Mathematical modeling of adhesive layer cracks utilizing integral equations
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Within recent years, Crack analysis in adhesive layers has become a topic of interest for many researchers. A common model which is used incorporates a 3-region elasticity problem consisting of only 2 materials, the adhesive layer bounded by 2 layers of a stiffer elastic substrate. Cracks have been experimentally observed to propagate in straight paths as well as wavy paths within the adhesive layer and even at its boundaries.
A theoretical model based on work done by Fleck, Hutchinson, and Suo (1991) is used to study crack path selection. Complex stress potential functions are employed to develop a symbolic derivation. The method of distributed dislocations is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were used to study the computational aspects of the problem. The focus of the research was to develop efficient modular software packages to be run on a standard PC system. Several numerical techniques were utilized to reduce computational time and control the numerical accuracy of the problem. Some of these techniques included a "numerical freeze" algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented.
- Masters Theses