1,720,982 research outputs found
A phase field approach to solidification and solute separation in water solutions
No full textWe propose a phase field model for the solid-liquid phase transition in a water-salt
(sodium chloride) solution in absence of macroscopic motion, under possibly non-isothermal conditions. A thermodynamic approach based on a free energy functional is assumed. The model consists
of three evolution equations: a time-dependent Ginzburg-Landau equation for the solid-liquid phase
change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics and the heat equation for the temperature change. The proposed system is aimed to contribute to the modeling of the brine channels formation in the ice of the polar seas
The Souza-Auricchio model for shape-memory alloys
No full textShape-memory alloys are active materials, their amazing thermo-electromechanical behavior is at the basis of a variety of innovative applications.
Many models have been set forth in order to describe this complex behavior.
Among these the so-called Souza-Auricchio model appears as remarkably simple in terms of mechanical assumptions yet accurate in the description of three-dimensional experiments and robust with respect to approximations. Our aim is to survey here the current literature on the Souza-Auricchio model, with a specic focus on modeling
A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys
No full textDegradation in shape-memory alloy response is a crucial concern for a variety of innovative applications. Under cyclic loadings, these materials generally experience permanent inelastic deformations. The onset of plasticization is known to be very sensitive to the microstructure of the polycrystalline specimen. Moving from recent experimental findings (Malard et al. in Funct Mater Lett 2:45-54, 2009 ; Acta Mater 59:1542-1556, 2011), we present a phenomenological model for permanent inelastic effects in shape-memory alloys taking into account the polycrystalline microstructure. In particular, the mechanical response under cyclic loadings is investigated in connection with the mean crystal grain size. Formulated within the variational frame of generalized standard materials, the model consists in an extension of the model in Auricchio et al. (Int J Plast 23:207-226, 2007) to the case of microstructure-dependent parameters. The mathematical setting is discussed and numerical simulations showing the capability of the model to reproduce experiments are presented
Existence and linearization for the Souza-Auricchio model at finite strain
No full textWe address the analysis of the Souza-Auricchio model for shape memory alloys in the finite-strain setting. The model is formulated in variational terms and the existence of quasistatic evolutions is obtained within the classical frame of energetic solvability. The finite-strain model is proved to converge to its small-strain counterpart for small deformations via a variational convergence argument
Finite plasticity in P^T P. Part I: constitutive model
No full textWe address a finite-plasticity model based on the symmetric tensor P^T P instead of the classical plastic strain P. Such a structure arises by assuming that the material behavior is invariant with respect to frametransformationsoftheintermediateconfiguration.The resulting variational model is lower dimensional, symmetric and based solely on the reference configuration. We discuss the existence of energetic solutions at the material-point level as well as the convergence of time discretizations. The linearization of the model for small deformations is ascertained via a rigorous evolution-Gamma-convergence argument. The constitutive model is combined with the equilibrium system in Part II where we prove the existence of quasistatic evolutions and ascertain the linearization limit (Grandi and Stefanelli in 2016)
A nonisothermal phase-field model for the ferromagnetic transition
No full textWe propose a model for nonisothermal ferromagnetic phase transition based on a phase field approach, in which the
phase parameter is related but not identified with the magnetization. The magnetization is split in a paramagnetic and in
a ferromagnetic contribution, dependent on a scalar phase parameter and identically null above the Curie temperature.
The dynamics of the magnetization below the Curie temperature is governed by the order parameter evolution equation
and by a Landau–Lifshitz type equation for the magnetization vector. In the simple situation of a uniaxial magnet,
it is shown how the order parameter dynamics reproduces the hysteresis effect of the magnetization
A phase field model for liquid-vapour phase transition
No full textWe propose a model describing the liquid-vapour phase transition
according to a phase-field method. A phase variable φ is introduced whose
equilibrium values φ = 0 and φ = 1 are associated with the liquid and vapour
phases. The phase field obeys Ginzburg-Landau equation and enters the consti-
tutive relation of the density, accounting for the sudden density jump occurring
at the phase transition. In this paper we concern ourselves especially with the
problems arising in the phase field approach due to the existence of the critical
point in the coexistence line, which entails the merging of the phases described
by φ
A thermodynamic approach to isotropic- nematic phase transitions in liquid crystals.
No full textWe propose a dynamical model for (non-isothermal) phase transitions in liquid crystals. Macroscopic motions of the liquid crystal (LC) are neglected, while the coupling with the electromagnetic field is considered. The LC is described in terms of the classical order tensor Q, which is split as Q=sN, where N is a normalized tensor. Two independent evolution laws are given for s and N. The model includes an evolutive equation for the temperature field obtained from an appropriate form of the energy balance, in which the internal powers associated to the equations for s and N are accounted for. The thermodynamic restrictions in the constitutive relations which ensure the Clausius–Duhem inequality have been pointed out
A phase field model for brine channels in sea ice
No full textIn this paper, we present a phenomenological mathematical model for describing the features of the brine channels in sea ice. The differential system is composed of the Ginzburg–Landau and Cahn–Hilliard equations, in addition to the heat equation, that controls the ice–liquid phase transition by the temperature and hence the establishment of brine channels. The compatibility of this system with the thermodynamic laws and a maximum theorem is prove
Phase transitions in shape memory alloys: A non-isothermal Ginzburg-Landau mode
No full textWe propose a model to describe non-isothermal transitions from the austenite to the martensite phase
occurring in shape memory materials. The phenomenon is set in the context of the Ginzburg-Landau
theory of phase transitions, postulating a free energy depending on the temperature, the stress and the
order parameter. In the one-dimensional case, when only two martensitic variants are involved and stress
and deformation have a fixed direction, our choice of free energy allows us to deduce a phase diagram
describing the main features of a typical SMA. The Ginzburg-Landau equation ruling the evolution
of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive
equation relating stress, strain and order parameter. The consistency of the model with the second law of
Thermodynamics in the form of the Clausius-Duhem inequality is proved. Finally a possible generalization
to a three-dimensional model is proposed, by introducing a tensor-valued order parameter
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