On the thermodynamics of smooth muscle contraction

Cell function is based on many dynamically complex networks of interacting biochemical reactions. Enzymes may increase the rate of only those reactions that are thermodynamically consistent. In this paper we specifically treat the contraction of smooth muscle cells from the continuum thermodynamics point of view by considering them as an open system where matter passes through the cell membrane. We systematically set up a well-known four-state kinetic model for the cross-bridge interaction of actin and myosin in smooth muscle, where the transition between each state is driven by forward and reverse reactions. Chemical, mechanical and energy balance laws are provided in local forms, while energy balance is also formulated in the more convenient temperature form. We derive the local (non-negative) production of entropy from which we deduce the reduced entropy inequality and the constitutive equations for the first Piola–Kirchhoff stress tensor, the heat flux, the ion and molecular flux and the entropy. One example for smooth muscle contraction is analyzed in more detail in order to provide orientation within the established general thermodynamic framework. In particular the stress evolution, heat generation, muscle shorting rate and a condition for muscle cooling are derived.     

Fundamentals of two-phase flow by the method of irreversible thermodynamics

The paper explores thermodynamic aspect of modelling two-phase systems by the methods of irreversible thermodynamics in both classical (CIT) and extended (EIT) formulation. The conservation laws for two-phase model-continuum are derived. Then, the entropy production is analysed for two-fluid and homogeneous systems. Different equations of state are taken into consideration, namely that corresponding to the accompanying equilibrium state of physical element and more complex resulting from EIT. Obtained expressions for rate of entropy production per unit volume allow to identify the dissipative mechanisms in the two-phase system and suggest the forms of phenomenological relations to be adopted in the constitutive equations.     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

Linear viscoelasticity and irreversible thermodynamics

The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.     

Formulation of a damage internal state variable model for amorphous glassy polymers

The following article proposes a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.     

Attenuation of the fourth sound in liquid helium II via extended thermodynamics

This work continues a study begun in previous works, where a non-standard model of liquid helium II is proposed, in which a small entropy transfer is associated with the superfluid component. In this work the influence of this superfluid entropy on the propagation of the fourth sound is analyzed. From experimental data for velocities and attenuations of the first and second sound, the model provides speed and attenuation coefficient of the fourth sound in a porous medium as a function of the ratio s_s/s between the superfluid entropy s_s and the total entropy s. These values are determined in the two limiting cases s_s/s=0 and =0.02, for various values of temperature and pressure.     

The rational mechanics and thermodynamics of polymeric fluids based upon the concept of a variable relaxed state

The conceptual framework of polymer continuum mechanics based upon Eckart's idea of a variable relaxed state is developed. No constitutive models are explicitly used. The theory admits four constitutive functions only, the scalar specific internal energy, the vectorial heat flux, and two tensorial fluxes representing non-elastic stress and flow (slippage). The non-linearity of the constitutive relations includes self-induced anisotropy (Leonov) with Reiner-Rivlin's equation representing a special example for this. — The effectiveness of this non-linear theory is demonstrated by treating elongational flows of polymer melts.     

Non-linear extended thermodynamics of real gases with 6 fields

We establish extended thermodynamics (ET) of real gases with 6 independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtain the symmetric hyperbolic system with respect to the main field. In near-equilibrium we recover the previous results. The correspondence between the ET 6-field theory and Meixner׳s theory of relaxation processes is discovered. The internal variable and the non-equilibrium temperature in Meixner׳s theory are expressed in terms of the quantities of the ET 6-field theory, in particular, the dynamic pressure. As an example, we present the cases of a rarefied polyatomic gas and study the monatomic-gas limit where the system converges to the Euler system of a perfect fluid.     

Determination of boundary conditions in extended thermodynamics via fluctuation theory

A system of equations from extended thermodynamics is proposed for the calculation of the temperature field in a rarefied gas at rest. Numerical simulations suggest that the temperature field in this case should exhibit boundary layers superposed on the classical Fourier solution. In order to derive such a field from the extended thermodynamics of moments, one needs boundary values for higher moments, which in practice cannot be assigned and controlled. We suggest that such boundary data emerge as mean values of thermal fluctuations and thus calculate them. The result agrees qualitatively with numerical simulations and it is quantitatively of the same order of magnitude.Received: 12 September 2003, Accepted: 9 October 2003, Published online: 23 January 2004 Correspondence to: E. Barbera     

Historical review of internal state variable theory for inelasticity

A review of the development and the usages of internal state variable (ISV) theory are presented in this paper. The history of different developments leading up the formulation of the watershed paper by Coleman and Gurtin is discussed. Following the Coleman and Gurtin thermodynamics, different researchers have employed the ISV theory for dislocations, creep, continuum damage mechanics (CDM), unified-creep-plasticity (UCP), polymers, composites, biomaterials, particulate materials, multiphase and multiphysics materials, materials processing, multiscale modeling, integrating materials science (structure–property relations) into applied mechanics formulations, and design optimization under uncertainty for use in practical engineering applications.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

