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A method is applied for the study of the field distributions in
metal matrix fiber reinforced composites with periodic microstructure in which
localized damage exists in the form of complete or partial fiber loss and
crack. In addition, the behavior of ceramic/metal periodically layered
composites with a single broken ceramic layer is determined. The pro-posed
analysis is based on continuum damage mechanics considerations, and the method
of solution combines three distinct approaches. In the first one, referred to
as the representative cell method, the periodic composite domain is reduced, in
conjunction with the discrete Fourier transform to a finite domain problem of a
single representative cell. This method has been previously applied on linear
thermoelastic, smart and electrostrictive composites, but is presently extended
and applied on elastoplastic composites (presently deformation and incremental
plasticity). In the second approach, the appropriate far-field boundary
conditions in the transform domain are applied in conjunction with the
high-fidelity generalized method of cells micromechanical model for the
prediction of the macroscopic behavior of the inelastic composite. The third
approach consists of the application of the inelastic higher-order theory for
the computation of the elastoplastic field in the transform domain. An inverse
transform provides the actual field. The effect of damage is included in the
analysis in the form of eigenstresses which are a priori unknown. Hence an
iterative procedure is employed to obtain a convergent solution.
The proposed method is verified by a comparison with an
analytical solution, and several applications illustrate the applicability of
the method for metal matrix composites with localized damage in the form of a
crack or fiber loss. Localized
damage; Cracked fiber reinforced materials; Representative cell method;
High-Fidelity generalized method of cells; Inelastic higher-order theory;
Elastoplastic composites. The micromechanical analysis of composites
with periodic microstructure is usually carried out by identifying and
analyzing a repeating unit cell. However, when localized effects such as one or
several cracks occur in the composite, the periodicity is lost and its behavior
cannot be determined directly by analyzing a repeating unit cell. If these
effects are nevertheless included in the analysis of the repeating unit cell,
the resulting behavior would correspond to that of a composite with periodic
(i.e., not localized) effects which obviously is an unrealistic situation.
In a recent article, Aboudi and Ryvkin proposed the analysis of
linearly elastic composites with localized damage by representing the effect of
the latter by eigenstresses. This analysis combines continuum damage mechanics
considerations with three different approaches. In the first one the idea of
using the eigenstresses to represent the nonlinear effects enables application
of the representative cell method, Ryvkin and Nuller, based on the discrete
Fourier transform which is applicable to linear problems. As a result the
initial problem formulated for a domain comprising a large number of cells is
reduced to a problem for a single representative cell. Appropriate far-field
boundary conditions (which are not influenced by the localized effects) in the
transform domain are applied in conjunction with the highfidelity generalized
method of cells (HFGMC) micromechanical model which forms the second approach.
The third approach consists of the application of the higher-order inelastic
theory, Aboudi et al. for the computation of the field in the transform domain.
An inverse transform provides the actual field. The effect of damage is
included in the analysis in the form of eigenstresses which are a priori unknown.
In Ryvkin and Aboudi, this approach has been also proven to be successful and
effective in the analysis of cracked layered elastic composites, where one or
several combinations of a transverse and two longitudinal cracks (H-cracks)
caused branching have been investigated. Furthermore, it has been successfully
applied for the prediction of the field distributions in
electro-magneto-thermoelastic composites with cracks, cavities and inclusions,
Aboudi. A brief review of various methods for the analysis of localized effects
in thermoelastic composites has been recently presented by Aboudi and Ryvkin.
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