Continuum Mechanics and Thermodynamics最新文献

In this paper we present a review of some of the foundations of micropolar continua. The focus is initially on the classical representation of fields in spatial or material description. We shall remind the reader that traditionally both are based on the notion of the indestructible material particle. We will give reasons why these traditional concepts may fail, namely if we wish to study more complex processes, such as agglomeration or crushing of matter. As a way out, we will present a suitable extension, which we call true spatial description. We shall also demonstrate that the classical twofold approach can lead to serious misunderstandings that may result in unnecessary scientific controversies. Further attention is paid to the various deformation measures that are encountered in the literature on micropolar materials. It will be discussed under which circumstances which one should preferably be used. In this context the kinetic equation for the microinertia tensor deserves particular attention: it was recently extended by a production term. This additional feature can be used to describe processes in matter associated with micromorphological change, for example during crushing and milling of substances. Here a continuum description in terms of material, indestructible particles is no longer possible, and true spatial notation becomes a must.

The aim of this paper is to develop a general constitutive scheme within continuum thermodynamics to describe the behavior of heat flow in deformable media. Starting from a classical thermodynamic approach, the rate-type constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. All constitutive functions are required to depend on a common set of independent variables and to be consistent with thermodynamics. The statement of the Second Law is formulated in a general nonlocal form, where the entropy production rate is prescribed by a non-negative constitutive function and the extra entropy flux obeys a no-flow boundary condition. The thermodynamic response is then developed based on a variant of the Coleman-Noll procedure. In the local formulation, the free energy potential and the rate of entropy production function are assumed to depend on temperature, temperature gradient and heat-flux vector along with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. Many linear and nonlinear models of the rate type are recovered (e.g., Cattaneo-Maxwell’s, Jeffreys-like, Green-Naghdi’s, Quintanilla’s and Burgers-like). Owing to the (weakly) nonlocal formulation of the second law, weakly nonlocal models based on the heat-flux vector and its gradients are obtained within this (classical) thermodynamic framework. In particular, the nonlocal Guyer-Krumhansl model and some nonlinear generalizations devised by Cimmelli and Sellitto are obtained. Finally, we propose a new model where the heat flux dependence on temperature gradients is allowed up to second-order.

The mathematical analysis is presented for calculating the film thickness at the contact center in the hydrodynamic lubricated rolling and sliding steel line contact with the equivalent contact radius on the scale of 100mm by considering the contact thermal and macroscopic elastoplastic deformations where the film thickness is ultra low so that the adsorbed layer-continuum fluid-adsorbed layer sandwich film occurs in the inlet zone and the non-continuum physically adsorbed molecule film occurs in the flattened contact area. The calculation was made for widely varying heavy loads, slide-roll ratios and contact hardness. It was found that the lubrication in the studied contact is qualitatively different from the classical elastohydrodynamic theory description in the condition of very low film thicknesses. The effect of the adsorbed layer makes the film thickness maintained even only with several fluid molecule sizes but much higher than the classical elastohydrodynamic theory calculation. The strong contact-fluid interaction yields the significantly higher film thickness than the weak or medium contact-fluid interactions. Both the increase of the slide-roll ratio and the reduction of the contact hardness rapidly reduce the central film thickness owing to the contact thermal and plastic deformations. The variations of the lubricating film thickness at the contact center with the rolling speed and load no longer follow classical elastohydrodynamic theories because of the strong effects of the adsorbed layer and the contact thermo-elastoplastic deformations. For heavy loads, high rolling speeds and appreciable slide-roll ratios, the effect of the contact thermo-elastoplastic deformation not only largely reduces the central film thickness but also greatly increases the sensitivity of the central film thickness to the load variation.

According to standard thermodynamics, heat spontaneously propagates from hot to cold reservoirs as time progresses towards the future. Consequently, one might assume that for the purpose of describing thermodynamic machines, a world in which heat spontaneously propagates from cold to hot (i.e., a world in which the heat equation has a different sign) would be simply the time reversal of our world. In this article, we explain why this is not the case. Thermodynamics is characterized by the universal approach to equilibrium states from arbitrary initial conditions, such that the final state of a thermodynamic equilibration process does not contain the information necessary to recreate the initial state. In particular, the initial state cannot be recreated by evolving the final state via the rule “heat always propagates from cold to hot”, as this rule would lead to temperature gradients on arbitrarily small scales (which is not a feature that the initial state will generally have had). This toy problem illustrates some general features of the role of the direction of time in thermodynamics. These features are discussed mathematically using the Mori-Zwanzig projection operator formalism.

