Related papers: Hydrodynamic phase field crystal approach to inter…
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 extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived…
A computational method is developed for the study of mechanical response and fracture behavior of phase field crystals (PFC), to overcome a limitation of the PFC dynamics which lacks an effective mechanism for describing fast mechanical…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g.…
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
We develop a preconditioner for the linear system arising from a finite element discretization of the Phase Field Crystal (PFC) equation. The PFC model serves as an atomic description of crystalline materials on diffusive time scales and…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain…
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…
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is…
Freestanding tubular crystals offer a general description of crystalline order on deformable surfaces with cylindrical topology, such as single-walled carbon nanotubes, microtubules, and recently reported colloidal assemblies. These systems…
We derive the amplitude expansion for a phase-field-crystal (APFC) model that captures the basic physics of magneto-structural interactions. The symmetry breaking due to magnetization is demonstrated, and the characterization of the…
In many processes for crystalline materials such as precipitation, heteroepitaxy, alloying, and phase transformation, lattice expansion or compression of embedded domains occurs. This can significantly alter the mechanical response of the…
A novel, concurrent multiscale approach to meso/macroscale plasticity is demonstrated. It utilizes a carefully designed coupling of a partial differential equation (pde) based theory of dislocation mediated crystal plasticity with…
We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between…
An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character).…
The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation.…