Interface problems in micromechanics and effective composite property analysis

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Alan J. Levy


Micromechanics, Fractures

Subject Categories

Engineering | Mechanical Engineering


This dissertation investigates the mechanical response of composite materials spanning three length scales using a multiscale modeling strategy. Microscale or micromechanical analysis considers phenomena at length scales on the order of reinforcement dimensions. Effective property analysis at mesoscale maps statistically representative domains onto continuum points using a representative volume element. Analysis of composite structures subjected to specific loading configurations occurs at the macroscale.

At the microscale level, the mechanics of a single composite cylinder with nonlinear interface between the inclusion and matrix is investigated. Here the nonlinear interface is defined to allow separation or slip of the fiber from the matrix according to prescribed nonlinear constitutive relations. Two distinct problems are considered: (a) when the bulk materials (i.e., the inclusion and matrix) are viscoelastic, and the interface is uniform; and (b) when the bulk materials are elastic, and the interface has (possibly crack-like) imperfections (i.e., is nonuniform). The solution for (a) extends the existing results of rigid interface viscoelastic composites to the realm of distributed composite damage. The study in (b) complements existing analyses of imperfection decohesion along straight interfaces, and of an arc crack at the interface between a circular elastic inclusion and an elastic matrix.

Analysis at the microscale is of interest in its own right, and is fundamental to the study of effective response of composite materials at the mesoscale. Research at this scale concerns how microstructural features determine the effective composite response. It involves the development of rational micromechanical models for viscoelastic composite response featuring nonlinear, uniform matrix-inclusion interfaces for the composite cylinder microstructure. The dilute estimate of the effective response of a composite with nonlinear, nonuniform interfaces is also analyzed. Specifically, transverse bulk response is obtained for a composite whose interfacial defects are randomly oriented.

At the macroscale level, structural response of nonlinear, uniform interface composite materials is studied through the constitutive relations obtained from effective property analyses. This is done primarily for the pure torsion of a circular composite rod containing unidirectional fibers aligned parallel to the rod axis. Quasistatic loading of linear elastic matrix composites, and time-dependent response of linear viscoelastic matrix composites are considered, respectively.


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