In this paper the effect of finite interface strength, and possible debonding, on the macroscopic response of a sample of fiber-reinforced composite material is computationally investigated via the finite element method. The sample consists of several fibers embedded in a homogeneous matrix, aligned in the longitudinal direction, and randomly distributed in the transverse direction. Plane strain conditions are enforced. Both the matrix and the fibers are assumed to behave in a linearly elastic manner. The approach is to employ unilateral constraints to model interface strength limits. However, because the debonded surfaces are unknown a priori, and depend on the internal fields, the originally linear elastic problem becomes nonlinear, and hence it must be solved in an iterative manner. Accordingly, a nested contact algorithm scheme is developed, based on an active set strategy, to efficiently simulate multiple interacting unilateral constraints. The nesting allows the nonlinear problem within a Newton step to be transformed into a sequence of linear sub-problems. Using the algorithm, numerical tests are performed on a widely used Aluminum/Boron fiber-reinforced composite combination to determine the effects of debonding on changes in macroscopic responses as a function of interface strength and loading. It is shown that the amount of debonded surface area correlates perfectly with the loss in the macroscopic stiffness of the material. This result lends credence to damage evolution laws, for homogenized material models, which employ interface separation surface area as the primary internal damage variable.
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