Related papers: Quasistatic crack growth in 2d-linearized elastici…
We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…
We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of…
In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and…
Two novel single-period cracks were observed in experiments of cutting a folded sheet with a blunt object and tearing a thin brittle sheet under the guidance of a meterstick. Additionally, we observed a period-doubling crack in the tearing…
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous space-time beam model for which no solution theory is available, it consists of a…
The velocity jump found in the crack propagation for rubbers has been a powerful tool for developing tough rubber materials. Although it is suggested by a theory that the jump could be observed widely for viscoelastic materials, the report…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evolution, as the size of the layers vanishes. The limit…
We consider a nonlocal curve evolution belonging to a hierarchy of models for the dynamics of an inextensible elastic filament in a 3D Stokes fluid. This model captures the principal part of a full free boundary problem for an elastic…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
We present results on a series of 2D atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible…
Using the weak convergence approach, we prove the large deviation principle (LDP) for solutions to quasilinear stochastic evolution equations with small Gaussian noise in the critical variational setting, a recently developed general…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model…
Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the…
Position based dynamics is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. We develop a novel approach to address problems with PBD for…
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…
Schreiber and Yukich [Ann. Probab. 36 (2008) 363-396] establish an asymptotic representation for random convex polytope geometry in the unit ball $\mathbb{B}^d, d\geq2$, in terms of the general theory of stabilizing functionals of Poisson…
We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the…