Christian Willberg

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

This paper reviews the state-of-the-art in numerical wave propagation analysis. The main focus in that regard is on guided wave-based structural health monitoring (SHM) applications. A brief introduction to SHM and SHM-related problems is given, and various numerical methods are then discussed and assessed with respect to their capability of simulating guided wave propagation phenomena. A detailed evaluation of the following methods is compiled: (i) analytical methods, (ii) semi-analytical methods, (iii) the local interaction simulation approach (LISA), (iv) finite element methods (FEMs), and (v) miscellaneous methods such as mass–spring lattice models (MSLMs), boundary element methods (BEMs), and fictitious domain methods. In the framework of the FEM, both time and frequency domain approaches are covered, and the advantages of using high order shape functions are also examined.

Continuous mode conversion of Lamb waves in CFRP plates

Online damage detection in thin walled light weight structures with Lamb waves is one common way to develop structural health monitoring (SHM) systems. Lamb waves occur in multiple modes, which can convert into each other under special conditions. The effect of mode conversion of Lamb waves is a well known phenomenon. Typically mode conversion takes place at structural changes regarding the geometry and material, e.g. damage, cracks, delaminations, etc and can be used as a criterion to get information about the health of the structure. However, experimentally we observed an unexpected continuous mode conversion (CMC) of Lamb waves in a multi-layer composite plate partially made of fabric material, which means, e.g., that the symmetric S0-mode continuously converts into the A0-mode without passing a discontinuity. This effect causes a considerably more complex wavefield and makes the detection and localization of failures more complicated. In this work, the new phenomenon of CMC is described and investigated experimentally as well as numerically. (Some figures may appear in colour only in the online journal)

Development, Validation and Comparison of Higher Order Finite Element Approaches to Compute the Propagation of Lamb Waves Efficiently

When considering structural health monitoring (SHM) applications efficient and powerful numerical methods are required to predict the behavior of ultrasonic guided waves and to design SHM systems. The existing commercial explicit finite element analysis tools based on standard linear displacement elements quickly reach their limits when applied to ultrasonic waves in thin plates, so called Lamb waves. It is known that the required temporal and spatial resolution causes enormous computational costs. One resort to overcome this problem is the application of special finite elements utilizing higher order polynomial shape functions (p > 2). The current paper is focused on the development of such higher order finite elements and the verification of their accuracy and performance. In the paper we compare and evaluate the capabilities of spectral finite elements, p-version finite elements and isogeometric finite elements. Their advantages and disadvantages with respect to ultrasonic wave propagation problems are discussed and their properties are demonstrated by solving a benchmark problem. Higher order finite elements with varying polynomial degrees in longitudinal and transversal direction (anisotropic ansatz space) are investigated and convergence studies are performed. The results of the convergence studies are summarized and a guideline to estimate the optimal discretization is prepared. If the required accuracy is known, the proposed guideline provides a helpful means to determine both the element size and the polynomial degree template for a given model.

The Phenomenon of Continuous Mode Conversion of Lamb Waves in CFRP Plates

The effect of mode conversion of Lamb waves is a well known phenomenon. Lamb waves occur in multiple modes, which can transform into each other under special conditions. Typically mode conversion takes place at discrete positions inside a structure, e.g. damages and edges. However, we observed a continuous mode conversion in a multi-layer composite plate. The symmetric S0-mode converts continuously into the A0-mode without passing a macroscopic discontinuity. In the paper this phenomenon of continuous mode conversion is investigated experimentally as well as numerically.

Virtual Sensors for SHM using Isogeometric Piezoelectric Finite Elements

Purpose – A design of sensor networks for structural health monitoring (SHM) with guided waves poses a hard challenge. Therefore different approaches are possible. A known one is the usage of probability of detection (POD) criteria. Here, areas of potential impact sensitivity are calculated for every sensor which leads to a POD. The number of sensors is increased until a demanded POD is reached. However, these calculations are usually based on finite element methods and underlie different assumptions and approximations which can cause different inaccuracies. These limitations are avoided by using an experimental data basis for virtual sensors in this paper. The paper aims to discuss these issues. Design/methodology/approach – An air-coupled ultrasound scanning technique is used for guided wave investigations. Recorded displacements of a structure surface are used as stimulation of virtual sensors which can be designed by software and positioned within available data field. For the calculation of sensor si...

Higher Order Finite Element Methods

The efficiency of numerical methods for wave propagation analysis is essential, as very fine spatial and temporal resolutions are required in order to properly describe all the phenomena of interest, such as scattering, reflection, mode conversion, and many more. These strict demands originate from the fact that high-frequency ultrasonic guided waves are investigated. In the current chapter, we focus on the finite element method (FEM) based on higher order basis functions and demonstrate its range of applicability. Thereby, we discuss the p-FEM, the spectral element method (SEM), and the isogeometric analysis (IGA). Additionally, convergence studies demonstrate the performance of the different higher order approaches with respect to wave propagation problems. The results illustrate that higher order methods are an effective numerical tool to decrease the numerical costs and to increase the accuracy. Furthermore, we can conclude that FE-based methods are principally able to tackle all wave propagation-related problems, but they are not necessarily the most efficient choice in all situations.

REAL-TIME FEM OF SOFT TISSUES FOR VIRTUAL SURGERY

Endoscopic techniques require small perforation holes only as entries for optical and surgical instruments; such enabling the treatment of injuries with a minimized damage of the surrounding health tissue. But the surgeon has to operate in a 3D domain by looking at a distorted 2D image at the screen. It is well known, that a good surgeon needs a continuous training to perform such operations reliable in a top quality. To overcome the high costs and tight ethical restrictions of animal based education and training has result in an increasing development and application of virtual surgery simulators [1]. One of the main issues of surgery simulators is to ensure simultaneously the real time performance of the device, the high-level image representation and an acceptable force-feedback behavior. The basics of such simulators are mathematical models of the involved soft tissues, which have to perform in a realistic physical manner, with dynamic nonlinear large deformations, including the interaction of the different constituents (instrument/organ, organ/organ, organ by itself, cutting, bleeding etc). In the paper the focus is on realistic organ models and the realization of a fast contact search and reaction algorithm.Copyright