A generalized fractional-order elastodynamic theory for non-local attenuating media
A generalized fractional-order elastodynamic theory for non-local attenuating media
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DOI：
10.1098/rspa.2020.0200
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发表时间：
2020-06-24
影响因子：
3.5
通讯作者：
Semperlotti, Fabio
中科院分区：
文献类型：
--
作者：
Patnaik, Sansit;Semperlotti, Fabio
本研究提出了一种广义弹性动力学理论，分数阶算子的基础上，能够模拟非本地衰减固体和复杂的非本地接口的弹性波的传播。经典的弹性动力学不能捕捉混合场输运过程，其特征在于同时传播和扩散。建议的连续介质力学配方，它结合了分数算子在时间和空间，提供了无与伦比的能力来预测最多样化的组合的多尺度，非本地，耗散和衰减弹性能量传输机制。尽管这一理论的许多功能和广泛的应用，这项工作的重点是行为和建模能力的空间分数项和其对固体的弹性动力学的影响。我们还推导出一个广义分数阶版本的折射和相应的菲涅耳系数的斯涅耳定律。这个公式允许预测的行为完全耦合的弹性波与非本地接口相互作用。通过直接数值模拟验证了理论结果。
This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non-local interfaces. Classical elastodynamics cannot capture hybrid field transport processes that are characterized by simultaneous propagation and diffusion. The proposed continuum mechanics formulation, which combines fractional operators in both time and space, offers unparalleled capabilities to predict the most diverse combinations of multiscale, non-local, dissipative and attenuating elastic energy transport mechanisms. Despite the many features of this theory and the broad range of applications, this work focuses on the behaviour and modelling capabilities of the space-fractional term and on its effect on the elastodynamics of solids. We also derive a generalized fractional-order version of Snell's Law of refraction and of the corresponding Fresnel's coefficients. This formulation allows predicting the behaviour of fully coupled elastic waves interacting with non-local interfaces. The theoretical results are validated via direct numerical simulations.