Chemically induced swelling of hydrogels

We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the model involves a supplemental interfacial equation imposing configurational force balance. We present a hybrid eXtended-Finite-Element/Level-Set Method for obtaining approximate solutions to the governing equations of the model. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued to engineer hydrogels with optimal response times.     

Finite element implementation of poroelasticity theory for swelling dynamics of hydrogels

Hydrogel can swell to many times of its dry volume, resulting in large deformation which is vital for its function. The swelling process is regulated by many physical and chemical mechanisms, and can, to some extent, be fairly described by the poroelasticity theory. Implementation of the poroelasticity theory in the framework of finite element method would aid the design and optimization of hydrogel-based soft devices. Choosing chemical potential and displacement as two field variables, we present the implementation of poroelasticity tailored for hydrogel swelling dynamics, detail the normalization of physical parameters and the treatment of boundary conditions. Several examples are presented to demonstrate the feasibility and correctness of the proposed strategy.     

Analysis of thermally induced multistable composites

This paper models the non-linear flexural response of laminates that have piecewise variation of lay-up in the planform, using finite element analysis. Attention is focused on the effects that thermal stresses have on the potential multiple shapes of a composite structure. Unsymmetric laminates may possess more than a single equilibrium configuration, and during the cool-down the solution thus bifurcates at a critical temperature. In static analyses, numerical solutions are often coaxed to converge into one or the other branch of the solution. A methodology to overcome this problem is presented. Such modelling is necessary to allow application of multistable composite within morphing aircraft structures as multistable composites could provide a viable solution for the realisation of shape-adaptable structures.     

Instability of thermally induced vibrations of carbon nanotubes

The dynamical stability of carbon nanotubes embedded in an elastic matrix under time-dependent axial loading is studied in this paper. The effects of van der Waals interaction forces between the inner and outer walls of nanotubes are taken into account. Using continuum mechanics, we apply an elastic layered shell model to solve the transverse parametric vibrations of a carbon nanotube. Both the Gaussian wide-band axial temperature changes and physically realizable temperature changes with known probability distributions are assumed as the tube axial loading. The energy-like functionals are used in the stability analysis. The emphasis is placed on a qualitative analysis of dynamic stability problem. Stability domains in the space of geometric, material and loading parameters are presented in analytical forms.     

Development of holographic techniques to study thermally induced deformation

Holography is used to study thermally induced deformation in a rock specimen extracted from a cubical sample taken during a geological survey. Experiments are conducted over small temperature increments on the order of a few degrees Fahrenheit, to suppress extraneous variations in optical path which could otherwise be introduced by temperature gradients and convection currents in the air surrounding the specimen. The concept of an optical rosette is introduced to predict principal strains and their corresponding directions from holographically obtained data. Values measured for thermal coefficients of expansion fall within the range of those documented by other investigators using more conventional experimental methods.     

Kinetics of smart hydrogels responding to electric field: A transient deformation analysis

A multiphysics model is presented in this paper for simulation of kinetics of the smart hydrogels subject to an externally applied electric field, especially for analysis of the transient deformation of the hydrogel. The model termed the multi-effect-coupling electric stimulus (MECe) takes account of the coupled chemo-electro-mechanical multiphysics domains and the multi-phase effect of polymeric network and interstitial liquid as well as ionic species. The MECe model is validated well by transient simulation and comparison with available experimental data. Kinetics of ionic concentration of diffusive species is simulated. Parameter studies on the hydrogel displacement are conducted in detail for influences of externally applied electric voltage, initially fixed-charge density and surrounding bath solution concentration.     

Finite element and sensitivity analysis of thermally induced flow instabilities

This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.     

Semi-analytical analysis of thermally induced damage in thin ceramic coatings

An efficient procedure to analyze damage evolution in brittle coatings under influence of thermal loads is suggested. The approach is based on a general computational scheme to determine damage evolution parameters, which incorporates an analytical solution of the appropriate interim boundary-value thermoelasticity problem. For thin inhomogeneous coatings, the simplification in the analysis is achieved by application of the mathematical model with generalized boundary conditions of thermomechanical conjugation of the substrate with environment via the coating. Efficiency of the suggested approach is illustrated by an example of damage evolution in the alumina coating on the titanium-alloy and tungsten substrates under uniform heating.     

Prediction of thermally induced fracture from notch and crack front

The strain energy density criterion is applied to predict fracture trajectories emanating from existing notch and crack front in nonisothermal environments. When temperature gradients are raised sufficiently high across a notch or crack, the resulting fracture trajectories are non-self-similar and curved in shape. Influence of mechanical loading is also considered in addition to stresses induced by thermal changes. Increase in the applied mechanical load tends to shift or restore the fracture trajectories toward the plane of notch or crack symmetry. The notch sharpness can be varied by adjusting the ration of the minor to major axes of an elliptical cavity. Narrowing the notch primarily increases the local intensity of the strain energy density function dW/dV that is inversely proportional to the radial distance measured from the focal point of the ellipse. This singular character of dW/dV prevails, in general, for all materials and loadings. Numerical results are obtained and displayed graphically for several examples involving fracture trajectory shapes that are not intuitively obvious.     

