Elasticity solutions are developed for finite multilayered domains weakened by aligned cracks that are in a state of generalized plane deformation under two types of end constraints. Multilayered domains consist of an arbitrary number of finite-length and finite-height isotropic, orthotropic or monoclinic layers typical of differently oriented, unidirectionally reinforced laminas arranged in any sequence in the plane in which the analysis is conducted. The solution methodology admits any number of arbitrarily distributed interacting or noninteracting cracks parallel to the horizontal bounding surfaces at specified elevations or interfaces. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to a system of coupled singular integral equations of the Cauchy type with kernels formulated in terms of the unknown displacement discontinuities. Solutions to these integral equations are obtained by representing the unknown interfacial displacement discontinuities in terms of Jacobi or Chebyshev polynomials with unknown coefficients. The application of orthogonality properties of these polynomials produces a system of algebraic equations that determines the unknown coefficients. Stress intensity factors and energy release rates are derived from dominant parts of the singular integral equations. In Part I of this paper we outline the analytical development of this technique. In Part II we verify this solution and present new fundamental results relevant to the existing and emerging technologies.
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January 2007
Technical Papers
Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part I: Theory
Linfeng Chen,
Linfeng Chen
Civil Engineering Department,
University of Virginia
, Charlottesville, VA 22904-4742
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Marek-Jerzy Pindera
Marek-Jerzy Pindera
Civil Engineering Department,
University of Virginia
, Charlottesville, VA 22904-4742
Search for other works by this author on:
Linfeng Chen
Civil Engineering Department,
University of Virginia
, Charlottesville, VA 22904-4742
Marek-Jerzy Pindera
Civil Engineering Department,
University of Virginia
, Charlottesville, VA 22904-4742J. Appl. Mech. Jan 2007, 74(1): 128-143 (16 pages)
Published Online: April 1, 2006
Article history
Received:
December 18, 2005
Revised:
April 1, 2006
Connected Content
This is a correction to:
Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part II: Numerical Results
Citation
Chen, L., and Pindera, M. (April 1, 2006). "Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part I: Theory." ASME. J. Appl. Mech. January 2007; 74(1): 128–143. https://doi.org/10.1115/1.2201883
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