Manda Krishnagoud, Wallace Robert J, Xie Shuqiao, Levrero-Florencio Francesc, Pankaj Pankaj
School of Engineering, The University of Edinburgh, The King's Buildings, EH9 3DW, Edinburgh, UK.
Department of Orthopaedics, The University of Edinburgh, Chancellors building, EH16 4SB, Edinburgh, UK.
Biomech Model Mechanobiol. 2017 Feb;16(1):173-189. doi: 10.1007/s10237-016-0809-y. Epub 2016 Jul 20.
The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness-density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep-recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples ([Formula: see text]). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery's nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep-recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening-softening behaviour with increasing stress.
小梁骨的与时间无关的弹性特性已得到广泛研究，并且已经提出了几种刚度-密度关系。尽管人们认识到小梁骨表现出与时间相关的力学行为，这是粘弹性材料的一种特性，但对这种行为的表征受到的关注有限。本研究的目的是通过一系列压缩蠕变-恢复实验来研究牛小梁骨的与时间相关的行为，并确定其非线性本构粘弹性材料参数。对圆柱形牛小梁骨样本（[公式：见正文]）进行了多载荷下的单轴压缩蠕变和恢复实验。发现蠕变响应很显著，并且即使在低应力/应变水平下也总是由可恢复和不可恢复应变组成。还发现这种响应随施加的应力呈非线性变化。开发了一种系统方法，用于从总的实验应变响应中分离出可恢复（非线性粘弹性）和不可恢复（永久）应变。我们发现沙佩里的非线性粘弹性本构模型描述了小梁骨的粘弹性响应，并从多载荷蠕变-恢复（MLCR）实验中估计了与该模型相关的参数。发现非线性粘弹性恢复柔度随应力水平增加呈现先减小后增加的趋势，这表明由于蠕变，小梁骨可能存在硬化和软化行为。从MLCR测试中获得的参数，以应力的二阶多项式函数表示，对所有样本都显示出类似的趋势，并且也表明随着应力增加存在硬化-软化行为。