Stochastic modeling of the thermally induced atmospheric flow at mesoscale

This paper presents a three-dimensional stochastic linear model of the atmospheric flow induced by the variability of heat flux over land surface. The primitive equations relating perturbation terms of wind field, geopotential and buoyancy are formulated as a system of stochastic partial differential equations and solved analytically. The solution is based on spectral representations of the homogeneous random fields. The flow intensity is found to be proportional to the standard deviation of the heat flux into the atmosphere. The intensity of the vertical motion becomes more sensitive to the differential heating with a larger length scale as altitude goes higher. Stability and synoptic wind inhibit the development of the flow. The proposed theory improves the understanding of the role that heterogeneous land surface plays in atmospheric circulations at the mesoscale.

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Sommario Questo lavoro presenta un modello stocastico lineare del moto atmosferico tridimensionale indotto dalla variabilità del flusso di calore sulla superficie del terreno. Le equazioni primitive che legano i termini perturbativi del campo di vento, del geopotenziale e del parametro di galleggiamento sono formulate come un sistema di equazioni stocastiche alle derivate parziali che vengono risolte analiticamente. Tale soluzione è basata su rappresentazioni spettrali di campi aleatori omogenei. L'intensità del moto risulta essere proporzionale alla deviazione standard del flusso di calore diretto verso l'atmosfera. L'intensità del moto in direzione verticale appare più sensibile al riscaldamento differenziale, con scale spaziali più grandi al crescere dell' altitudine. La stabilità ed il flusso sinottico tendono ad inibire lo sviluppo del moto. La teoria qui proposta migliora la comprensione del ruolo che la superficie eterogenea del terreno gioca nella circolazione atmosferica alla meso-scala.

     

Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers

Shape memory polymers (SMPs) are polymers that can demonstrate programmable shape memory effects. Typically, an SMP is pre-deformed from an initial shape to a deformed shape by applying a mechanical load at the temperature T_H>T_g. It will maintain this deformed shape after subsequently lowering the temperature to T_L<T_g and removing the externally mechanical load. The shape memory effect is activated by increasing the temperature to T_D>T_g, where the initial shape is recovered. In this paper, the finite deformation thermo-mechanical behaviors of amorphous SMPs are experimentally investigated. Based on the experimental observations and an understanding of the underlying physical mechanism of the shape memory behavior, a three-dimensional (3D) constitutive model is developed to describe the finite deformation thermo-mechanical response of SMPs. The model in this paper has been implemented into an ABAQUS user material subroutine (UMAT) for finite element analysis, and numerical simulations of the thermo-mechanical experiments verify the efficiency of the model. This model will serve as a modeling tool for the design of more complicated SMP-based structures and devices.     

The frequency criterion for thermally induced vibrations in elastic beams

Summary Thermally induced vibration in elastic beams, also known as thermal flutter, has not yet found a satisfactory treatment. The sheer weight of complications has so far rendered, and may indeed permanently render, a unified treatment impossible. In the present paper a frequency criterion is established which essentially defines the strength of the thermal excitation. Since damping is inevitably present, the thermal excitation must be large enough to overcome damping. After introducing a thermal time constant it is shown that at a critical frequency, the thermal excitation reaches a maximum. For practical cases, this critical frequency is very small, as typical structural frequencies go. Thus only systems with very low eigenfrequencies can be expected to tend to flutter thermally.

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Übersicht Durch Wärmeeinstrahlung verursachtes Schwingungsverhalten von Tubularbalken, sogenanntes Wärmeflattern, hat bisher noch keine zufriedenstellende allgemeingültige Beschreibung gefunden. Die Zahl der verschiedenen Einflüsse, die berücksichtigt werden müßten, ist in der Tat so groß, das es bisher noch nicht gelungen ist, den Problemkreis in seiner Gesamtheit zu erfassen und es sieht ganz so aus, als ob dies vielleicht nie gelingen wird. In der vorliegenden Arbeit wird ein Frequenzkriterium erstellt, das auf der Stärke der Schwingungserregung durch die Wärmeeinstrahlung beruht. Da Dämpfung bestimmt existiert, muß die Schwingungserregung durch die Wärmeeinstrahlung nicht nur vorhanden, sondern auch größer als die Dämpfung sein. Nach Einführung einer Wärmezeitkonstanten wird gezeigt, daß die Schwingungserregung ihren Höchstwert erreicht, wenn die Eigenfrequenz des Tubularbalkens einen gewissen kritischen Wert annimmt. In allen Fällen von praktischem Interesse ist diese kritische Frequenz übrigens so gering, daß nur bei Balken mit extrem niedriger Eigenfrequenz mit Wärmeflattern gerechnet werden kann.

