相关论文: Autonomy and Singularity in Dynamic Fracture

We investigate experimentally and theoretically the dynamics of a crack front during the micro-instabilities taking place in heterogeneous materials between two successive equilibrium positions. We focus specifically on the spatio-temporal…

When fast cracks become unstable to microscopic branching (micro-branching), fracture no longer occurs in an effective 2D medium. We follow in-plane crack front dynamics via real-time measurements in brittle gels as micro-branching unfolds…

We study the smoothness of the topological equivalence between a linear equation and its nonlinear perturbation, which is regarded as unbounded. To the best of our knowledge, it has not previously been considered such study in the…

A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress…

We study a nonlinear and nonlocal elliptic equation posed on the flat torus. While constant solutions always exist, we show that uniqueness fails in general. Using spectral analysis and the Crandall--Rabinowitz bifurcation theorem, we prove…

We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $ f(x,t) - i \mu \gamma^0 \Psi$, where both $f$ and $\Psi$ are…

We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The…

This paper introduces a three-dimensional (3-D) mathematical and computational framework for the characterization of crack-tip fields in star-shaped cracks within porous elastic solids. A core emphasis of this model is its direct…

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…

Important physical observations in rupture dynamics such as static fault friction, short-slip, self-healing, and supershear phenomenon in cracks are studied. A continuum model of rupture dynamics is developed using the field dislocation…

We study the self-compactification of extra dimensions via higher curvature gravity, f(R), where f(R) is the generic function of the Ricci scalar R. First, we reduce pure f(R) theory to a scalar-tensor theory by a conformal transformation.…

Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…

In order to study the stability of mode-I fracture, we consider a crack moving along the centerline of a very wide strip and compute its steady-state response to a small, spatially periodic shear stress. We find that, in the presence of…

We consider the model of modified gravity with dynamical torsion. This model was previously found to have promising stability properties about various backgrounds. Here we study the stability of linear perturbations about the…

In this paper, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to the presence of a small elastic linear…

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these…

Most of the research concerting crack propagation in discrete media is concerned with specific types of external loading: displacements on the boundaries, or constant energy fluxes or feeding waves originating from infinity. In this paper…

We consider the effect of differing coefficients of static and dynamic friction coefficients on the behaviour of contacts involving microslip. The classic solutions of Cattaneo and Mindlin are unchanged if the transition in coefficients is…

We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models…

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on…