基于内变量理论的一种广义粘弹性本构方程

以Ｂｉｏｔ理论为基础，将弹性应变与非弹性尖变均取作状态为量，引入耗散势，建立了一种率相关非弹性本构关系及演变方程，进而导出一种广义的粘弹性本构方程。     

Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation

The universal (i.e. independent of the constitutive equations) thermodynamic driving force for coherent interface reorientation during first-order phase transformations in solids is derived for small and finite strains. The derivation is performed for a representative volume with plane interfaces, homogeneous stresses and strains in phases and macroscopically homogeneous boundary conditions. Dissipation function for coupled interface (or multiple parallel interfaces) reorientation and propagation is derived for combined athermal and drag interface friction. The relation between the rates of single and multiple interface reorientation and propagation and the corresponding driving forces are derived using extremum principles of irreversible thermodynamics. They are used to derive complete system of equations for evolution of martensitic microstructure (consisting of austenite and a fine mixture of two martensitic variants) in a representative volume under complex thermomechanical loading. Viscous dissipation at the interface level introduces size dependence in the kinetic equation for the rate of volume fraction. General relationships for a representative volume with moving interfaces under piece-wise homogeneous boundary conditions are derived. It was found that the driving force for interface reorientation appears when macroscopically homogeneous stress or strain are prescribed, which corresponds to experiments. Boundary conditions are satisfied in an averaged way. In Part 2 of the paper [Levitas, V.I., Ozsoy, I.B., 2008. Micromechanical modeling of stress-induced phase transformations. Part 2. Computational algorithms and examples. Int. J. Plasticity (2008)], the developed theory is applied to the numerical modeling of the evolution of martensitic microstructure under three-dimensional thermomechanical loading during cubic-tetragonal and tetragonal-orthorhombic phase transformations.     

Constitutive equations of the differential type as approximations

Constitutive equations of the differential type are often considered as approximations to constitutive equations of the after-effect type. In this case, conclusions drawn from them in conjunction with the Clausius-Duhem inequality are unfounded and untenable.     

Towards a constitutive law for the unsteady contact stress in granular media

In order to build a unified modelling for granular media by means of Eulerian averaged equations, it is necessary to study two contributions in the effective Cauchy stress tensor: the first one concerns solid and fluid matter, including contact and collisions between grains; the second one focuses on the random movements of grains and fluid, similar to Reynolds stress for turbulent flows. It is shown that the point of view of piecewise continuous media already used for two phase flows allows one to derive a constitutive equation for the first contribution, under the form of a partial differential equation. Similarly as for the Reynolds stress in turbulent flows, this equation cannot be written only in terms of averaged quantities without adequate approximations. The structure of the closed equation is discussed with respect to irreversible thermodynamics, and in connection with some already existing models. It is emphasised that numerical simulations by the discrete elements method can be used in order to validate these approximations, through numerical experiments statistically considered. Finally an extension of this approach to the second contribution of the effective Cauchy stress tensor is briefly discussed, showing how the modelling of both contributions have to be coupled.      

Modelling of the interface between a thin film and a substrate within a strain gradient plasticity framework

Interfaces play an important role for the plastic deformation at the micron scale. In this paper, two types of interface models for isotropic materials are developed and applied in a thin film analysis. The first type, which can also be motivated from dislocation theory, assumes that the plastic work at the interface is stored as a surface energy that is linear in plastic strain. In the second model, the plastic work is completely dissipated and there is no build-up of a surface energy. Both formulations introduce one length scale parameter for the bulk material and one for the interface, which together control the film behaviour. It is demonstrated that the two interface models give equivalent results for a monotonous, increasing load. The combined influence of bulk and interface is numerically studied and it is shown that size effects are obtained, which are controlled by the length scale parameters of bulk and interface.     

The frequency response of dynamic friction: Model comparisons

Any linearised theory of the initiation of friction-excited vibration via instability of the state of steady sliding requires information about the dynamic friction force in the form of a frequency response function for sliding friction. Recent measurements of this function for an interface consisting of a nylon pin against a glass disc are used to probe the underlying constitutive law. Results are compared to linearised predictions from the simplest rate-state model of friction, and a rate-temperature model. In both cases the observed variation with frequency is not compatible with the model predictions, although there are some significant points of similarity. The most striking result relates to variation of the normal load: any theory embodying the Coulomb relation F∝N would predict behaviour entirely at variance with the measurements, even though the steady friction force obtained during the same measurements does follow the Coulomb law.