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Dedicated to Prof. Dr.-Ing. Th. Lehmann on the occasion of his sixtieth birthday     

光纤陀螺热致漂移误差的模糊补偿(英文)

针对光纤陀螺启动过程中的热致漂移误差问题,研究了一种模糊模型补偿方案。依据Shupe非互易性理论和Mohr加热模型试验的结论,以光纤环内侧温度和温度变化率为输入,以陀螺漂移为输出,建立了二输入一输出模糊模型。利用全温范围(-25℃～45℃)内光纤陀螺的恒温静态试验数据,基于自适应神经网络模糊推理系统的自学习功能,辨识出模糊规则库。通过实时施行模糊推理可实现光纤陀螺温度漂移的在线自动补偿。室温验证试验表明,陀螺的零偏稳定性由补偿前的0.037(°)/h提高到0.017(°)/h,陀螺启动时间由补偿前的30 min减少为2 min。     

3D thermally induced analysis of annular plates of functionally graded materials

Within the framework of three-dimensional elasticity theory, this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field. The present analytical solutions are validated through comparisons against those available in open literature. A parametric study is conducted to examine the effects of gradient distribution, different temperature fields, different diameter ratio and boundary conditions on the deformation and stress fields of the plate. The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials(FGM)annular plates.     

On the thermally induced bistability of composite cylindrical shells for morphing structures

The multistability of composite thin structures has shown potential for morphing applications. The present work combines a Ritz model with path-following algorithms to study bistable cylindrical panels. Polynomial discretisations of the displacements field are used to predict stable shapes’ geometry and other aspects of the nonlinear structural behaviour. In order to improve the inherently poor conditioning properties of Ritz approximations of slender structures, a non-dimensional Shell Lamination Theory with Sanders nonlinear strains is developed and presented. An investigation on the relative importance of different nonlinear strain terms is shown to provide useful insight into the applicability of common assumptions about shell kinematics. In the current approach, we continue numerical solutions in parameter space, that is, we path-follow equilibrium configurations as the control parameter varies, find stable and unstable configurations and identify bifurcations. The numerics is carried out using a set of in-house Matlab® routines for numerical continuation. Results are compared with detailed finite elements analysis throughout the course of the paper.     

Stressed microstructures in thermally induced M9R-M18R martensites

We revisit the phase transformation that produces ‘long-period stacking’ M9R-M18R martensites in Cu-based shape-memory alloys and analyze some associated microstructures, in particular, the typical wedge-shaped configuration. Our basic premise is that the cubic-to-monoclinic martensitic phase change in these alloys is, geometrically, but a slight modification of the well-known bcc-to-9R transformation occurring in various elemental crystals, whose lattice strain is, at the microlevel, the same Bain strain as for the bcc-to-fcc transformation. For the memory alloys we thus determine the ‘near-Bain’ microstrain, thereby analyzing the faulted, long-period stacking martensite as a mesoscale structure derived from compatibility with the austenite. We compute the transformation-twin systems, habit planes, average deformation and stacking-fault density of the 9R, 18R, M9R or M18R martensites, as they arise from the compatibility conditions between the parent and product lattices. We confirm earlier conclusions that a stress-free wedge is not kinematically compatible in these materials. However, we show that this microstructure is ‘close enough’ to compatibility, finding that its stress levels are low and should cause only minimal plastification and damage in the crystal. The wedge is therefore rationalized as a viable path for the transformation also in these substances. We verify this to hold for all the lattice parameters reported for Cu-based alloys. In general, we conclude that martensitic microstructures can be stressed to a degree also in good memory materials. Furthermore, we find that the lattice-parameter relations, guaranteeing the zero-stress compatibility of special configurations favoring the transformation and its reversibility, do not need to be strictly enforced in these crystals, because the residual stresses in microstructures are low regardless of lattice-parameter values.     

Mechanics of thermophoretic and thermally induced edge forces in carbon nanotube nanodevices

A double walled carbon nanotube thermal actuator consisting of a short outer tube sliding along a long inner tube under a temperature gradient is used as a model system to investigate the mechanics of thermophoretic and thermally induced edge forces in nanoscale contact based on the theory of lattice dynamics. It is shown that the total thermophoretic force has two components: a gradient force due to the change in van der Waals energy in the direction of temperature gradient and an unbalanced edge force due to the temperature difference between the two tube ends. Closed-form analytical expressions are derived for the gradient and unbalanced edge forces, with results in excellent agreement with molecular dynamics simulations. This study represents a first analytical study of thermophoretic and thermally induced edge forces between two solid bodies, and may have far reaching implications on thermomechanical nanodevices and nanoscale contact.     

Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.