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Viscoelastic-stiffness tensor of anisotropic media from oscillatory numerical experiments

机译：各向异性数值模拟的粘弹性刚度张量

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摘要

A finely layered media behaves as an anisotropic medium when the dominat wavelengths are much larger than the layer thickness. If the constituent are anelastic, a generalization of Backus averaging predicts that the medium is effectively a transversely isotropic viscoelastic (TIV) medium. To test and validate the theory, we present a novel procedure to determine the complex and frequency-dependent stiffness components of a TIV medium. The methodology consists in performing numerical compressibility and shear harmonic tests on a representative sample of the material. These tests are described by a collection of non-coercive elliptic boundary-value problems formulated in the space-frequency domain, which are solved using a Galerkin finite-element procedure. Results on the existence and uniqueness of the continuous and discrete problems as well as optimal error estimates for the Galerkin finite-element method are derived. Numerical examples illustrates the implementation of the numerical oscillatory tests to determine the set of complex and frequency-dependent effective TIV coefficients and the associated phase velocities and quality factors for a periodic sequence of epoxy and glass thin layers. The results are compared to the analytical phase velocities and quality factors predicted by the Backus/Carcione theory.
机译：当主波长远大于层厚度时，精细的介质充当各向异性介质。如果成分是非弹性的，则Backus平均的一般化将预测该介质实际上是横向各向同性的粘弹性（TIV）介质。为了测试和验证该理论，我们提出了一种新颖的程序来确定TIV介质的复杂且依赖于频率的刚度分量。该方法包括对材料的代表性样品进行数值可压缩性和剪切谐波测试。这些测试是通过在空频域中公式化的非矫正椭圆形边值问题集合来描述的，这些问题使用Galerkin有限元程序来解决。得出有关连续和离散问题的存在与唯一性的结果，以及Galerkin有限元方法的最佳误差估计。数值示例说明了数字振动测试的实现，以确定环氧树脂和玻璃薄层的周期性序列的一组复杂且与频率相关的有效TIV系数以及相关的相速度和品质因数。将结果与Backus / Carcione理论预测的分析相速度和质量因子进行比较。

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