相关论文: Steady-State Cracks in Viscoelastic Lattice Models…
The paper is devoted to the study of quasi-static brittle crack evolution. We work under the following assumptions: a linear elastic body, with or without initial cracks inside, evolves in a quasi-static manner under an imposed path of…
New inelastic X-ray scattering experiments have been performed on liquid lithium in a wide wavevector range. With respect to the previous measurements, the instrumental resolution, improved up to 1.5 meV, allows to accurately investigate…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
Models of faults incorporating slip rate- and state-dependent friction have reproduced phenomena from spontaneous slow, aseismic slip to earthquake-generating dynamic rupture. Numerical explorations of model parameter space regularly show…
Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to…
The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability with constant coefficients, the problem has a free boundary…
We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…
In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors, for visco-elasticity with large deformations and conditional compatibility, where the…
The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system…
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived…
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
Dynamical stability of the crack front line that propagates between two plates is studied numerically using the simple two-dimensional mass-spring model. It is demonstrated that the straight front line is unstable for low speed while it…
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
The three-dimensional elastic-plastic deformation is considered. The catastrophe theory underlies the construction of this process model. It was shown that the variety of stable states consists on elastic states and can be depicted as a…
We present our recent study on rough adhesive contacts of viscoelastic materials in steady-state sliding, focusing on the interplay between adhesion and viscoelasticity by means of a novel energy approach. We investigate tribological…
In this paper we present analytical studies of three-dimensional viscous and inviscid simplified Bardina turbulence models with periodic boundary conditions. The global existence and uniqueness of weak solutions to the viscous model has…