Related papers: Autonomy and Singularity in Dynamic Fracture
We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to…
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} ({\bPsi} \Psi)^{\kappa+1}$ in the presence of various external electromagnetic fields. Starting from the exact…
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…
Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile ofthe elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the…
We investigate equations of motion and future singularities of $f(R,T)$ gravity where $R$ is the Ricci scalar and $T$ is the trace of stress-energy tensor. Future singularities for two kinds of equation of state (barotropic perfect fluid…
Various fields such as mechanical engineering, materials science, etc., have seen a widespread use of linear elastic fracture mechanics (LEFM) at the continuum scale. LEFM is also routinely applied to the atomic scale. However, its…
We study the selftrapping properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the…
A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…
We argue that nucleation of brittle cracks in initially flawless soft elastic solids is preceded by a nonlinear elastic instability, which cannot be captured without accounting for geometrical precise description of finite elastic…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
Numerical stability is of great significance for discrete-time dynamic vehicle model. Among the unstable factors, low-speed singularity stands out as one of the most challenging issues, which arises from that the denominator of tire side…
Rayleigh-Taylor instability (RTI) has critical importance for a broad range of processes in nature and technology, from supernovae to plasma fusion. In most instances RTI is driven by variable acceleration whereas the bulk of existing…
An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the…
Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending…
The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor's dislocation model is adopted and implemented…
We consider the time-dependent Navier-Stokes equations in a half-space with boundary data on the line $(x,y)=(x_0,y)$ assumed to be time-periodic (or stationary) with a fixed asymptotic velocity ${\bf u}_{\infty}=(1,0)$ at infinity. We show…
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…
The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist.…
The nonuniqueness of rational expectations is explained: in the stochastic, discrete-time, linear, constant-coefficients case, the associated free parameters are coefficients that determine the public's most immediate reactions to shocks.…
Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale…