Influence of imperfect elastic contact condition on the antiplane effective properties of piezoelectric fibrous composites

A fiber-reinforced periodic piezoelectric composite, where the constituents exhibit transverse isotropic properties, is considered. The fiber cross-section is circular and the periodicity is the same in two orthogonal directions. Imperfect mechanic contact conditions at the interphase between the matrix and fibers are represented in parametric form. In order to analyze the influence of the imperfect interface effect over the behavior of the composite, the effective axial piezoelectric moduli are obtained by means of the Asymptotic Homogenization Method. Some numerical examples are given.     

Predicting the properties of disoriented fibrous composites

International Applied Mechanics -     

Predicting the nonlinear strain properties of fibrous metal composites

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 9, pp. 45–51, September, 1989.     

Exact relations for the anti-plane effective magneto-electro-elastic coefficients of two-phase fibrous composites

Two-phase fiber-reinforced magneto-electro-elastic composites are considered. The constituents exhibit transverse isotropy and the composite is assumed to have global monoclinic symmetry. The Milgrom–Shtrikman compatibility conditions are applied to obtain explicitly exact relations for the eighteen anti-plane effective coefficients. Such relations are written in terms of nine equalities of fourth-order determinants. These fourth-order determinants exhibit the regularity of a third-order minor formed by the response matrix of the matrix material and are completed by a row and/or column of the response matrices of the fibers material and the composite, respectively. Other two less explored alternative theories, namely, a second type of the Milgrom–Shtrikman conditions, which involve only effective coefficients, and Milgrom's version of the original Milgrom–Shtrikman conditions, are followed in order to derive twenty and forty exact relations, respectively. Particular and limit cases are recovered from the obtained relations.     

Theoretical analysis of electric, magnetic and magnetoelectric properties of nano-structured multiferroic composites

Electric, magnetic and magnetoelectric properties of the nano-structured multiferroic composites were studied by using an energy formulation with the consideration of the surface, interface, and size effect. Coupled thermodynamic evolution equations with respect to the spontaneous polarization and magnetization were established, in which the elastic fields in the matrix and inclusions were solved based on the Eshelby's equivalent inclusion concept and the Mori–Tanaka method. Physical properties of the composite, such as the spontaneous order parameters, piezoelectric/piezomagnetic properties, and the magnetoelectric coupling effect are highly dependent on the stress state and the microstructures of the nano-composites. Magnetoelectric coupling voltage coefficient was unstable in the vicinity of the critical size and disappeared below the critical size. The model is versatile enough for various composite structures.     

Closed-form solutions to the static transverse deformation of a spider orb-web

Meccanica - This paper deals with the study of the Dirichlet and Poisson problem for the infinitesimal transverse deformation of a spider orb-web in statical regime. The mechanical model is a...     

Bounds on the non-local effective elastic properties of composites

The paper deals with the effective linear elastic behaviour of random media subjected to inhomogeneous mean fields. The effective constitutive laws are known to be non-local. Therefore, the effective elastic moduli show dispersion, i.e¹ they depend on the “wave vector” k of the mean field. In this paper the well-known Hashin-Shtrikman bounds (1962) for the Lamé parameters of isotropic multi-phase mixtures are generalized to inhomogeneous mean fields k ≠ 0. The bounds involve two-point correlations of random elastic moduli. In the limit k → ∞ the bounds converge to the exact result. The interest is focussed on composites with cell structures and on binary mixtures. To illustrate the results, numerical evaluations are carried out for a binary cell material composed of nearly spherical grains of equal size.     

Dynamic effective property of fibrous piezoelectric composites with spring- or membrane-type imperfect interfaces

The present paper studies the dynamic effective property of piezoelectric composites embedded with cylindrical piezoelectric fibers under anti-plane harmonic electro-elastic waves. By using the dynamic generalized self-consistent method (DGSM) of electro-elastic coupling wave, the problem of randomly distributed cylindrical fibers in a piezoelectric medium can be analyzed in terms of a representative volume element with a coated fiber embedded in an equivalent effective medium. The interfaces between the fibers and the matrix are assumed to be imperfect which are here modeled as spring- or membrane-type interfaces. Through wave function expansion method and an iterative method, the effective piezoelectrically stiffened shear modulus and the effective wave number are obtained. Examples are conducted to verify the present solutions and to illustrate the dependence of the effective piezoelectrically stiffened shear modulus on the wave number (frequency) as well as the interface properties. The special size effect related to interfacial imperfection is also discussed.     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National Natural Science Foundation of China     

