Rouze Ned C, Caenen Annette, Nightingale Kathryn R
Department of Biomedical Engineering, Duke University, Durham, NC 27708, United States of America.
Department of Electronics and Information Systems, Ghent University, Ghent, Belgium.
Phys Med Biol. 2022 Apr 27;67(9). doi: 10.1088/1361-6560/ac5bfc.
Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch.Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities.Sample results are presented for the Arruda-Boyce, Mooney-Rivlin, and Isihara material models using model parameters previously determined in a phantom.Results for the Mooney-Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda-Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.
由于传播方向、剪切波偏振和材料对称性之间存在复杂关系，在各向异性材料中，通过观察剪切波传播来确定材料的弹性特性是困难的。在本研究中，我们推导了在具有单轴拉伸的不可压缩超弹性材料中，SH和SV传播模式的相速度作为传播方向函数的表达式。通过在初始有限变形上叠加增量小振幅运动，将波动纳入材料模型。利用从材料应变能函数导出的柯西应力张量构建SH和SV传播模式的运动方程。SH和SV传播模式的群速度由与角度相关的相速度导出。使用先前在体模中确定的模型参数，给出了Arruda-Boyce、Mooney-Rivlin和Isihara材料模型的示例结果。Mooney-Rivlin和Isihara模型的结果表明存在剪切分裂，即SH和SV传播模式在穿过材料对称轴传播时具有不相等的群速度。此外，对于足够大的拉伸，Arruda-Boyce和Isihara材料模型在与材料对称轴成约15°角处显示出SV模式具有三值群速度的尖点结构。
