A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

Heinemann, Christian; Kraus, Christiane; Rocca, Elisabetta; Rossi, Riccarda

doi:10.1007/s00205-017-1102-7

Cited by 15 publications

(13 citation statements)

References 41 publications

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“…Nevertheless, direct observation of the interface between the active and passive phases and results from PIV illustrating a mixing region between the two phases suggests that the interphase boundary may be represented as a diffuse interface with a finite thickness with the density of active motile bacteria varying very sharply across a boundary layer thickness, We hypothesize that, similarly, the boundary between the passive (immobile) and active (swarming) bacteria may be treated as an diffuse interface possessing an intrinsic time dependent thickness, w . We surmise that continuous phase-field order parameters can be used to define a mathematically defined diffuse boundary interface as done in previous investigations involving interface phenomena 36 and phase transition/separation and damage problems in thermoviscoelastic materials 37,38 .…”

Section: Resultsmentioning

confidence: 93%

The propagation of active-passive interfaces in bacterial swarms

2018

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Propagating interfaces are ubiquitous in nature, underlying instabilities and pattern formation in biology and material science. Physical principles governing interface growth are well understood in passive settings; however, our understanding of interfaces in active systems is still in its infancy. Here, we study the evolution of an active-passive interface using a model active matter system, bacterial swarms. We use ultra-violet light exposure to create compact domains of passive bacteria within Serratia marcescens swarms, thereby creating interfaces separating motile and immotile cells. Post-exposure, the boundary re-shapes and erodes due to self-emergent collective flows. We demonstrate that the active-passive boundary acts as a diffuse interface with mechanical properties set by the flow. Intriguingly, interfacial velocity couples to local swarm speed and interface curvature, raising the possibility that an active analogue to classic Gibbs-Thomson-Stefan conditions may control this boundary propagation.

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Section: Resultsmentioning

confidence: 93%

The propagation of active-passive interfaces in bacterial swarms

2018

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“…For the analysis of general models for partial, isotropic damage with a rate-independent damage evolution we refer to the works, e.g., [40][41][42][43] and to the monography [44] for an overview on rate-independent processes. The viscous, rate-dependent counterpart is studied, e.g., in the works [26,[45][46][47], also in combination with dynamics, heat transport, and phase separation, and vanishing-viscosity limits from viscous damage models at small strains to rateindependent ones are investigated in the series of works [48][49][50].…”

Section: Comparison With Other Results In Literaturementioning

confidence: 99%

Analysis and simulations for a phase‐field fracture model at finite strains based on modified invariants

2020

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Phase‐field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase‐field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phase‐field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right Cauchy‐Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time‐discrete solutions converge in a weak sense to a solution of the time‐continuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results.

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“…It has been extended to various contexts, from the evolution of non-isothermal nematic liquid crystals [10,14], to models for damage and phase separation in thermo-visco-elastic solids in R d , d ∈ {2, 3}, cf. [19,26]. In the latter papers the existence of 'entropic' solutions was proved under the condition that…”

Section: Introductionmentioning

confidence: 99%

Global existence for a highly nonlinear temperature-dependent system modeling nonlocal adhesive contact

Bonfanti¹,

Colturato²,

Rossi³

2021

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In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system combines heat equations, in the bulk domain and on the contact surface, with mechanical force balances, including micro-forces, that result in the equation for the displacements and in the flow rule for the damage-type internal variable describing the state of the adhesive bonds. Nonlocal effects are accounted for by terms featuring integral operators on the contact surface.The analysis of this system poses several difficulties due to its overall highly nonlinear character, and in particular to the presence of quadratic terms, in the rates of the strain tensor and of the internal variable, that feature in the bulk and surface heat equations. Another major challenge is related to proving strict positivity for the bulk and surface temperatures.We tackle these issues by very careful estimates that enable us to prove the existence of global-in-time solutions and could be useful in other contexts. All calculations are rigorously rendered on an accurately devised time discretization scheme in which the limit passage is carried out via variational techniques.

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A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

Cited by 15 publications

References 41 publications

The propagation of active-passive interfaces in bacterial swarms

The propagation of active-passive interfaces in bacterial swarms

Analysis and simulations for a phase‐field fracture model at finite strains based on modified invariants

Global existence for a highly nonlinear temperature-dependent system modeling nonlocal adhesive contact

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