Jacob Aboudi

Micromechanical analysis of composites by the generalized cells model

Abstract In the original formulation of the micromechanical method of cells, designated for the analysis of fibrous composites with periodic structure, the repeating volume element consists of four interacting subcells. The various capabilities and reability of the micromechanical model were verified in a recent review paper and a monograph. The present investigation offers a generalization of the method to an arbitrary number of subcells for the modeling of multiphase periodic composites. Such a generalization is particularly advantageous when dealing with elastic-plastic composites, since yielding and plastic flow of a metallic phase may take place at different locations. Effective constitutive laws that govern overall behavior of the elastic-viscoplastic composite material are established. These laws are given in terms of relationships between the average stress-rate and strain-rate of the inelastic multiphase composite. Comparisons between the response of boron/aluminum composite obtained by the present model and a finite element solution are given.

Higher-Order Theory for Functionally Graded Materials

This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composites functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.

Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites

A homogenization micromechanical method is employed for the prediction of the effective moduli of electro-magneto-thermo-elastic composites. These include the effective elastic, piezoelectric, piezomagnetic, dielectric, magnetic permeability and electromagnetic coupling moduli, as well as the effective thermal expansion coefficients and the associated pyroelectric and pyromagnetic constants. Comparisons between the present homogenization theory, the generalized method of cells and the Mori-Tanaka predictions are given. Results are presented for fibrous and periodically bilaminated composites.

Buckling analysis of functionally graded plates subjected to uniaxial loading

Elastic bifurcational buckling of functionally graded plates under in-plane compressive loading is studied. It is supposed that the gradients of material properties throughout the structure are produced by a spatial distribution of the local reinforcement volume fraction v f = v f (x, y, z). To analyze the problem, a method based on a combination of micromechanical and structural approaches is employed. This establishes the effective constitutive behavior at every point of a nonhomogeneous composite plate and provides a buckling criterion. The derived criterion enables one to calculate the critical buckling load R x cr for a given distribution v f (x, y, z). Furthermore, with the aim to improve the buckling resistance of the functionally graded plate, the functional R x cr (v f ) is maximized. This yields an optimal spatial distribution v f (x, y, z) of the reinforcement phase. Results are presented for both short- and long-fiber SiC/Al plates in which the fibers are nonuniformly distributed in the x-, y-, or z-directions. The effects of length-to-width ratio of the plate, and of different types of boundary conditions are studied. Buckling load improvements of up to 100%, as compared to the corresponding uniformly reinforced structure, are shown.

Damage in composites: modeling of imperfect bonding

Abstract A model is presented in which the effect of damage due to imperfect bonding between the constituents of composite materials is incorporated. The interface decohesion is described by two parameters which completely determine the degree of adhesion at the interfaces in the normal and tangential directions. Perfect bonding, perfect lubrication and complete debonding are obtained as special cases. The proposed model predicts the overall moduli and coefficients of thermal expansion of composites in the presence of imperfect bonding.

Higher-order theory for periodic multiphase materials with inelastic phases

Abstract An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the materials periodic microstructure. The models analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The models predictive accuracy in generating both the effective inelastic stress-strain response and the local stress and inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model and with finite-element results for transverse loading.

A continuum theory for fiber-reinforced elastic-viscoplastic composites

Abstract A higher order continuum theory with microstructure is derived for the modeling of the 3-dimensional motion of fiber-reinforced composites in which both the matrix and fibers constituents are assumed to be elastic-viscoplastic work-hardening materials. The fibers are unidirectional with rectangular cross section and are imbedded in the matrix in the form of a doubly periodic array. The derivation of the theory is systematic and can be applied to various types of non-elastic composites to the desired degree of expansion. An appropriate reduction of the theory gives the average behavior of the viscoplastic composite in the form of effective rate-dependent stress-strain curves. In the special case of perfectly elastic constituents the reduction gives the approximate effective moduli of the composite.

Micromechanical analysis of thermo-inelastic multiphase short-fiber composites

Abstract A micromechanical formulation is presented for the prediction of the overall thermoinelastic behavior of multiphase composites which consist of short fibers. The analysis is an extension of the generalized method of cells that was previously derived for inelastic composites with continuous fibers, and the reliability of which was critically examined in several situations. The resulting three-dimensional formulation is extremely general, wherein the analysis of thermo-inelastic composites with continuous fibers as well as particulate and porous inelastic materials are merely special cases.

Thermoelastic theory for the response of materials functionally graded in two directions

A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates.

The Generalized Method of Cells and High-Fidelity Generalized Method of Cells Micromechanical Models—A Review

ABSTRACT The models of the generalized method of cells and the recently developed high-fidelity generalized method of cells are reviewed. These two methods are micromechanical theories that are capable of providing the overall behavior of periodic multiphase materials of various types, including thermoelastic, viscoelastic, thermo-inelastic, and electromagnetothermoelastic materials. Both infinitesimal and finite deformation analyses of multiphase composites are discussed.