Ciampa Francesco, Barbieri Ettore, Meo Michele
Material Research Centre, Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom.
The School of Engineering and Material Science, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.
J Acoust Soc Am. 2014 Jun;135(6):3209-20. doi: 10.1121/1.4868476.
This paper presents a nonlinear elastic material model able to simulate the nonlinear effects generated by the interaction of acoustic/ultrasonic waves with damage precursors and micro-cracks in a variety of materials. Such a constitutive model is implemented in an in-house finite element code and exhibits a multiscale nature where the macroscopic behavior of damaged structures can be represented through a contribution of a number of mesoscopic elements, which are composed by a statistical collection of microscopic units. By means of the semi-analytical Landau formulation and Preisach-Mayergoyz space representation, this multiscale model allows the description of the structural response under continuous harmonic excitation of micro-damaged materials showing both anharmonic and dissipative hysteretic effects. In this manner, nonlinear effects observed experimentally, such as the generation of both even and odd harmonics, can be reproduced. In addition, by using Kelvin eigentensors and eigenelastic constants, the wave propagation problem in both isotropic and orthotropic solids was extended to the three-dimensional Cartesian space. The developed model has been verified for a number of different geometrical and material configurations. Particularly, the influence of a small region with classical and non-classical elasticity and the variations of the input amplitudes on the harmonics generation were analyzed.
本文提出了一种非线性弹性材料模型，该模型能够模拟声波/超声波与各种材料中的损伤前驱体和微裂纹相互作用所产生的非线性效应。这样一个本构模型在一个内部有限元代码中实现，具有多尺度性质，其中受损结构的宏观行为可以通过许多细观单元的贡献来表示，这些细观单元由微观单元的统计集合组成。借助半解析朗道公式和普雷萨克 - 迈尔戈伊兹空间表示，这个多尺度模型允许描述微损伤材料在连续谐波激励下的结构响应，呈现出非谐波和耗散滞后效应。通过这种方式，可以再现实验中观察到的非线性效应，如偶次和奇次谐波的产生。此外，通过使用开尔文本征张量和本征弹性常数，各向同性和正交各向异性固体中的波传播问题被扩展到三维笛卡尔空间。所开发的模型已针对许多不同的几何和材料配置进行了验证。特别是，分析了具有经典和非经典弹性的小区域的影响以及输入振幅变化对谐波产生的影响。
