Jacobs Nathan T, Cortes Daniel H, Vresilovic Edward J, Elliott Dawn M
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 220 South 33rd Street, Philadelphia, PA 19104, USA.
J Biomech Eng. 2013 Feb;135(2):021004. doi: 10.1115/1.4023503.
Planar biaxial tension remains a critical loading modality for fibrous soft tissue and is widely used to characterize tissue mechanical response, evaluate treatments, develop constitutive formulas, and obtain material properties for use in finite element studies. Although the application of tension on all edges of the test specimen represents the in situ environment, there remains a need to address the interpretation of experimental results. Unlike uniaxial tension, in biaxial tension the applied forces at the loading clamps do not transmit fully to the region of interest (ROI), which may lead to improper material characterization if not accounted for. In this study, we reviewed the tensile biaxial literature over the last ten years, noting experimental and analysis challenges. In response to these challenges, we used finite element simulations to quantify load transmission from the clamps to the ROI in biaxial tension and to formulate a correction factor that can be used to determine ROI stresses. Additionally, the impact of sample geometry, material anisotropy, and tissue orientation on the correction factor were determined. Large stress concentrations were evident in both square and cruciform geometries and for all levels of anisotropy. In general, stress concentrations were greater for the square geometry than the cruciform geometry. For both square and cruciform geometries, materials with fibers aligned parallel to the loading axes reduced stress concentrations compared to the isotropic tissue, resulting in more of the applied load being transferred to the ROI. In contrast, fiber-reinforced specimens oriented such that the fibers aligned at an angle to the loading axes produced very large stress concentrations across the clamps and shielding in the ROI. A correction factor technique was introduced that can be used to calculate the stresses in the ROI from the measured experimental loads at the clamps. Application of a correction factor to experimental biaxial results may lead to more accurate representation of the mechanical response of fibrous soft tissue.
平面双轴拉伸仍然是纤维软组织的一种关键加载方式，被广泛用于表征组织的力学响应、评估治疗效果、推导本构公式以及获取用于有限元研究的材料特性。尽管在测试样本的所有边缘施加张力代表了原位环境，但仍需要解决实验结果的解释问题。与单轴拉伸不同，在双轴拉伸中，加载夹具处施加的力不会完全传递到感兴趣区域（ROI），如果不考虑这一点，可能会导致材料表征不当。在本研究中，我们回顾了过去十年的双轴拉伸文献，指出了实验和分析方面的挑战。针对这些挑战，我们使用有限元模拟来量化双轴拉伸中从夹具到ROI的载荷传递，并制定一个校正因子，可用于确定ROI应力。此外，还确定了样本几何形状、材料各向异性和组织取向对校正因子的影响。在方形和十字形几何形状以及所有各向异性水平下，都明显存在大的应力集中。一般来说，方形几何形状的应力集中比十字形几何形状更大。对于方形和十字形几何形状，与各向同性组织相比，纤维平行于加载轴排列的材料降低了应力集中，导致更多的外加负载传递到ROI。相比之下，纤维增强样本的取向使得纤维与加载轴成一定角度排列，在夹具上产生了非常大的应力集中，并在ROI中产生了屏蔽效应。引入了一种校正因子技术，可用于根据夹具处测量的实验载荷计算ROI中的应力。将校正因子应用于双轴拉伸实验结果可能会更准确地表示纤维软组织的力学响应。
