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An explicit, analytical theory for the percolation threshold, percolation saturation, and effective conductivity of a two-component system involving randomly oriented ellipsoidal inclusions is proposed. The ellipsoids may take the shape of a needle, prolate or oblate spheroid, sphere, or disk. This theory is based upon consideration of Ponte Castaneda--Willis [P. Ponte Castaneda and J. R. Willis, J. Mech. Phys. Solids 43, 1919 (1995)] microstructure in conjunction with Hashin--Shtrikman [Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962)] upper bound. Two critical volume concentrations, c* and c**, that represent the respective percolation threshold at which the conductive network begins to develop, and the percolation saturation, are identified. During this very short range of concentration, the electrical conductivity of the composite is found to exhibit a very sharp increase, while over the entire range, the calcutilated conductivity exhibits the widely reported sigmoidal shape. Comparison with measurement on a multi-walled carbon nanotube/alumina composite indicates that the theory could capture the major features of the experimentally observed trends sufficiently well. [ABSTRACT FROM AUTHOR]

A previous study of a single load-unload cycle of an adhesive contact between an elastic-plastic microscopic sphere and a rigid flat is extended here for several load-unload cycles. The interacting forces between the sphere and the flat obey the Lennard–Jones potential. Kinematic hardening is assumed for the sphere material to account for possible plastic shakedown, and the difference between kinematic and isotropic hardenings is discussed. The main goal of the current work is to investigate the evolution of the load-approach curves for the elastic-plastic spherical contact during its cyclic loading-unloading. These curves are presented for different physical conditions, represented by three main dimensionless parameters, which affect the behavior of the elastic-plastic adhesive contact. A transition value of the Tabor parameter is found, below which the load-approach curves are always continuous and jump-in and jump-out instabilities are not expected. [ABSTRACT FROM AUTHOR]

A recent experiment has shown that the force required to pull off a flat circular rigid punch in adhesive contact with an array of elastic fibrils is sensitive to the thickness of the elastic backing layer to which these fibrils are attached. This result motivates us to study the effect of sample compliance on the adhesion of fibril arrays. A closed form expression for the compliance of such arrays attached to a backing layer of finite thickness is derived. Our model is based on the assumption that the adhesive strength of a fibril is deterministic. In addition, we show that the normalized pull-off force is inversely proportional to the square root of a single dimensionless parameter β. For large β, the pull-off force is low as it is governed by the stress concentration at the punch edge. For small β, this pull-off force reaches a theoretical limit that is governed by the ability of fibrils to share load equally [equal load sharing (ELS) limit]. The pull-off force predicted by our model is compared with new experimental data. Our model shows the correct trend but underestimates the pull-off force in the ELS limit. The difference between our theoretical predictions and experimental results is attributed to alignment difficulties in the experiments and the fact that the adhesive strength of fibrils is governed by local statistics. [ABSTRACT FROM AUTHOR]