Mechanics of inhomogeneous large deformation of photo-thermal sensitive hydrogels

A polymer network can imbibe copious amounts of solvent and swell, the resulting state is known as a gel. Depending on its constituents, a gel is able to deform under the influence of various external stimuli, such as temperature, pH-value and light. In this work, we investigate the photo-thermal mechanics of deformation of temperature sensitive hydrogels impregnated with light-absorbing nano-particles. The field theory of photo-thermal sensitive gels is developed by incorporating effects of photochemical heating into the thermodynamic theory of neutral and temperature sensitive hydrogels. This is achieved by considering the equilibrium thermodynamics of a swelling gel through a variational approach. The phase transition phenomenon of these gels, and the factors affecting their deformations, are studied. To facilitate the simulation of large inhomogeneous deformations subjected to geometrical constraints, a finite element model is developed using a user-defined subroutine in ABAQUS, and by modeling the gel as a hyperelastic material. This numerical approach is validated through case studies involving gels undergoing phase coexistence and buckling when exposed to irradiation of varying intensities, and as a microvalve in microfluidic application.     

Inhomogeneous large deformation study of temperature-sensitive hydrogel

In this paper, inhomogeneous deformation of a temperature-sensitive hydrogel has been studied and analyzed under arbitrary geometric and boundary conditions. We present the governing equations and equilibrium conditions of an isothermal process based on the monophase gel field theory of hydrogel via a variational approach. We have adopted and implemented an explicit form of energy for temperature-sensitive hydrogel in a three-dimensional finite element method (FEM) using a user-supply subroutine in ABAQUS. For verification purpose, a few numerical results obtained by the proposed approach are compared with existing experimental data and analytical solutions. They are all in good agreement. We also provide several examples to show the possible applications of the proposed method to explain various complex phenomena, including the bifurcation, buckling of membrane, buckling of thin film on compliant substrate and the opening and closure of flowers.     

Combustion with phase transition

The paper deals with a mathematical problem describing an exothermic chemical reaction in a diffusing substance possibly undergoing a change of phase. Global well-posedness in the classical sense is proved for the corresponding system of PDEs. Moreover, cases in which the phases are separated by sharp interphases or by transition regions are discussed. The limit case of negligible diffusion is also considered.

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Sommario Si studia il problema matematico che descrive una reazione chimica esotermica in una sostanza che diffonde e puo' subire cambiamenti di fase. Si dimostra esistenza globale in senso classico del relativo sistema di equazioni alle derivate parziali e si discute la possibilita' che le fasi siano separate da una regione di transizione e non da una netta superficie di interfase. Il caso limite di assenza di diffusione e' anche brevemente esaminato.

     

Transient analysis of temperature-sensitive neutral hydrogels

A model for transient deformation of neutral hydrogels that takes into account conservation of momentum, energy and mass for the solid polymer and fluid phase is derived, nondimensionalized and analyzed. Slow- and fast-response hydrogels are studied for three cases based on the response of (i) a spherical hydrogel, (ii) a constrained hydrogel slab to a step change in temperature, and (iii) the deformation in a temperature gradient. Model predictions for case (i) are shown to agree well with experiments for swelling and shrinking. For case (ii), solvent can be seen entering at the sides and flowing into the interior and towards the corners, such that the corners undergo a faster deformation than the sides. Immersed in a temperature gradient, case (iii), the hydrogel undergoes a bending motion and reaches a curved equilibrium shape, similar to the bending motion of polyelectrolyte hydrogels subjected to an external electric field. The benefit of the scale analysis conducted here, to predict correctly, prior to numerical computations, important characteristics such as stress, osmotic pressure and deformation times, is also highlighted.     

Mechanics of physisorption on elastomer surface

Mechanical aspects of physisorption on elastomeric substrates are studied via a continuum model in combination with the Lennard-Jones potential. In light of the incompressibility of elastomers, it is shown that the presence of a zero-dimensional adsorbate gives rise to a distributed force on the surface of the substrate. The induced surface deformation is determined, and the adsorption force and energy which depend on the substrate stiffness are derived. The results are then used to examine mutual interaction between two like adsorbates with small spacing, showing complicated attraction and repulsion arising from elastic deformation of the substrate. The dipole and quadruple moments of an adsorbate are also calculated, and the multipole approximation is adopted to quantify the interaction when the two adsorbates are separated remotely.     

Thermomechanics of shells undergoing phase transition

The resultant, two-dimensional thermomechanics of shells undergoing diffusionless, displacive phase transitions of martensitic type of the shell material is developed. In particular, we extend the resultant surface entropy inequality by introducing two temperature fields on the shell base surface: the referential mean temperature and its deviation, with corresponding dual fields: the referential entropy and its deviation. Additionally, several extra surface fields related to the deviation fields are introduced to assure that the resultant surface entropy inequality be direct implication of the entropy inequality of continuum thermomechanics. The corresponding constitutive equations for thermoelastic and thermoviscoelastic shells of differential type are worked out. Within this formulation of shell thermomechanics, we also derive the thermodynamic continuity condition along the curvilinear phase interface and propose the kinetic equation allowing one to determine position and quasistatic motion of the interface relative to the base surface. The theoretical model is illustrated by two axisymmetric numerical examples of stretching and bending of the circular plate undergoing phase transition within the range of small deformations.     

