Linear problem of water-ice phase transitions in unsaturated soils

The approach proposed by Menot is developed. The problem of the freezing of an unsaturated soil is formulated for a compressible gas and equal component pressures. An analytic solution is obtained in the linear approximation. The results indicate the strong dependence of the ice saturation on the permeability of the soil and the applied pressure gradient.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 68–73, May–June, 1990.     

An invariant formulation for phase field models in ferroelectrics

This paper introduces an electro-mechanically coupled phase field model for ferroelectric domain evolution based on an invariant formulation for transversely isotropic piezoelectric material behavior. The thermodynamic framework rests upon Gurtin’s notion of a micro-force system in conjunction with an associated micro-force balance. This leads to a formulation of the second law, from which a generalized Ginzburg–Landau evolution equation is derived. The invariant formulation of the thermodynamic potential provides a consistent way to obtain the order parameter dependent elastic stiffness, piezoelectric, and dielectric tensor. The model is reduced to 2d and implemented into a finite element framework. The material constants used in the simulations are adapted to meet the thermodynamic condition of a vanishing micro-force. It is found that the thermodynamic potential taken from the literature has to be extended in order to avoid a loss of positive definiteness of the stiffness and the dielectric tensor. The small-signal response is investigated in the presence and in the absence of the additional regularizing terms in the potential. The simulations show the pathological behavior of the model in case these terms are not taken into account. The paper closes with microstructure simulations concerning a ferroelectric nanodot subjected to an electric field, a cracked single crystal, and a ferroelectric bi-crystal.     

WAVE INTERACTIONS IN SULICIU MODEL FOR DYNAMIC PHASE TRANSITIONS

Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis.For any given initial data with two pieces of constant states,the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states,the solution may be constructed from the Riemann solutions,with each two adjacent states connected by elementary waves.A new Riemann problem forms when these two waves collide.Through the exploration of these Riemann problems,the outcome of wave interactions may be classified in a suitable parametric space.     

Stress induced phase transitions in silicon

Silicon has a tremendous importance as an electronic, structural and optical material. Modeling the interaction of a silicon surface with a pointed asperity at room temperature is a major step towards the understanding of various phenomena related to brittle as well as ductile regime machining of this semiconductor. If subjected to pressure or contact loading, silicon undergoes a series of stress-driven phase transitions accompanied by large volume changes. In order to understand the material's response for complex non-hydrostatic loading situations, dedicated constitutive models are required. While a significant body of literature exists for the dislocation dominated high-temperature deformation regime, the constitutive laws used for the technologically relevant rapid low-temperature loading have severe limitations, as they do not account for the relevant phase transitions. We developed a novel finite deformation constitutive model set within the framework of thermodynamics with internal variables that captures the stress induced semiconductor-to-metal ($\mathrm{cd-Si}\to \mathrm{\beta }\mathrm{-Si}$), metal-to-amorphous ($\mathrm{\beta }\mathrm{-Si}\to \mathrm{a-Si}$) as well as amorphous-to-amorphous ($\mathrm{a-Si}\to \mathrm{hda-Si}$, $\mathrm{hda-Si}\to \mathrm{a-Si}$) transitions. The model parameters were identified in part directly from diamond anvil cell data and in part from instrumented indentation by the solution of an inverse problem. The constitutive model was verified by successfully predicting the transformation stress under uniaxial compression and load–displacement curves for different indenters for single loading–unloading cycles as well as repeated indentation. To the authors' knowledge this is the first constitutive model that is able to adequately describe cyclic indentation in silicon.     

The viscosity-capillarity criterion for shocks and phase transitions

This paper considers admissibility criteria for non-linear conservation laws based on (i) viscosity and (ii) capillarity and viscosity. It is shown by means of specific examples that while (ii) yields results consistent with experiment for materials exhibiting phase transitions,e.g. a van der Waals fluid, (i) does not.     

On the asymptotic behavior of a phase-field model for elastic phase transitions

We study the asymptotic behavior of a one-dimensional, dynamical model of solid-solid elastic transitions in which the phase is determined by an order parameter. The system is composed of two coupled evolution equations, the mechanical equation of elasticity which is hyperbolic and a parabolic equation in the order parameter. Due to the strong coupling and the lack of smoothing in the hyperbolic equation, the asymptotic behavior of solutions is difficult to determine using standard methods of gradient-like systems. However, we show that under suitable assumptions all solutions approach the equilibrium set weakly, while the phase field stabilizes strongly.     

