Related papers: A phase-field approach to Eulerian interfacial ene…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large…
Mechanical contact between solids is almost exclusively modeled in Lagrangian frameworks. While these frameworks have been developed extensively and applied successfully to numerous contact problems, they generally require complex…
In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…
We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is…
We consider the problem of minimizing the Willmore energy connected surfaces with prescribed surface area which are confined to a finite container. To this end, we approximate the surface by a phase field function $u$ taking values close to…
The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
We present a phase-field approximation of sharp-interface energies defined on partitions, designed for modeling grain boundaries in polycrystals. The independent variable takes values in the orthogonal group $\mathrm{O}(d)$ modulo a lattice…
A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With…
We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in…
In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on $\mathbb{R}^n$ defined by two coupled phase fields $u,v$. The first phase field $u$ is the…
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…
Recent advancements have demonstrated that fully Eulerian methods can effectively model frictionless contact between deformable solids. Unlike traditional Lagrangian approaches, which require contact detection and resolution algorithms, the…
We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…
In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and prove a compactness and lower bound estimate in the sharp…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
Motivated by solid-solid phase transitions in elastic thin films, we perform a Gamma-convergence analysis for a singularly perturbed energy describing second order phase transitions in a domain of vanishing thickness. Under a two-wells…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…