Related papers: A variational treatment of material configurations…
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 investigate in the framework of Landau theory the distortion of the strain fields at the interface of two dissimilar ferroelastic oxides that undergo a structural cubic-to-tetragonal phase transition. Simple analytical solutions are…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations…
The rate of curvature-driven grain growth in polycrystalline materials is well-known to be limited by interface dissipation. We show analytically and by simulations that, for systems forming modulated phases or non-equilibrium patterns with…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on \emph{general…
The sliding motion of objects is typically governed by their friction with the underlying surface. Compared to translational friction, however, rotational friction has received much less attention. Here, we experimentally and theoretically…
Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
A variational approach is employed to find stationary solutions to a free boundary problem modeling an idealized electrostatically actuated MEMS device made of an elastic plate coated with a thin dielectric film and suspended above a rigid…
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…
The mechanisms of void growth and coalescence are key contributors to the ductile failure of crystalline materials. At the grain scale, single crystal plastic anisotropy induces large strain localization leading to complex shape evolutions.…
The growth of crystal surfaces, under non-equilibrium conditions, involves the displacement of mono-atomic steps by atom diffusion and atom incorporations into steps. The time-evolution of the growing crystal surface is thus governed by a…
The configuration and evolution of coexisting mesoscopic domains with contrasting material properties are critical in creating novel functionality through emergent physical properties. However, current approaches that map the domain…
We study the interface between a solid trapped within a bath of liquid by a suitably shaped non-uniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields or a surface template. We…
We discuss the Hu-Washizu (HW) variational principle from a geometric standpoint. The mainstay of the present approach is to treat quantities defined on the co-tangent bundles of reference and deformed configurations as primal. Such a…
Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to…
We investigate compound drops composed of two immiscible nonvolatile partially wetting liquids that slide down an inclined homogeneous smooth solid substrate based on a mesoscopic hydrodynamic two-layer model in full-curvature formulation.…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the…