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TECHNICAL PAPERS

# Crack Identification in Thin Plates With Anisotropic Damage Model and Vibration Measurements

[+] Author and Article Information
D. Wu, S. S. Law

Department of Civil and Structural Engineering,  Hong Kong Polytechnic University, Yuk Choi Road, Hunghom Kowloon, Hong Kong

J. Appl. Mech 72(6), 852-861 (Feb 07, 2005) (10 pages) doi:10.1115/1.1985432 History: Received December 31, 2003; Revised February 07, 2005

## Abstract

Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed for a two-dimensional plate element with an edge-parallel crack. The cracked plate element is represented by a plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. Instead of using the effective stress concept, strain equivalence, or strain energy equivalence principles, the vector of damage variables is identified based on the principle of equivalent static and dynamic behaviors. A nonmodel-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison to results from existing strain energy equivalence theory.

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## Figures

Figure 1

The effective stiffness model from strain energy equivalence principle

Figure 2

Thin plate element hosting a through crack parallel to its edge

Figure 3

Figure 4

Finite element model of the cracked thin plate

Figure 5

Correction factor on stress intensity factor for finite plate

Figure 6

Identified crack parameter for the numerical example of thin plate

Figure 7

Diagram of the experimental system

Figure 8

(a) Artificial cracks (session I) in the plate specimen. (b) Finite element meshes to model the cracked plate specimen.

Figure 9

Damage variables from experiment and finite element model

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