Shen Yanfeng, Cesnik Carlos E S
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
Ultrasonics. 2017 Feb;74:106-123. doi: 10.1016/j.ultras.2016.10.001. Epub 2016 Oct 6.
This article presents a parallel algorithm to model the nonlinear dynamic interactions between ultrasonic guided waves and fatigue cracks. The Local Interaction Simulation Approach (LISA) is further developed to capture the contact-impact clapping phenomena during the wave crack interactions based on the penalty method. Initial opening and closure distributions are considered to approximate the 3-D rough crack microscopic features. A Coulomb friction model is integrated to capture the stick-slip contact motions between the crack surfaces. The LISA procedure is parallelized via the Compute Unified Device Architecture (CUDA), which enables parallel computing on powerful graphic cards. The explicit contact formulation, the parallel algorithm, as well as the GPU-based implementation facilitate LISA's high computational efficiency over the conventional finite element method (FEM). This article starts with the theoretical formulation and numerical implementation of the proposed algorithm, followed by the solution behavior study and numerical verification against a commercial finite element code. Numerical case studies are conducted on Lamb wave interactions with fatigue cracks. Several nonlinear ultrasonic phenomena are addressed. The classical nonlinear higher harmonic and DC response are successfully captured. The nonlinear mode conversion at a through-thickness and a half-thickness fatigue crack is investigated. Threshold behaviors, induced by initial openings and closures of rough crack surfaces, are depicted by the proposed contact LISA model.
本文提出了一种用于模拟超声导波与疲劳裂纹之间非线性动态相互作用的并行算法。基于罚函数法，对局部相互作用模拟方法（LISA）进行了进一步开发，以捕捉波与裂纹相互作用过程中的接触-冲击拍击现象。考虑了初始开口和闭合分布，以近似三维粗糙裂纹的微观特征。集成了库仑摩擦模型，以捕捉裂纹表面之间的粘滑接触运动。通过计算统一设备架构（CUDA）对LISA程序进行并行化处理，这使得在功能强大的图形卡上进行并行计算成为可能。显式接触公式、并行算法以及基于GPU的实现方式，使得LISA相对于传统有限元方法（FEM）具有更高的计算效率。本文首先介绍了所提算法的理论公式和数值实现，随后进行了解决方案行为研究以及与商业有限元代码的数值验证。对兰姆波与疲劳裂纹的相互作用进行了数值案例研究。探讨了几种非线性超声现象。成功捕捉到了经典的非线性高次谐波和直流响应。研究了贯穿厚度和半厚度疲劳裂纹处的非线性模式转换。所提出的接触LISA模型描述了由粗糙裂纹表面的初始开口和闭合引起的阈值行为。
