A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

We design a new mesoscopic thin-film model for shape-memory materials which takes into account thermomechanical effects. Starting from a microscopic thermodynamical bulk model, we guide the reader through a suitable dimension reduction procedure followed by a scale transition valid for specimen large in area up to a limiting model which describes microstructure by means of parametrized measures. All our models obey the second law of thermodynamics and possess suitable weak solutions. This is shown for the resulting thin-film models by making the procedure described above mathematically rigorous. The main emphasis is, thus, put on modeling and mathematical treatment of joint interactions of mechanical and thermal effects accompanying phase transitions and on reduction in specimen dimensions and transition of material scales.     

Direct laser-driven ramp compression studies of iron: A first step toward the reproduction of planetary core conditions

The study of iron under quasi-isentropic compression using high energy lasers, might allow to understand its thermodynamical properties, in particular its melting line in conditions of pressure and temperature relevant to Earth-like planetary cores (330–1500 GPa, 5000–8000 K). However, the iron alpha-epsilon solid–solid phase transition at 13 GPa favors shock formation during the quasi-isentropic compression process which can depart from the appropriate thermodynamical path. Understanding this shock formation mechanism is a key issue for being able to reproduce Earth-like planetary core conditions in the laboratory by ramp compression. In this article, we will present recent results of direct laser-driven quasi-isentropic compression experiments on iron samples obtained on the LULI 2000 and LIL laser facilities.     

Numerical investigation of the mechanism of asymmetric vortex flows

A robust iterative method suitable for the numerical simulation of high angle of-attack vortex flows is established based upon the multiple line vortex model (MLVM). With symmetric or asymmetric positions of separation lines given, the first converged solution at an angle of attack as high as 60 degree is obtained by means of the present method. Numerical experiments for a tangent-ogive forebody indicate the viscous onset mechanism of asymmetric vortex flows over a body of revolution at high angles of attack and zero sideslip.     

A one-dimensional continuum model for ferroelectric ceramics

In this article, we introduce a one-dimensional continuum model for ferroelectric ceramics within a thermodynamical framework. The model consists of a free energy potential, a switching criterion, and a kinetic relation. The free energy potential is given as a function of polarization, strain, and two internal variables – remanent polarization and remanent strain. A polarization switching is described by evolutions of the two internal variables and evolution laws called kinetics are proposed based on the second law of thermodynamics. The predictions of the model are compared with experimental observations. It is suggested to model unpoled domains in the fully poled state for improved model responses.     

The inelastic behavior of metals subject to loading reversal

One of the consequences of memory effects in the plastic deformation of metals is the Bauschinger effect (Civilingenieur 27 (1881) 289–348), which manifests itself as a difference in the values of the yield stress in tension and compression for a material that has undergone plastic deformation. The Bauschinger effect has been modeled with the kinematic hardening rules e.g., Ziegler (Quart. Appl. Math. 17 (1959) 55) and Chaboche (Int. J. Plasticity 2 (1986) 149). These models, though, are not able to reproduce the stress-strain response accurately at points of loading reversal: it has been observed (Acta Metall. 34 (1986) 1553; Mater. Sci. Engineering A113 (1989) 441) that, for some materials, the stress has a plateau after the loading is reversed. This is not reflected by the kinematic hardening rule nor by its modifications. In this paper we will develop a general three dimensional model that is able to reproduce the stress–strain response at loading reversals and can be applied also to more general changes of loading direction. The central idea of our model is to link the hardening behavior of the material to thermodynamical quantities such as the stored energy due to cold work and the rate of dissipation. The predictions of the theory show good agreement with the stress–strain curve and also with the manner in which the stored energy varies with the inelastic strain, as obtained from experiments (Progress in Materials Science (1973) Vol. 17. Pergamon, Oxford; Trans. Met. Soc. AIME 224 (1962) 719).     

Air–water counter-current slug flow data in vertical-to-horizontal pipes containing orifice type obstructions

This paper presents experimental counter-current air–water flow data on the onset of flooding and slugging, the slug propagation velocity, the predominant slug frequency and the average void fraction collected by using different size orifices installed at two locations in a horizontal pipe. For the flow conditions covered during these experiments, it was observed that there is no significant difference between the onset of flooding and the onset of slugging when an orifice is installed in the horizontal run. However, a difference was observed for the experiments carried out without orifices. Furthermore, the position of the orifice with respect to the elbow does not affect the onset of flooding and slugging. When an orifice is installed in the horizontal run, it was observed that slugs occur due to the mutual interaction (constructive interference) of two waves traveling in opposite directions. This means that a completely different mechanism seems to govern the formation of slugs in counter-current two-phase flows in horizontal partially blocked pipes. This is in contrast to that described for the slugging phenomena in co-current flow, where wave instability seems to be the principal mechanisms responsible of bridging the pipe. The mutual interaction of waves traveling in opposite directions seems to control the behaviour of the slug propagation velocity, the slug frequency and average void fraction with increasing the gas superficial velocity.     