This study develops a novel thermoelastic model for an unbounded micropolar half-space produced by a magnetic field having constant intensity. A novel spatiotemporal nonlocal elasticity theory is proposed by taking into account one dynamical scalar nonlocal kernel. In line with the theory, an isotropic nonlocal elasticity model of the Klein-Gordon type is formulated, incorporating both a characteristic internal length scale and an essential internal time scale parameter. The Moore-Gibson-Thompson theory, which is adjacent to the memory responses, governs the micropolar medium’s heat transport mechanism. While the boundary is free of traction, the micropolar medium experiences a time-harmonic thermal loading. The solutions to the governing equations have been obtained using Laplace and Fourier transform techniques. Numerical estimates of each of the physical fields have been performed for the analysis of the effectiveness of the nonlocality parameters of space and time, the micropolar parameters and the time-delay also. The significance of various kernels involved in the heat conduction process and the influence of magnetic field have also been concluded.

We investigate the propagation of anti-plane shear waves localized within a multi-layered interface of a square lattice. The structure consists of two infinite half-spaces, either identical or dissimilar in their bulk properties, separated by a three-row interface that may be stiffer or softer than the surrounding media. A discrete square-lattice model is employed, in which particles of mass are connected by elastic bonds whose properties vary between regions. Using a lattice-dynamics approach, we derive the dispersion relation for waves propagating along the interface for different material contrasts between the bulks and the interface.

This study proposes a modification to the yield condition that addresses the mathematical constraints inherent in the Directional Distortional Hardening models developed by Feigenbaum and Dafalias. The modified model resolves both the mathematical inconsistency found in the ’complete model’ and the limitations of the ‘r-model’. In the complete model, inconsistency arises between the distortional term in the yield surface and the plastic part of the free energy in the absence of kinematic hardening. Additionally, the ‘r-model’ fails to capture the flattening of the yield surface in the reverse loading direction due to the absence of a fourth-order anisotropic tensor structure in the distortional term. To address these issues, the proposed model introduces a decoupled distortional hardening term in the yield function. This modification enables the simultaneous representation of both flattening and sharpening of the yield surface, and permits isotropic hardening with distortion even without kinematic hardening. A consistent mathematical formulation based on rational thermodynamics and a corresponding numerical algorithm are also developed, establishing a foundation for future experimental investigations and model validation.

The biharmonic operator naturally emerges in the modeling of various physical phenomena and plays, in particular, a prominent role in linear elasticity. Understanding its properties is, therefore, crucial in the consolidation of mechanical science. In his 1984 article, E.H. Mansfield introduced an alternative differential operator that can replace the Laplacian in the expression of the homogeneous biharmonic equation in (mathbb {R}^2). Despite its potential for further investigations and applications, this result has remained unnoticed so far. The present work generalizes and explores some of the properties of Mansfield’s operator through analytical derivations and symbolic computations. With the proposed generalization of the operator in (mathbb {R}^n), its essential properties are established, and its expressions in five new coordinate systems are derived. The unique status of the Laplacian and Mansfield’s operator in expressing biharmonic equations in (mathbb {R}^2) is assessed. The interrelation between the kernels of the biharmonic, harmonic, and Mansfield’s operators is demonstrated. Eventually, the structure of the biharmonic terms of the classical Michell solution is clarified through the introduction of the operator. In addition to popularizing and generalizing the original work of E.H. Mansfield, the results and methodologies described in this article can initiate further research, such as the study and extensions of the generalized operator, the reexamination of classical solutions to elasticity problems, and the definition of new polyharmonic operators.

The micromechanical models of the isotropic conductive and elastic polycrystalline solid featuring a general imperfect interface have been developed. In terms of conductivity, the imperfect grain bonding conditions assume a jump of temperature and normal heat flux across the interface. In terms of elasticity, they allow for a jump in displacement and normal traction vectors. The self-consistent homogenization scheme for a polycrystalline solid is formulated in terms of the induced dipole moments and property distribution tensors. The explicit formulas for the effective conductivity and elastic moduli of polycrystalline material are derived from the multipole expansion solution to the model problems under the zero dipole moment condition of the imperfectly bonded inhomogeneity in the effective medium. As a practical application of the developed model, the conductivity and elastic stiffness of the intergranular boundaries of polycrystalline cubic boron nitride are evaluated using the laboratory test data on its macroscopic thermal conductivity and elastic moduli. The interface parameters are found to be strongly dependent on the sintering temperature and hence can serve as an indicator of the consolidation degree of a sintered polycrystalline solid.