Periodic Elastic Composites Research Articles

Photonic band gaps in periodic elastic composites 2-D hexagonal lattices

The acoustic band structure of periodic elastic composites were calculated using position-dependent density and elastic constant. The specific system investigated is made up of a periodic array of parallel metallic rods of circular cross section whose intersections with a perpendicular plane from a hexagonal lattice. The rods are embedded in a background medium with different elastic constant and density. The transverse polarization was considered—with displacement u(r,t) parallel to the cylinders (and perpendicular to the Bloch wave vectors). The absolute band gaps extending throughout the first Brillouin zone were found in the low-frequency regime. The specific case studied was Cu(Al) cylinders in the Al(Cu) background. A direct comparison of the hexagonal case with the square-lattice pattern (Kushwaha et al., preceding abstract in this session) reveals that the widths of these band gaps are larger in the case of hexagonal lattices. The precise dependence of the gaps on the filling fraction is investigated.

On crack problems in periodic two-layered elastic composites

This paper deals with the two-dimensional static problems of the interface crack in a periodically layered space. Within the framework of the homogenized model of the linear elasticity with microlocal parameters [19, 20] the exact solutions of the considered problems are obtained. The stress singularities at the crack tips are discussed in detail from the viewpoint of the fracture theory.

Plane contact problems for a periodic two-layered elastic composite

This paper deals with the two-dimensional static punch problems in the presence of friction for a periodically layered half-space. Within the framework of the homogenized model of linear elasticity with microlocal parameters [8–11] the exact solutions of the considered problems are obtained. The case of the indentation of the composite body by a rigid rectangular punch has been discussed in detail.

Micromorphic effects in a modelling of periodic multilayered elastic composites

The paper deals with the problems of modelling of multilayered periodic composites. The proposed models take into account certain micromorphic effects resulting from the periodic structure of the body. The governing equations describing motions and stresses of the nonhomogeneous elastic materials with microperiodic structure in the nonlinear as well as linear cases have been derived. As an example the time-harmonic vibrations of laminated medium consisting of alternating layers of two homogeneous, isotropic, linear-elastic materials have been discussed.

Dispersion relations and mode shapes for waves in laminated viscoelastic composites by variational methods

The propagation of oscillatory waves through periodic elastic composites has been analysed on the basis of the Floquet theory. This leads to self-adjoint differential equation systems which it was proved convenient to solve by variational methods. Many composites, such as the light-weight high-strength boron-epoxy material, consist of strong reinforcing components in a plastic matrix. The latter can exhibit viscoelastic properties which can have a significant influence on wave propagation characteristics. Replacement of the elastic constant by the viscoelastic complex modulus changes the mathematical structure so that the differential equation system is no longer self-adjoint. However, a modification of the variational principles is suggested which retains formal self-adjointness, and yields variational principles which contain additional boundary terms. These are applied to the determination of wave speeds and mode shapes for a laminated composite made of homogeneous elastic reinforcing plates in a homogeneous viscoelastic matrix for plane waves propagating normally to the reinforcing plates. These results agree well with the exact solution which can be evaluated in this simple case. The variational principles permit solutions for periodic, but otherwise arbitrary variation of material properties.

Harmonic waves in three-dimensional elastic composites

For a periodic elastic composite which consists of a matrix and fibers with finite dimensions (i.e. a three-dimensional problem), here are given estimates for eigenfrequencies and eigenfunctions. Calculations are based on a new quotient which has been proposed by Nemat-Nasser. The periodic character of the eigenfrequencies is pointed out, and illustrative examples are given.