Antiplane magneto-electro-elastic effective properties of three-phase fiber composites

In the present work, applying the asymptotic homogenization method (AHM), the derivation of the antiplane effective properties for three-phase magneto-electro-elastic fiber unidirectional reinforced composite with parallelogram cell symmetry is reported. Closed analytical expressions for the antiplane local problems on the periodic cell and the corresponding effective coefficients are provided. Matrix and inclusions materials belong to symmetry class 6mm. Numerical results are reported and compared with the eigenfunction expansion-variational method (EEVM) and other theoretical models. Good agreements are found for these comparisons. In addition, with the herein implemented solution, it is possible to reproduce the effective properties of the reduced cases such as piezoelectric or elastic composites obtaining good agreements with previous reports.     

Closed-form and asymptotic solutions for an interactive buckling model

Exact, closed-form, solutions to a recent interactive buckling model proposed by Budiansky and Hutchinson (1979) are presented in full for the first time. These exhibit a form of Bifurcation involving looping equilibrium paths, identified recently from topological considerations, and are put forward as evidence of its typicality. A second, related, typical form is also identified in the response of the model. The predictions of two different asymptotic approaches, the first from traditional structural mechanics and the second making use of the mathematical concept of determinacy, are compared with the exact solutions.     

Apparent and effective mechanical properties of linear matrix-inclusion random composites: Improved bounds for the effective behavior

This paper is devoted to the derivation of improved bounds for the effective behavior of linear elastic matrix-inclusion composites based on a strategy which is inspired by both the works of Huet, 1990, Danielsson et al., 2007. As shown by the former author, the effective properties of random linear composites can be bounded by ensemble averages of their apparent elastic moduli defined on square (or cubic) volume elements (VEs) and computed with either affine displacement Boundary Conditions (BC) or uniform traction BC. However, in the case of a large contrast of the constituents, the discrepancy between the upper and lower bounds remains significant, even for large values of the VE size. This occurs because the contribution to the total potential (or complementary) energy of the particles (or pores) which intersect the edges of the VE becomes unphysically very large when uniform BC are directly applied to the particles. To avoid such limitations, we considerer non-square (or non-cubic) VEs consisting in simply connex assemblages of cells, each cell being composed of an inclusion surrounded by the matrix, thus forbidding any direct application of BC to the particles. Such VEs are generated by extending the scheme proposed by Danielsson et al. (2007) in the context of periodic random microstructures to fully random microstructures. By applying the classical energy bounding theorems to the non-square VEs, new bounds for the effective behavior are derived. Their application to a two-phase composite composed of an isotropic matrix and aligned identical fibers randomly distributed in the transverse plane leads to sharper bounds which converge quickly with the VE size, even for infinite contrasts.     

Elastic-plastic behavior of fibrous composites

The elastic-plastic behavior of fibrous composites is explored with self-consistent models. The overall and local yield surfaces, instantaneous moduli, thermal coefficients, plastic strains and thermal microstresses are calculated for selected material systems, using R. Hill's (1965) model, and a modified scheme. Axisymmetric mechanical loads and uniform thermal changes are considered and the extension to shear loads is discussed. A limited comparison of the calculated microstresses is made with available experimental results.     

Effect of overlapping inclusions on effective elastic properties of composites

We are considering, in this study, to quantify the difference between two morphologies: heterogeneous materials with overlapping identical spherical inclusions and heterogeneous materials with identical hard one. Coupling with numerical simulations, the statistical analysis of microstructures morphology was used to evaluate the representativeness of results. The methodology, developed in Kanit et al. (2003), is used to determine exactly the integral range (IR), variance and covariance of each microstructure type. The obtained results show that the integral range of microstructures with hard spheres, is simply, the volume of one inclusion in the deterministic representative volume element, and for microstructures with overlapping spheres, is 8 times the integral range in the case of hard spheres. The obtained results suggest us to define a new concept what we propose to name the Equivalent Morphology Concept (EMC). The relationships between parameters of two microstructures are presented.     

Local effective thermoelastic properties of graded random structure matrix composites

Summary  We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated. Received 11 November 1999; accepted for publication 4 May 2000