General Integral Representation Formula for the Effective Elastic Tensor of Two-phase Composites

Two-parameter integral representation formula for the effective elastic moduli of two-phase composites

On the representation formula for well-ordered elastic composites: a convergence of measure approach

The aim of this paper is to derive an integral representation formula for the effective elasticity tensor for a two-component well-ordered composite of elastic materials without using a third reference medium and without assuming the completeness of the eigenspace of the operator Ĝ defined in (2.16) in (J. Mech. Phys. Solids 1984; 32(1):41–62). As shown in (J. Mech. Phys. Solids 1984; 32(1):41–...

On the integral representation formula for a two-component elastic composite

The aim of this paper is to derive, in the Hilbert space setting, an integral representation formula for the e ective elasticity tensor for a two-component composite of elastic materials, not necessarily wellordered. This integral representation formula implies a relation which links the e ective elastic moduli to the N -point correlation functions of the microstructure. Such relation not only ...

Effective Stiffness Tensor of Composite Media-i. Exact Series Expansions

The problem of determining exact expressions for the effective stiffness tensor macroscopically anisotropic, two-phase composite media of arbitrary microstructure in arbitrary space dimension d is considered. We depart from previous treatments by introducing an integral equation for the “cavity” strain field. This leads to new, exact series expansions for the effective stiffness tensor of macro...

Exact Expression for the Effective Elastic Tensor of Disordered Composites

We derive new, exact series expansions for the effective elastic tensor of anisotropic, d-dimensional, two-phase disordered composites whose nth-order tensor coefficients are integrals involving n-point correlation functions that characterize the structure. These series expansions, valid for any structure, perturb about certain optimal dispersions. Third-order truncation of the expansions resul...