Related papers: Phase-field gradient theory
To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in…
The following is a thermodynamic analysis of a III order (and some aspects of a IV order) phase transition. Such a transition can occur in a superconductor if the normal state is a diamagnet. The equation for a phase boundary in an H-T (H…
When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent…
We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
A consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the…
Soft spheres interacting via a hard core and range of attractive and repulsive "soft-shoulder" potentials self-assemble into clusters forming a variety of mesophases. We combine a mean field theory developed from a lattice model with a…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues. Such tissues consist of one or more solid and fluid phases and can demonstrate nonlinear…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…
A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for…
In this work, a ternary phase-field model for two-phase flows in complex geometries is proposed. In this model, one of the three components in the classical ternary Cahn-Hilliard model is considered as the solid phase, and only one…
In this study, we address damage initiation and micro-crack formation in ductile failure of polycrystalline metals. We show how our recently published thermodynamic framework for ductile phase-field fracture of single crystals can be…
A phase-field model is used to capture the surfactant-driven formation of fracture patterns in particulate monolayers. The model is intended for the regime of closely-packed systems in which the mechanical response of the monolayer can be…
The motion of microstructural interfaces is important in modeling materials that undergo twinning and structural phase transformations. Continuum models fall into two classes: sharp-interface models, where interfaces are singular surfaces;…
The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
Phase separation in complex systems is a ubiquitous phenomenon. While simple theories predict coarsening until only macroscopically large phases remain, concrete models often exhibit patterns with finite length scales. To unify such models,…
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…