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 ...

We have prepared GexAsySe1−x−y glasses with mean coordination numbers MCNs from 2.2 to 2.86. Tg was found to generally increase with increasing MCN while the glass density showed a maximum at MCN 2.45 and a minimum at MCN 2.65. The elastic moduli of the glasses were estimated from the shear and compressional wave velocities measured by ultrasonic pulse interferometry. For the first time we simu...

Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If Dedicated to John W. Cahn, on the occasion of his 70th birthday

Combining several materials (“phases”) into a composite material permits creation of new materials with tunable overall response, e.g., elastic properties, which can be related to the elastic moduli, arrangement, and concentrations of the composite’s phases. A recent advance predicts use of one phase having correctly tuned non-positive-definite elastic moduli (i.e., negative stiffness) in a two...

Recent progress on studies of the nanoscale mechanical responses in disordered systems has highlighted a strong degree of heterogeneity in the elastic moduli. In this contribution, using computer simulations, we study the elastic heterogeneities in athermal amorphous solids--composed of isotropic static sphere packings--near the jamming transition. We employ techniques based on linear response ...

Elastic properties of materials are an important factor in their integration in applications. Chemical vapor deposited (CVD) monolayer semiconductors are proposed as key components in industrial-scale flexible devices and building blocks of two-dimensional (2D) van der Waals heterostructures. However, their mechanical and elastic properties have not been fully characterized. Here we report high...

OBJECTIVES The aim was to determine the Young's modulus (E), bulk modulus (B), shear modulus (G) and Poisson's ratio (nu) of a series of composite restorative materials and to correlate them with their filler volume-fractions. METHODS Twelve model resin-composite formulations, with systematically varied volume-fraction (Tokuyama), a flowable resin-composite (Point 4 flowable, Kerr) and two hy...

Ultrasonic measurements of elastic moduli of composite materials have traditionally been made on either small specimens cut from a iar ger component or by using a scanning technique with the specimen immersed in a water bath. A phase-insensitive array has been developed for rapid nondestructive measurement of in-plane elastic moduli. The array characteristics allow for determinat ion of energy ...

Recently, a new technique has been developed, which allows quantitative nanoscale mapping of elastic moduli by means of a hybrid nanoindentation and force modulation instrument. We introduce a procedure for finding the experimental parameters that provide an optimal modulus contrast. Application of the procedure on three different material systems demonstrated the technique’s capability to reso...

Abstract The issue of how to find the best acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are determined which minimize the orientation averaged squared-norm of the difference in the acoustical tensors. The optimal moduli are derived explicitly and turn out to be identical to those obtained by minimizing the Euclidean distance function, or equivalently...