Elastic properties of inhomogeneous media with chaotic structure

Abstract

The elastic properties of an inhomogeneous medium with chaotic structure were derived within the framework of a fractal model using the iterative averaging approach. The predicted values of a critical index for the bulk elastic modulus and of the Poisson ratio in the vicinity of a percolation threshold were in fair agreement with the available experimental data for inhomogeneous composites.

Growing lysozyme crystals under various physicochemical conditions: Computer modelling

“…Interface control with peculiar viscoelastic effects at the interface [33], in which auxetic-type nucleation effects may or may not facilitate the growth pace, was studied in [34]. Phase diagram-based solution control, was the subject of intense studies by Haas and Drenth in [35].…”

Seismic singularities at upper-mantle phase transitions: a site percolation model

“…Major support of our percolation model is provided by (1) theoretical and experimental results in the field of mechanical engineering demonstrating that the elastic moduli of a binary mixture are controlled by the percolation properties of the strongest phase (e.g. de Gennes 1976; Ledbetter et al 1984;Gai et al 1984;Deptuck et al 1985;Turusov et al 1986;Marion & Nur 1989;Favier et al 1997;Novikov et al 2001;Saidi et al 2003), (2) the identification of singularities at the expected depths and the quantitative determination of the exponents from seismic data, and (3) the good fit obtained between the synthetic and receiver-function images. However, the limited spatial extent of this study does not allow us to make a global statement on the order of the singularities, which may vary regionally.…”

“…It is well known in solid‐state physics and mechanical engineering that a binary mixture is elastically strong if its strong component forms a connected cluster, and weak otherwise (e.g. Ledbetter et al 1984; Gai et al 1984; Deptuck et al 1985; Turusov et al 1986; Marion & Nur 1989; Favier et al 1997; Novikov et al 2001; for other applications of percolation theory to mechanics, see de Gennes 1976, or Roux & Guyon 1985). Thus a realistic elastic model of the coexistence region must take into account the connectivity (or lack of connectivity) of the HP phase.…”

“…The upper HS bound must be used when the strong component forms the connected matrix, while the lower one applies otherwise (e.g. Marion & Nur 1989; Favier et al 1997; Novikov et al 2001; Saidi et al 2003). Accordingly, the bulk modulus K of the coexistence region above z c is given by the lower HS bound: where a LP = 3 K LP /(3 K LP + 4 G LP ) and the subscripts LP and HP refer to the mineralogical phases involved in the phase transition.…”

Electrical Conductivity of Nanocomposites

“…The performed analysis shows that the effective conductivity increases with decreasing radius R of the filler particles, according to formula (17).…”