The dynamic response of subsurface cracks in fiber reinforced composites is analytically studied. The response of layered half-space and three-layered plate with two interface cracks excited by a plane SH-wave and line load respectively are studied by formulating the problem as integral equations in the frequency domain. The governing equations along with boundary, regularity and continuity conditions across the interface are reduced to a coupled set of singular integral equations by using Betti's reciprocal theorem along with the Green's functions. In addition, the transient response of an orthotropic half-space with a subsurface crack subjected to inplane line load at an arbitrary angle is analyzed. Two new Green's functions for the uncracked medium are developed and used along with the representation theorem to derive the scattered field. Satisfaction of the traction free condition at the crack surfaces gives rise to a system of singular integral equations. Singular integrals involved in the analysis are computed numerically by removing the poles. Part of the integrals containing the poles are then obtained analytically by using residue theorem. The solution of singular integral equations are obtained by expanding the unknown crack opening displacements (COD) in terms of a complete set of Chebychev polynomials. The problem is first solved in the frequency domain, the time histories are then obtained numerically by inverting the spectra via Fast Fourier Transform (FFT) routine. Numerical results are presented for isotropic and anisotropic materials for several different crack geometries. The results show significant influence of crack geometries and material properties on the COD and surface response of composites.

Approved for public release; distribution is unlimited. / The objective of this study was to develop an analytical model of the basic hierarchical structure of the human bone. The model computed the stiffness of composite collagen fibers comprised of collagen fibrils and hydroxyapatite mineral crystals. Next, the stiffness of the concentric lamella was computed utilizing the stiffness of the collagen fibers and layer information. Finally, the effective stiffness of the bone was estimated. In order to determine the stiffness of the collagen fiber, a three-dimensional finite element model was developed and a simple analytical model was derived. The simple analytical model was validated using the finite element results. The lamination theory of unidirectional fibrous composites was used to calculate the stiffness of the lamella and eventually the bone stiffness. A series of parametric studies were conducted to understand what parameter(s) affected the stiffness of the bone most significantly. This information will be useful when an artificial bone structure is designed. / http://hdl.handle.net/10945/1123 / Lieutenant, United States Navy

The compressive behavior of continuous fiber composites is not as well understood as their tensile behavior because research and industrial applications have until recently focused on the latter. Furthermore, most theoretical and experimental studies on the compression of composites have examined the case of unidirectional specimens with fibers along the loading direction (0�� fibers). While this is a logical approach since it isolates the failure mode specific to this geometry (kinking), the study of multidirectional laminates is essential because these are used in all practical applications. Few theories model the compressive behavior of multidirectional laminates. None of the theories account for the stress field or the sequence and interaction of the various observed failure modes (kinking, delamination, matrix failure) specific to the multidirectional configuration. The principal objective of this investigation is to construct a realistic theory to model the compressive behavior of multidirectional composites. Compression experiments have repeatedly shown that the initial failure mode was in-plane kinking of 0�� fibers initiated at the edges of the specimens. We decided to base our compressive failure theory upon interlaminar stresses because in multidirectional laminates these are known to exist in a boundary layer along the edges. This required development of an analytical theory giving the amplitude of these stresses at the free edges. We then incorporated these stresses into a new general microbuckling equation for 0�� fibers. The global laminate failure strain was determined through several fiber and matrix failure criteria. Theoretical predictions were compared with experimental results obtained from compression testing of graphite/thermoplastic laminates with the same ply sequence but different off-axis ply angles. The theory correlated well with experiments and confirmed that in-plane kinking was the critical failure mode at low and medium angles, while revealing that out-of-plane buckling was responsible for failure at high angles. Furthermore, the theory correctly predicted the sequence of various fiber and matrix failure modes. / Graduation date: 1997

Graduation date: 1994

Thesis (Ph. D.)--School of Mechanical Engineering, Georgia Institute of Technology, 2004. Directed by Kenneth A. Cunefare. / Vita. Includes bibliographical references (leaves 129-136).

Thesis (M.S.)--West Virginia University, 2004. / Title from document title page. Document formatted into pages; contains ix, 70 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 69-70).

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Dr. Steve Johnson; Committee Member: Dr. Jianmin Qu; Committee Member: Dr. Rick Neu. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, March 2003. / Thesis advisor(s): Young W. Kwon. Includes bibliographical references (p. 45). Also available online.

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