Shock wave induced phase transition in \alpha-FePO_4

Shock wave induced response of the berlinite form of FePO has been investigated up to 8.5 GPa. The X-ray diffraction measurements on the shock recovered samples reveal transition to the mixture of an amorphous phase and an orthorhombic phase around 5 GPa. The proportion of the amorphous material in the recovered sample is found to decrease at higher pressure. The results are interpreted in terms of a three-level free energy diagram for the crystal to amorphous transitions. Received 26 May 1997 / Accepted 1 September 1997     

A nonlinear field theory of deformable dielectrics

Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.     

An investigation of thermodynamic states during high-pressure fuel injection using equilibrium thermodynamics

A numerical investigation of mixing processes between an injected fuel (an n-alkane) and a chamber inert gas (nitrogen) was carried out for high-pressure fuel injection. The objective is to determine conditions for the coexistence of both liquid and gas phases under the typical ambient conditions encountered in diesel engines. A phenomenological investigation was built by coupling phase stability analysis with the energy conservation equation. Phase changes (including separation and combination) are predicted to occur so as to yield the lowest Gibbs free energy. It is also shown that predicted states without considering phase transitions can be very different from the corresponding thermodynamically correct states. By comparing four n-alkane/nitrogen mixtures it is shown that the lower limit of the two-phase region occurs at similar temperatures. However, heavy n-alkane/nitrogen mixtures have a larger upper limit, and phase separation occurs at higher temperatures. The present model predicts the existence of multiple phases locally in the dense spray jet under high temperature and pressure ambient conditions due to the significant reduction of the mixture temperature caused by vaporization and cooling.     

Diffuse-interface modeling of phase segregation in liquid mixtures

We simulate the phase separation of a binary mixture that is deeply quenched into the unstable range of its phase diagram. The mixture is described through the diffuse-interface model and the governing equations are integrated in 2D and 3D in a periodic box and in a channel using a pseudo-spectral method. Spinodal decomposition patterns for critical and off-critical mixtures are studied, revealing the scaling laws of the characteristic lengthscale and composition of single-phase microdomains, together with their dependence on the Peclet number. Comparison between 2D and 3D results reveals that 2D simulations capture, even quantitatively, the main features of the phenomenon. However, while the agreement between 2D and 3D simulations is excellent when the mixture is confined in a periodic box, it appears to be less pronounced in a channel-like geometry.     

Mechanics of soft active materials with phase evolution

This paper studies the mechanics of soft active materials where the actuation is generated due to the formation of phases that are stress-free at the moment of their creation and therefore experience no deformation in the associated configuration. Phase formation is a continuous time-dependent process, which results in individual phases forming at different times and in different configurations of the material body, and thus it is coupled with mechanical deformation. Subsequent deformation of the material body results in individual phases experiencing different states of deformation and the overall material response results from the combined responses of the individual phases weighted by their respective volume fractions. Therefore, a great challenge in modeling the mechanics of soft active materials with evolving phases is to track the deformation and evolution of individual phases formed at different times and in different configurations. In this paper, a generalized one-dimensional model framework is presented to address this challenge. However, this model proves to be computationally inefficient. In response, an effective phase model is developed that tracks the combined deformation histories of new phases through a single, effective deformation. Both the general and effective phase models are evaluated with two fundamentally distinct phase evolution rules for three common mechanical problems: extension, stress relaxation, and creep. The first evolution rule represents a discrete transition from one phase to another while the second rule corresponds to a general transition from several phases into one phase. The effective phase model demonstrates excellent agreement with the generalized theory for all three mechanical problems considered under both types of evolution rules.     

On hydrodynamic instabilities,chaos and phase transition

Ellipticity as the underlying mechanism for instabilities of physical systems is highlighted in the study of model nonlinear evolution equations with dissipation and the study of phase transition in Van der Waals fluid. Interesting results include spiky solutions, chaotic behavior in the context of partial differential equations, as well as the nucleation process due to ellipticity in phase transition.     

