Related papers: Phase-field gradient theory
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
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…
Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We present the microbalance including the microforces, the first- and second-order microstresses for the Swift--Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We…
This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer, Maass, & Dieterich [1], Goldstein, Miranville, & Schimperna [2], and Knopf, Lam, Liu & Metzger, [3]. As…
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…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…
In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of…
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of all constituting ions. One feature of active…
We overview the basic concepts, models, and methods related to the multi-field continuum theory of solids with complex structures. The multi-field theory is formulated for structural solids by introducing a macrocell consisting of several…
A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
Thermofield dynamics has proven to be a very useful theory in high-energy physics, particularly since it permits the treatment of both time- and temperature-dependence on an equal footing. We here show that it also has an excellent…
A novel numerical approach to analyze the mechanical behavior within composite materials including the inelastic regime up to final failure is presented. Therefore, a second-gradient theory is combined with phase-field methods to fracture.…
In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism,…