Stress Analysis of Layered Elastic Solids With Cracks Using the Fast Fourier Transform and Conjugate Gradient Techniques

The fast Fourier transform (FFT) technique has recently been applied to stress analyses of layered elastic solids, with a great deal of success. However, the existing FFT-based methods are limited to intact solids. This paper explores the possibility of using FFT for stress analyses of layered elastic solids containing cracks. A new numerical approach is developed by combining three-dimensional FFT with the theory of periodic eigenstrain and the conjugate gradient method. The new method is primarily designed for analyzing complex three-dimensional crack patterns in layered solids, such as those produced in thin protective coatings by roughness-induced contact stresses. The method should be particularly advantageous for studying crack propagation in coatings, as it does not require remeshing when the crack shape changes. Numerical examples illustrating advantages as well as limitations of the method are presented. Some unexpected results that were obtained for multiple cracks in a thin coating are discussed.