The dynamic effect on mechanical contacts between nanoparticles

Abstract

The rich behaviors of high-speed mechanical contacts at the nanoscale have been studied. The seldom observed elastic-plastic transition governed by Hertz and Thornton models has been clearly unveiled, the origins of the hardening effect and the deformation mechanism of nanoscale plasticity have been discussed in terms of structural changes after compression and a series of physical quantities are measured including contact forces, contact radius, contact stress, coefficient of restitution and total impact time. Our simulation results closely resemble experiments and/or theoretical predictions: (i) when impact speed v is higher than Y/ρc0, the elastic-plastic deformation transition occurs, (ii) the yielded apparent elastic modulus and hardness are larger than those of the bulk, (iii) the initiating yield stress Y and hardness P0 still satisfy P0 ≈ 1.6Y, (iv) particle's volume decreases during compression, (v) contact radius a follows a [proportionality] v(2/5), (vi) at v ≥ 2000 m s(-1), the coefficient of restitution follows e [proportionality] v(-1/4) and (vii) the total time of impact follows Tc [proportionality] v(-1/5). However, there also exist many quantitative differences. The contact radius and final contact radius are underestimated by the continuum predictions while the total impact time is overestimated, but all of them reasonably agree with theoretical predictions with an increase of contact area and impact speed. The theoretical equation is adapted to predict the final contact radius during normal impact, in which the contact radius at zero load is also formulated.

A computational stochastic multiscale methodology for MEMS structures involving adhesive contact

“…The apparent adhesive contact forces are constructed from V PC using the analytical function described in Eq. (22). Ten generated apparent adhesive contact forces are illustrated in Fig.…”

“…(21), from a given apparent contact force and also can reconstruct that apparent contact force knowing its physical parameters vector using Eq. (22). In other words, an apparent contact force can be represented by its parameters vector v, Eq.…”

“…2(b), using the methodology described in Section 2.2.2 and fitted via the analytical function defined by Eq. (22). They are then integrated into a 1D elastic FE model of cantilever beam using Eq.…”

“…(22). The stochastic model is constructed based on a set of m explicitly evaluated apparent contact forces, from which the set of m corresponding physical parameters vectors {v (1) , .…”

“…Mathematically speaking, the apparent contact force is an average force integrated on the apparent interacting area defining by meso-scale length l meso . In the literature, two main classes of methods can be found to evaluate the apparent contact forces for the adhesive problems: (i) analytical methods such as the Greenwood and Williamson (GW) approach [15,16]; and (ii) numerical methods such as FE models [17,18,19,20], molecular dynamics (MD) models [21,22,23], or FE-MD hybrid models [24]. The first candidate, the GW approach, uses the statistical parameters of the contact surfaces [25] to deduce the equivalent asperity contact model on which the asperity contact theories [26,27,28,29] are applied to evaluate the contact forces.…”