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

I. A. Polonsky; L. M. Keer

doi:10.1115/1.1381394

Journal of Applied Mechanics | Volume 68 | Issue 5 | TECHNICAL PAPERS

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TECHNICAL PAPERS

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

I. A. Polonsky and L. M. Keer

[+] Author and Article Information

I. A. Polonsky, L. M. Keer

Department of Civil Engineering, Northwestern University, Evanston, IL 60208-3109

J. Appl. Mech 68(5), 708-714 (Mar 13, 2001) (7 pages) doi:10.1115/1.1381394 History: Received August 21, 2000; Revised March 13, 2001

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Layered solid containing contact-induced cracks (shown as thick black lines). Counterpart roughness is exaggerated. The y-direction is normal to the picture plane.

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Discretization of the cracked layer. Grid nodes are shown as circles. Nodes carrying eigenstrain are filled.

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Crack-opening displacement distribution along a crack radius for a penny-shaped crack: numerical solution (diamonds) and analytical solution (solid line)

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Multiple cracks in a thin coating: (x,z) view (a) and (y,z) view (b)

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Distribution of the normal stress σ_xx in the main crack plane for tensile loading; single crack case (a) and multiple crack cases (b)

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Distribution of the shear stress σ_xz in the main crack plane for contact loading: single crack case (a) and multiple crack case (b)

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Polonsky IA, Keer LM. Stress Analysis of Layered Elastic Solids With Cracks Using the Fast Fourier Transform and Conjugate Gradient Techniques. ASME. J. Appl. Mech. 2001;68(5):708-714. doi:10.1115/1.1381394.

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

References

Figures

Layered solid containing contact-induced cracks (shown as thick black lines). Counterpart roughness is exaggerated. The y-direction is normal to the picture plane.

Discretization of the cracked layer. Grid nodes are shown as circles. Nodes carrying eigenstrain are filled.

Crack-opening displacement distribution along a crack radius for a penny-shaped crack: numerical solution (diamonds) and analytical solution (solid line)

Multiple cracks in a thin coating: (x,z) view (a) and (y,z) view (b)

Distribution of the normal stress σ_xx in the main crack plane for tensile loading; single crack case (a) and multiple crack cases (b)

Distribution of the shear stress σ_xz in the main crack plane for contact loading: single crack case (a) and multiple crack case (b)

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

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

References

Figures

Layered solid containing contact-induced cracks (shown as thick black lines). Counterpart roughness is exaggerated. The y-direction is normal to the picture plane.

Discretization of the cracked layer. Grid nodes are shown as circles. Nodes carrying eigenstrain are filled.

Crack-opening displacement distribution along a crack radius for a penny-shaped crack: numerical solution (diamonds) and analytical solution (solid line)

Multiple cracks in a thin coating: (x,z) view (a) and (y,z) view (b)

Distribution of the normal stress σxx in the main crack plane for tensile loading; single crack case (a) and multiple crack cases (b)

Distribution of the shear stress σxz in the main crack plane for contact loading: single crack case (a) and multiple crack case (b)

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

Distribution of the normal stress σ_xx in the main crack plane for tensile loading; single crack case (a) and multiple crack cases (b)

Distribution of the shear stress σ_xz in the main crack plane for contact loading: single crack case (a) and multiple crack case (b)