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Publication Date



UM campus only

Degree Type


Degree Name

Doctor of Philosophy (PHD)


Mechanical Engineering (Engineering)

Date of Defense


First Committee Member

Qingda Yang

Second Committee Member

Singiresu S. Rao

Third Committee Member

Xiangyang Zhou

Fourth Committee Member

Jizhou Song

Fifth Committee Member

Brian Metrovich


Advanced composites are playing a rapidly increasing role in all fields of material and structural related engineering practices. Damage tolerance analysis must be a critical integral part of composite structural design. The predictive capabilities of existing models have met with limited success because they typically can not account for multiple damage evolution and their coupling. As a result, current composite design is heavily dependent upon lengthy and costly test programs and empirical design methods. There is an urgent need for efficient numerical tools that are capable of analyzing the progressive failure caused by nonlinearly coupled, multiple damage evolution in composite materials. Such numerical tools are a necessity in achieving virtual testing of composites and other heterogeneous materials. In this thesis, an advanced finite element method named augmented finite element method (A-FEM) has been developed. This method is capable of incorporating nonlinear cohesive damage descriptions for major damage modes observed in composite materials. It also allows for arbitrary nucleation and propagation of such cohesive damages upon satisfactory of prescribed initiation and propagation criterion. Major advantages of the A-FEM include: 1) arbitrary cohesive cracking without the need of remeshing; 2) full compatibility with existing FEM packages; and 3) easy inclusion of intra-element material heterogeneity. The numerical capabilities of the A-FEM have been demonstrated through direct comparisons between prediction results and experimental observations of typical composite tests including 3-point bending of unidirectional laminates, open-hole tension of quasi-isotropic laminates, and double-notched tension of orthogonal laminates. In all these tests, A-FEM can predict not only the qualitative damage patterns but also quantitatively the nonlinear stress-strain curves and other history-dependent results. The excellent numerical capability of A-FEM in accurately accounting for multiple cracking in composites enables the use of A-FEM as a multi-scale numerical platform for virtual testing of composites. This has been demonstrated by a series of representative volume element (RVE) analyses which explicitly considered microscopic matrix cracking and fiber matrix interface debonding. In these cases the A-FEM successfully predicted the cohesive failure descriptions which can be used for macroscopic composite failure analyses. At the sublaminate scale, the problem of a transverse tunneling crack and its induced local delamination has been studied in detail. Two major coupling modes, which depends on the mode-I to mode-II fracture toughness ratio and cohesive strength values, has been revealed and their implications in composite engineering has been fully discussed. Finally, future improvements to the A-FEM so that it can be more powerful in serving as a numerical platform for virtual testing of composites are discussed.


Representative Volume Element; Fracture; Cohesive Zone Model; Finite Element Method; Laminate; Composite