Related papers: An atomistic-to-continuum analysis of crystal clea…
The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here we highlight the…
Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlet-type. Crack paths are described in terms of curvature varifolds so that we…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…
We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in…
The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice…
Dislocation nucleation in homogeneous crystals initially unfolds as a linear symmetry-breaking elastic instability. In the absence of explicit nucleation centers, such instability develops simultaneously all over the crystal and due to the…
We consider the temporal decay estimates for weak solutions to the two-dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non-uniform decay \begin{align*} \|u(t)\|_{L^{2}}+\|\nabla…
Statistics and thermally activated dynamics of crack nucleation and propagation in a two-dimensional heterogeneous material containing quenched randomly distributed defects are studied theoretically. Using the generalized Griffith criterion…
The effect of geometrical shape of eroding absolutely rigid particles on the threshold rate of failure has been studied. The Shtaerman-Kilchevsky theory of quasi-static blunt impact, which generalizes Hertz's classical impact theory, is…
This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the…
A continuum model of fracture that describes, in principle, the propagation and interaction of arbitrary distributions of cracks and voids with evolving topology without a fracture criterion is developed. It involves a 'law of motion' for…
The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a…
The critical value of the atom-field coupling strength for a finite number of atoms is deter- mined by means of both, semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
Fatigue crack advance induced by the application of cyclic quasistatic loads is investigated both numerically and analytically using a lattice spring model. The system has a quasi-one-dimensional geometry, and consists in two symmetrical…
Our previous molecular dynamic simulation studies of simple two-dimensional (2D) systems \cite{matt_big} suggested that both geometrical defects (localized, large-amplitude deviations from hexagonal ordering) and topological defects…
This paper verifies two laws for plastic flows of face-centered cubic crystals that deform at constant strain rates and fixed ambient temperatures. The first law relates steady-state flow stress to ambient temperature and strain rate. The…
We study theoretically Doppler laser-cooling of a cluster of 2-level atoms confined in a linear ion trap. Using several consecutive steps of averaging we derive, from the full quantum mechanical master equation, an equation for the total…
We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized…