Nolan D R, McGarry J P
Biomedical Engineering, National University of Ireland, Galway, Galway, Ireland.
Biomedical Engineering, National University of Ireland, Galway, Galway, Ireland.
J Mech Behav Biomed Mater. 2016 Jan;53:187-199. doi: 10.1016/j.jmbbm.2015.08.019. Epub 2015 Aug 19.
Biaxial tests are commonly used to investigate the mechanical behaviour of soft biological tissues and polymers. In the current paper we uncover a fundamental problem associated with the calculation of material stress from measured force in standard biaxial tests. In addition to measured forces, localised unmeasured shear forces also occur at the clamps and the inability to quantify such forces has significant implications for the calculation of material stress from simplified force-equilibrium relationships. Unmeasured shear forces are shown to arise due to two distinct competing contributions: (1) negative shear force due to stretching of the orthogonal clamp, and (2) positive shear force as a result of material Poisson-effect. The clamp shear force is highly dependent on the specimen geometry and the clamp displacement ratio, as consequently, is the measured force-stress relationship. Additionally in this study we demonstrate that commonly accepted formulae for the estimation of material stress in the central region of a cruciform specimen are highly inaccurate. A reliable empirical correction factor for the general case of isotropic materials must be a function of specimen geometry and the biaxial clamp displacement ratio. Finally we demonstrate that a correction factor for the general case of non-linear anisotropic materials is not feasible and we suggest the use of inverse finite element analysis as a practical means of interpreting experimental data for such complex materials.
双轴测试常用于研究软生物组织和聚合物的力学行为。在当前论文中，我们揭示了标准双轴测试中从测量力计算材料应力时存在的一个基本问题。除了测量力外，夹具处还会出现局部未测量的剪切力，而无法量化这些力对根据简化的力平衡关系计算材料应力具有重大影响。结果表明，未测量的剪切力是由两种不同的相互竞争的因素引起的：（1）由于正交夹具拉伸产生的负剪切力，以及（2）材料泊松效应导致的正剪切力。夹具剪切力高度依赖于试样几何形状和夹具位移比，因此测量的力-应力关系也如此。此外，在本研究中我们证明，用于估计十字形试样中心区域材料应力的常用公式非常不准确。对于各向同性材料的一般情况，可靠的经验校正因子必须是试样几何形状和双轴夹具位移比的函数。最后，我们证明对于非线性各向异性材料的一般情况，校正因子是不可行的，并且我们建议使用逆有限元分析作为解释此类复杂材料实验数据的一种实用方法。
