Related papers: A general criterion for solid instability and its …
Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent…
Strain-based theory on elastic instabilities is being widely employed for studying onset of plasticity, phase transition or melting in crystals. And size effects, observed in nano-materials or solids under dynamic loadings, needs to account…
We study the necking dynamics of a filament of complex fluid or soft solid in uniaxial tensile stretching at constant imposed Hencky strain rate $\dot\varepsilon$, by means of linear stability analysis and nonlinear (slender filament)…
We study the necking of a filament of complex fluid or soft solid subject to uniaxial tensile stretching, under conditions of constant imposed stress and force, by means of linear stability analysis and nonlinear simulations. We demonstrate…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considere criterion, we find the onset of instability to relate closely to the onset of…
Here we study the instability of the vortex motion caused by vortex velocity non-monotonous dependence of the friction force in the presence of a gyro-force. We demonstrate that even a weak gyro-force renders the condition for onset of…
The well-known Jeans criterion describes the onset of instabilities in an infinite, homogeneous, self-gravitating medium supported by pressure. Most realistic astrophysical systems, however, are not isolated - instead they are under the…
A dense suspension of the cornstarch flowing on a very inclined wall finally forms some ridge-like patterns of the free surface. The onset of pattern formation is the primary target to elucidate the mechanism. In this work, based on the…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline,…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any…
The essence of shear instability is fully revealed both mathematically and physically. A general sufficient and necessary stable criterion is obtained analytically within linear context. It is the analogue of Kelvin-Arnol'd theorem, i.e.,…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the…
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…
In alloy solidification, the transport processes of heat and solute result in morphological instability of the interface, forming different patterns of solidification structure and determining the mechanical properties of components. As the…
Cracks in soft materials exhibit diverse dynamic patterns, involving straight, oscillation, branching, and supershear fracture. Here, we successfully reproduce these crack morphologies in a two-dimensional pre-strained fracture scenario and…