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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…

Analysis of PDEs · Mathematics 2020-05-13 Diego Grandi , Martin Kružík , Edoardo Mainini , Ulisse Stefanelli

We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by M. Silhavy [32, 33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is…

Mathematical Physics · Physics 2019-05-22 Diego Grandi , Martin Kruzik , Edoardo Mainini , Ulisse Stefanelli

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…

Computational Physics · Physics 2015-12-16 Boris Valkov , Chris H. Rycroft , Ken Kamrin

In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…

Computational Physics · Physics 2022-02-08 Biswajeet Rath , Xiaoyu Mao , Rajeev K. Jaiman

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…

Soft Condensed Matter · Physics 2024-12-20 Flavio Lorez , Mohit Pundir , David S. Kammer

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…

Analysis of PDEs · Mathematics 2016-02-05 Leonid Berlyand , Mykhailo Potomkin , Volodymyr Rybalko

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…

Optimization and Control · Mathematics 2025-08-06 Luise Blank , Harald Garcke , Claudia Hecht , Christoph Rupprecht

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…

Analysis of PDEs · Mathematics 2023-07-10 Stefano Almi , Ulisse Stefanelli

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…

Analysis of PDEs · Mathematics 2020-12-24 Charles M. Elliott , Luke Hatcher , Björn Stinner

Using a fixed Eulerian mesh, the phase-field method has been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid-structure interaction. Nevertheless, multiphase fluids…

Fluid Dynamics · Physics 2024-02-19 Xiaoyu Mao , Rajeev Jaiman

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

Optimization and Control · Mathematics 2025-12-17 Yixin Tan , Fang Feng , Shengfeng Zhu

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…

Soft Condensed Matter · Physics 2024-12-20 Flavio Lorez , Mohit Pundir

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the…

Fluid Dynamics · Physics 2021-06-30 Armin Shahmardi , Marco Edoardo Rosti , Outi Tammisola , Luca Brandt

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…

Soft Condensed Matter · Physics 2009-10-31 K. R. Elder , Martin Grant , Nikolas Provatas , J. M. Kosterlitz

Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…

Fluid Dynamics · Physics 2023-10-03 Giuseppe Orlando , Paolo Francesco Barbante , Luca Bonaventura

Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…

Fluid Dynamics · Physics 2013-03-12 Harald Garcke , Kei Fong Lam , Björn Stinner

Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric…

Materials Science · Physics 2018-05-22 Quan Zhao

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…

Numerical Analysis · Mathematics 2018-01-17 Eduard Rohan , Vladimír Lukeš

In this paper, we present an Eulerian-Lagrangian methodology to simulate the interaction between a fluid-fluid interface and a solid particle in the presence of wetting effects. The target physical problem is represented by ternary phase…

Fluid Dynamics · Physics 2023-09-21 Fernando Kevin Miranda S. Cruz , Cristian Marchioli
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