Moving inelastic discontinuities and applications to martensitic phase transition

Summary In this work, equations of the kinetics and kinematics are developed for heterogeneous materials containing inelastic discontinuities with moving boundaries. From the derived free energy and the power of external forces one obtains the driving force acting on the moving boundary. Introducing the interface operators and some hypothesis on inelastic fields, one gets the driving force for the formation of an ellipsoidal domain. The theoretical model is illustrated by the derivation of nucleation and growth conditions of a martensitic plate inside an inhomogeneous plastic strain field. The obtained results are combined with a study of the kinetics and kinematics to derive the constitutive equation of an austenitic single crystal, from which the overall behavior of polycrystalline TRIP steels is deduced using the self-consistent scale-transition method. Comparison with experimental data shows a good agreement. Received 7 May 1999; accepted for publication 14 June 1999     

A preparation method of functionally graded materials with phase transition under shock loading

The propagation of phase boundary in a material undergoing shock induced irreversible phase transition is studied theoretically using a model based on simple-mixture rule. It is found that along with the decay of the phase boundary, a functionally graded material (FGM) forms in the mixed-phase region. Such FGMs are composed of parent phase and product phase, and the composition and physical properties are changing continuously without apparent macro-interfaces. The effect of stress boundary conditions on formation of the FGM is investigated in detail with a numerical method. The possibility of producing FGMs with impact method is proposed and the limit of this method is discussed.     

A chemo-electro-mechanical model for simulation of responsive deformation of glucose-sensitive hydrogels with the effect of enzyme catalysis

A multi-effect-coupling glucose-stimulus (MECglu) model is developed and solved numerically for the swelling behavior of soft smart hydrogels responding to changes in the environmental glucose concentration. The model considers the effect of the glucose oxidation reaction catalyzed by enzymes including glucose oxidase and catalase. It is composed of the Nernst-Planck equation for the mobile species in the solvent, the Poisson equation for the electric potential, and a nonlinear mechanical equation for the large deformations of the hydrogel that arise due to the conversion of chemical energy to mechanical. Based on the theory of the chemo-electro-mechanical-coupled fields, the formulation of the fixed charge groups bound onto the cross-linked polymer network is associated with the change of the ambient solution pH. The MECglu model is validated by comparison between the steady-state computation and experimental equilibrium swelling curves, and good agreement is obtained. A parameter study is then conducted by steady-state simulations to ascertain the impact of various solvent parameters on the responsive swelling behavior of the hydrogel. One key parameter is the glucose concentration, which is varied within the range of practical physiological glucose concentrations from 0 to 16.5 mM (300 mg/ml) to support the design and optimization of an insulin delivery system based on a glucose-sensitive hydrogel with immobilized glucose oxidase and catalase. The influence of oxygen and glucose concentrations in the solvent is then further studied for the distributive profiles of reacting and diffusive species concentrations, the electric potential, the displacement, as well as the swelling ratio of the glucose-sensitive hydrogel.     

Localized transition waves in bistable-bond lattices

Discrete two-dimensional square- and triangular-cell lattices consisting of point particles connected by bistable bonds are considered. The bonds follow a trimeric piecewise linear force-elongation diagram. Initially, Hooke's law is valid as the first branch of the diagram; then, when the elongation reaches the critical value, the tensile force drops to the other. The latter branch can be parallel with the former (mathematically this case is simpler) or have a different inclination. For a prestressed lattice the dynamic transition is found analytically as a wave localized between two neighboring lines of the lattice particles. The transition wave itself and dissipation waves carrying energy away from the transition front are described. The conditions are determined which allow the transition wave to exist. The transition wave speed as a function of the prestress is found. It is also found that, for the case of the transition leading to an increased tangent modulus of the bond, there exists nondivergent tail waves exponentially localized in a vicinity of the transition line behind the transition front. The previously obtained solutions for crack dynamics in lattices appear now as a partial case corresponding to the second branch having zero resistance. At the same time, the lattice-with-a-moving-crack fundamental solutions are essentially used here in obtaining those for the localized transition waves in the bistable-bond lattices. Steady-state dynamic regimes in infinite elastic and viscoelastic lattices are studied analytically, while numerical simulations are used for the related transient regimes in the square-cell lattice. The numerical simulations confirm the existence of the single-line transition waves and reveal multiple-line waves. The analytical results are compared to the ones obtained for a continuous elastic model and for a related version of one-dimensional Frenkel-Kontorova model.     

(Adiabatic) phase boundaries in a bistable chain with twist and stretch

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.     

On the structure of the Hugoniot relation for a shock-induced martensitic phase transition

The Hugoniot curve relates the pressure and volume behind a shock wave, with the temperature having been eliminated. This paper studies the Hugoniot curve behind a propagating sharp interface between two material phases for a solid in which an impact-induced phase transition has taken place. For a solid capable of existing in only one phase, compressive impact produces a shock wave moving into material, say, at rest in an unstressed state at the ambient temperature. If the specimen can exist in either of two material phases, sufficiently severe impact may produce a disturbance with a two-wave structure: a shock wave in the low-pressure phase of the material, followed by a phase boundary separating the low- and high-pressure phases. We use a theory of phase transitions in thermoelastic materials to construct the Hugoniot curve behind the phase boundary in this two-wave circumstance. The kinetic relation controlling the evolution of the phase transition is an essential ingredient in this process.      

Combined stress waves with phase transition in thin-walled tubes简

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the σ-axis in the στ-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the "fast" and "slow" phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.     

Large conversion of energy in dielectric elastomers by electromechanical phase transition

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electrome-chanical cycle consisting of only unbulged states.