Related papers: A quasi-static model for craquelure patterns
A phase-field approach becomes a more popular candidate in modeling crack propagation. It uses a scalar auxiliary variable, namely a phase-field variable, to model a discontinuity zone in a continuity domain. Furthermore, the fourth-order…
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…
The quasistatic approximation is a useful but questionable simplification for analyzing step instabilities during the growth/evaporation of vicinal surfaces. Using this approximation, we characterized in Part I of this work the effect on…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
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…
Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…
We present a novel constitutive model using the framework of strain-limiting theories of elasticity for an evolution of quasi-static anti-plane fracture. The classical linear elastic fracture mechanics (LEFM), with conventional linear…
We present a non-linear stability analysis of quasi-static slip in a spring-block model. The sliding interface is governed by rate- and state-dependent friction, with an intermediate state evolution law that spans between aging and slip…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
We define a notion of quasi-static evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi-static growth of brittle…
Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of non-equilibrium statistical physics. Recently, it has been proposed that the nature of the yielding transition is controlled by…
A phase-field crystal model based on the density-field approach incorporating high-order interparticle direct correlations is developed to study vapor-liquid-solid coexistence and transitions within a single continuum description.…
Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…
The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack…
Planar sliding of objects is modeled and analyzed. The model can be used for non-prehensile manipulation of objects lying on a surface. We study possible motions generated by frictional contacts, such as those arising between a soft finger…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
Conventional phase-field models often drive solid-solid interfaces to coalesce when in close proximity. This feature limits their use for processes like diffusion bonding, where the interfaces might need to remain distinct under certain…
This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical…
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the motion of discrete dislocations, this work performs a rigorous…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…