Solution of nonlinear heat-conduction problems in a medium with phase transitions

A new method is proposed for solving one-dimensional nonlinear heat-conduction problems in a medium having any number of phase transitions (nonlinear Stefan problems). The method consists of a direct calculation of the isotherms and reduces to the Cauchy problem for a system of ordinary differential equations.The author thanks V. M. Kartvelishvili, a student at the Moscow Physicotechnical Institute, for writing the program and carrying out the calculations on a BÉSM-3M computer. The author thanks L. A. Chudov for useful comments.     

Backbone transitions and invariant tori in forced micromechanical oscillators with optical detection

Micromechanical oscillators often display rich dynamics due to nonlinearities in their response, actuation, and detection. This paper investigates the complicated response of a forced micromechanical oscillator. In particular, we investigate a thermally induced transition in the resonant response of a forced micromechanical oscillator with optical detection; and the branches of invariant tori formed at subsequent bifurcations that occur with increasing laser power. We use perturbation theory and continuation algorithms to investigate and compute these branches of invariant tori. The results of both methods are compared.     

Shocks versus kinks in a discrete model of displacive phase transitions

We consider dynamics of phase boundaries in a bistable one-dimensional lattice with harmonic long-range interactions. Using Fourier transform and Wiener–Hopf technique, we construct traveling wave solutions that represent both subsonic phase boundaries (kinks) and intersonic ones (shocks). We derive the kinetic relation for kinks that provides a needed closure for the continuum theory. We show that the different structure of the roots of the dispersion relation in the case of shocks introduces an additional free parameter in these solutions, which thus do not require a kinetic relation on the macroscopic level. The case of ferromagnetic second-neighbor interactions is analyzed in detail. We show that the model parameters have a significant effect on the existence, structure, and stability of the traveling waves, as well as their behavior near the sonic limit.     

Material forces and phase transitions in elasticity

A computational scheme for the determination of the interface in a strain-induced phase-transition problem for an elastic bar is proposed. The algorithm is based on the material force notion and more specifically on the simultaneous solution of equilibrium equations for the physical and material forces. The weak form of both equations is derived with the aid of a variational principle that accounts for the variations of the dependent and the independent variables. The whole scheme concludes in a nonlinear algebraic system which is numerically solved by the Newton method. The numerical results thus derived seem to be quite encouraging for further application of the concept of material forces in computations related to phase transition problems. The austenite–martensite transformation could be a possible application of the proposed model.     

On the phase transitions in fluid mixtures

Summary The integral equations of balance for a binary fluid mixture are stated when the mixture presents two phases which are separated by an interface. The equilibrium conditions are derived together with the Gibbs phase rule for plane interfaces. The theory is extended to the mixture with three phases.

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Sommario Si scrivono le equazioni integrali del bilancio per una miscela fluida binaria che una interfaccia separa dalla miscela del suo vapore. Si derivano le condizioni di equilibrio e, nel caso di interfaccia piana, la regola delle fasi di Gibbs. La teoria proposta è poi estesa a sistemi di miscela binaria con tre fasi.

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This paper is made under the auspices of G.N.F.M. of the Italian C.N.R.     

Interfacial and inhomogeneity penalties in phase transitions

Non-convex free energies permit phase transitions to occur. The ensuing state of a body is non-homogeneous and endowed with interphase boundaries. Both the inhomogeneity and the interfaces may contribute to the free energy and thus affect the onset of the phase transition. The paper investigates these effects in a one-dimensional setting and for deformation control. The main conclusion is that the incipient phase mixture is characterized by a stable kernel of small but finite phase fraction. This kernel must not be confused with the unstable nucleus whose energy maximum must be overcome before the kernel can form. We consider also the energy landscape of partial equilibria in which the load is uniform but the phase fraction and the number of interfaces have not yet reached equilibrium.Received: 6 July 2002, Accepted: 18 February 2003, Published online: 9 May 2003PACS: 64.60.-i     

On configurational weak phase transitions in graphene

We report a study on configurational weak phase transitions for a freestanding monolayer graphene. Firstly, we characterize weak transformation neighborhoods by suitably bounding the metric components. Then, we distinguish between structural and configurational phase changes and elaborate on the second class of them. We evaluate the irreducible invariant subspaces corresponding to these phase changes and lay down symmetry-breaking as well as symmetry-preserving stretches. In the reduced bifurcation diagram, symmetry-preserving stretches are related to a turning point with a change of stability but not of symmetry. Symmetry-breaking stretches are related to a first-order weak phase transition. We evaluate symmetry-breaking stretches as well as their generating cosets. The reduced bifurcation diagram consists of three transcritical bifurcating curves which are all unstable but can be stabilized producing a subcritical bifurcation. We, also, shortly comment on the hysteretical behavior that might appear in this case.