model is the first to predict the failure and densification of trabecular bone up to large compression independently of finite element mesh size. The current development enables the analysis of trabecular bone compaction as in osteoporotic fractures and implant migration, where large deformation of bone plays a key role.
研究小梁骨强度和压实情况对于骨折风险预测至关重要。在1%-2%的压缩应变下，小梁骨会发生应变软化，这可能导致经典局部损伤-塑性模型出现数值不稳定性和网格依赖性。本研究的目的是通过减少大压缩下有限元网格尺寸的影响，改进我们的骨连续损伤-塑性模型。
这种虚假的数值现象可以通过将累积塑性应变的非局部效应纳入本构定律来规避。为此，开发了一种骨的过非局部隐式梯度模型，并使用用户单元子程序在有限元软件ABAQUS中实现。该模型检测骨失效区域的能力通过16例人小梁骨活检的实验逐步加载数据进行测试。
与局部损伤-塑性模型相比，非局部模型的数值结果显示有限元网格依赖性降低。此外，它有助于降低大应变压缩模拟的计算成本。
据我们所知，所提出的模型是第一个独立于有限元网格尺寸预测小梁骨直至大压缩时的失效和致密化的模型。当前的进展使得能够分析小梁骨压实情况，如在骨质疏松性骨折和植入物迁移中，其中骨的大变形起着关键作用。
