Related papers: Crack propagation as a free boundary problem
It is often observed that thermal stress enhances crack propagation in materials, and conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by…
We consider a controlled reaction-diffusion equation, motivated by a pest eradication problem. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. In this direction, the first part of the paper…
We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the…
Rock formations are very often characterized by the presence of fractures that have grown subcritically over geological time scales and under evolving stress fields. In mechanically layered systems, such fractures can either become…
A minimal model is constructed for two-dimensional fracture propagation. The heterogeneous process zone is presumed to suppress stress relaxation rate, leading to non-quasistatic behavior. Using the Yoffe solution, I construct and solve a…
Despite extensive theoretical treatment of short- to long-crack transitions, direct experimental quantification of how elastic and plastic energy contributions evolve at the crack tip during arrest has remained absent. In this study, we…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
In this paper we study a free boundary problem for the growth of multi-layer tumors in necrotic phase. The tumor region is strip-like and divided into necrotic region and proliferating region with two free boundaries. The upper free…
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…
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…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
In this work, we present crack propagation experiments evaluated by digital image correlation (DIC) for a carbon black filled ethylene propylene diene monomer rubber (EPDM) and numerical modeling with the help of variational phase-field…
Various kinds of heterogeneity in solids including atomistic discreteness affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in…
This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…
Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the…
In earlier papers (Leblond et.al., 2011, 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a "double'' propagation criterion combining Griffith (1920)'s energetic…
The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence…
The temporal evolution of mechanical energy and spatially-averaged crack speed are both monitored in slowly fracturing artificial rocks. Both signals display an irregular burst-like dynamics, with power-law distributed fluctuations spanning…
Crack-tip fields within a transversely isotropic strain-limiting elastic body are investigated under the influence of piecewise linear slope boundary loads. The mechanical response is characterized via a nonlinear constitutive framework…