Rheological analysis of the structural properties effecting the percutaneous absorption and stability in pharmaceutical organogels

This study presents the organogels of glyceryl monostearate emulsifiers and coconut oil as an alternative for developing the traditional organogels. We investigated how the emulsifier type affects the semisolid consistency and the drug release. In these aspects we compared glyceryl monostearate organogels (GMSO) to commercially available references, while studying the effect of the individual constituents on the structural and functional properties.Rheology provided indirect information on the structure, relevant from an application point of view. We observed that glyceryl monostearate as an organogelator results in a network with elastic nature and moderate crosslink energy. The products had low viscosity and low yield value which means practically an easily spreadable pharmaceutical dosage form with soft consistency.Modelling the percutaneous absorption in vitro, we observed that the diffusion of the piroxicam incorporated was significantly affected by the thermodynamical potency of piroxicam, which was favoured by the emulsifier. The glyceryl monostearate enhanced the partition of the suspended drug, resulting in higher drug release.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

We present a fully general, three dimensional, constitutive model for Shape Memory Alloys (SMAs), aimed at describing all of the salient features of SMA evolutionary response under complex thermomechanical loading conditions. In this, we utilize the mathematical formulation we have constructed, along with a single set of the model’s material parameters, to demonstrate the capturing of numerous responses that are experimentally observed in the available SMA literature. This includes uniaxial, multi-axial, proportional, non-proportional, monotonic, cyclic, as well as other complex thermomechanical loading conditions, in conjunction with a wide range of temperature variations. The success of the presented model is mainly attributed to the following two main factors. First, we use multiple inelastic mechanisms to organize the exchange between the energy stored and energy dissipated during the deformation history. Second, we adhere strictly to the well established mathematical and thermodynamical requirements of convexity, associativity, normality, etc. in formulating the evolution equations governing the model behavior, written in terms of the generalized internal stress/strain tensorial variables associated with the individual inelastic mechanisms. This has led to two important advantages: (a) it directly enabled us to obtain the limiting/critical transformation surfaces in the spaces of both stress and strain, as importantly required in capturing SMA behavior; (b) as a byproduct, this also led, naturally, to the exhibition of the apparent deviation from normality, when the transformation strain rate vectors are plotted together with the surfaces in the space of external/global stresses, that has been demonstrated in some recent multi-axial, non-proportional experiments.     

Experimental and numerical investigation of nonlinear thermocapillary oscillations in an annular geometry

The present work investigates thermocapillary flow in a cylindrical configuration using large Prandtl number liquids. The flow is studied using coordinated simulations and experimental optical methods such as PIV and flow visualization. In this way, properties of the oscillatory state can be obtained in great detail. Considerable attention is given to the search for the parameters influencing the onset of the instability. It is found that the onset of oscillations can be correlated using a thermocapillary Reynolds number. The oscillations take the form of a standing wave close to the onset, which is replaced by a travelling wave for stronger forcing. The selection of azimuthal wave number of the oscillatory mode is determined from geometrical parameters, and resembles the wave number selection in vortex ring instabilities. Throughout we obtain good agreement between experiments and simulations using a mathematical model with an undeformed adiabatic free surface.     

A mechanical model for the adhesive contact with local sliding induced by a tangential force

Adhesion has been demonstrated to play an important role in contact and friction between objects at small scales. While various models have been established for adhesive contact under normal forces, studies on the adhesive contact under tangential force have been far fewer, which if any, are mostly confined to the non-slipping situations. In the present work, a model has been proposed for adhesive contact with local sliding under tangential forces. Herein, the onset of local sliding in adhesive contact has been addressed by assuming the nucleation of dislocations. By analogy with the emission of dislocations at a crack tip, the critical tangential force for the onset of sliding has been determined, and its effect on the evolution of contact size has also been studied. Comparison with relevant experiments has verified the validity of the present model.     

Simplified model for prediction of dynamic damage and fracture of ductile materials

A simplified model for prediction of dynamic damage and fracture of ductile material has been proposed. The plastic flow of matrix and the void growth are dealt with separately after we show that two separated loading sub-surfaces and corresponding normality rules for matrix and damage exist. The equation of the loading sub-surface for the matrix plastic flow is derived by the means of introducing a mapping damage-free solid of matrix material, whose constitutive relation is supposed to have been determined via Hopkinson bar experiments. Based on the results of recovered experiments the law of damage evolution is phenomenally established. The model has been applied to predict some spall experiments carried out on tantalum, and results show it predicts the experiments very well.     

Time dependent analysis of the evolution of the distribution of drop sizes of liquid droplets in a free-molecule stream

This paper deals with the study of the time-evolution of the distribution of drop sizes, velocities and temperatures of a cloud of droplets shot, with a given initial velocity and temperature and a given distribution of drop sizes, into a gas volume at fixed thermodynamical conditions. The mean free path of the gas molecules was large compared with the mean diameter of a droplet. The study is based on a phase-transition physical model, proposed by Bellomo (1974), which takes into account the kinetic theory of liquids and gases and the physics of gas-surface interaction. This model has proved suitable for time-dependent non equilibrium phenomena and has given theoretical results very close to experimental ones.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

On a thermodynamical consistent constitutive law based on the concept of internal variables

A multiaxial constitutive law describing the behaviour of polycrystalline ice in a phenomenological way will be introduced. Internal variables represent the hardening and softening of the material and also a modified inelastic work. The equations are implemented in a thermodynamical frame.To derive the unknown functions and parameters a strategy is developed, facilitating the fitting in a simple and fast manner.Finally, the comparison between computations and experiments shows a good agreement.     

Mechanical and thermodynamical basis for theories of generalized continuous media

We study the essential theoretical foundations to construct a model which represents the mechanical and thermodynamical behaviour of a real material. Particular reference is made to the case where the classical model of Cauchy's continuum is not sufficient. Special attention is devoted to distinguishing between the constitutive features of the material on the one hand and what results from the postulated physical principles on the other. The subject develops on general lines and allows us to point out possible advances consistent with our assumptions. Finally we apply the proposed theory to prove an important restriction on the admissible constitutive equations.     

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.