The effective transverse response of fiber reinforced composites with nonlinear interfaces

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Alan J. Levy


Interface bonding, Composite response, Fiber-reinforced, Nonlinear interfaces, Composites

Subject Categories

Materials Science and Engineering | Mechanical Engineering


In this dissertation detailed analyses of two previously unsolved problems in the mechanics of composite media are presented. Both related problems involve the prediction of the effective response of a class of nonlinear two-phase composite consisting of linear elastic inclusions randomly embedded in a linear elastic matrix and separated from it by interfaces characterized by general nonlinear cohesive zones of vanishing thickness. The first problem is to predict the response of such a composite consisting of a dilute distribution of inclusions. The second, more difficult problem concerns the prediction of composite response when the inclusions are distributed at finite concentration.

Throughout this work the direct method of composite materials theory is employed, which consists of writing exact relations that mediate between local nonlinear inclusion fields and global nonlinear aggregate response. For the dilute estimate local fields are obtained from a representative inclusion problem consisting of a solitary inclusion separated from a remotely stressed (or strained) unbounded matrix by a nonlinear cohesive zone. To account for aspects of inclusion-inclusion interaction at finite concentration the Mori-Tanaka mean field model is employed to predict local inclusion fields. A proof that self-consistency is preserved for this model when interfaces are allowed to separate nonlinearly is also presented. Both the dilute and mean field problems give rise to effective constitutive relations that fall within the conceptual framework of continuum damage mechanics, i.e., stress-strain relations containing internal "damage" variables which themselves are governed by "damage" evolution relations. In this work however the damage variables have geometrical meaning on the microscale. They are expansion coefficients arising in an eigenfunction representation of displacement jump at a representative inclusion-matrix interface. Also, in this work damage evolution equations are not phenomenological but are exact (nonlinear) integral equations.

Detailed calculations of stress-strain response are presented for the case where the inclusions are taken to be infinitely long circular cylindrical fibers and the loading is assumed to be transverse to the fiber direction. The focus is on this case because transverse shear response is the most difficult to predict (as compared to axial tension and anti-plane shear). In this work interfaces are generally characterized by nonlinear relations that allow for normal separation and shear slip and a number of different models are used in the calculations. Graphs of effective stress-strain behaviour are obtained which demonstrate the effects of interface parameters and fiber volume concentration on response. In particular the effects of these parameters on bifurcation of equilibrium separation in the solitary fiber problem and on overall composite stability are demonstrated.


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