Continuum Mechanics and Thermodynamics最新文献

This study introduces a novel investigation into a thermoelastic response of functionally graded materials (FGMs) by incorporating bidirectional non-homogeneity within the Moore–Gibson–Thompson thermoelasticity framework. The primary innovation lies in analyzing material properties with exponential variation in two directions, advancing beyond the conventional unidirectional gradation prevalent in existing literature. This work contributes a robust formulation and analytical solution of governing equations for this complex bidirectional case, employing the normal mode technique to derive explicit expressions for displacement components, temperature distribution, and stress fields. Numerical simulations, conducted using MATLAB, illustrate the model’s application at a specific time point, offering actionable insights. Results reveal that bidirectional gradation significantly enhances the material stiffness, reducing normal displacement compared to homogeneous or unidirectionally graded materials. Notably, the model achieves a nearly uniform tangential stress distribution, minimizing stress concentrations and bolstering resistance to shear failure. However, it induces a substantial, nonlinear increase in normal stress, which can be leveraged for targeted load-bearing applications. The thermal response is highly tailorable; bidirectional gradation enables a balanced temperature distribution, mitigating both the exponential rise from horizontal gradation and the gradual decrease from vertical gradation. These findings position the proposed model as a powerful engineering tool. By optimizing gradation parameters, engineers can design FGMs with customized thermomechanical properties, ideal for high-performance applications in aerospace, thermal barrier systems, and structural components under extreme conditions.

This paper presents a closed-form formulation for the linear buckling and near-critical single-mode post-buckling response of sandwich cylindrical shells with functionally graded graphene nanoplatelet (FG-GNP) reinforced face sheets and an auxetic honeycomb core under external pressure and a thermal environment. The shell kinematics follow First-order Shear Deformation Theory (FSDT). Face-sheet properties are obtained from a temperature-dependent Halpin–Tsai scheme combined with a power-law through-thickness gradation, while the auxetic core is represented by equivalent orthotropic constants. A Winkler–Pasternak foundation is included. A single-harmonic Galerkin reduction yields a (5times 5) generalized eigenproblem for both simply supported (SS) and clamped–clamped (CC) boundary conditions; for CC edges, an energy-equivalent axial wavenumber is used to represent end restraint without introducing numerical mode shapes. For the baseline configuration, the minimum critical pressures are approximately 15.86 MPa at (m,n)=(1,10) for SS and 19.96 MPa at (0,11) for CC. Increasing temperature difference reduces (p_{cr}), whereas the foundation markedly increases it; larger FG index k (less GNP-rich faces) also decreases (p_{cr}). The Koiter single-mode expansion predicts a stable (hardening) post-buckling branch for the cases examined. The model is intended as a fast analytical screening and benchmarking tool under the stated assumptions.

In this paper, using the example of mass balance for a continuous medium, a kinematic approach based on the concept of local volumetric flow is proposed for the transition from a discrete to a continuous description. This approach takes into account the possibility of discontinuities in the flow derivative at the boundaries of an elementary layer and allows one to derive the balance equation in differential form, eliminating the need for integral relations. It is shown that the inequality of jumps in the derivatives at the left and right boundaries is equivalent to the assumption of mass concentration at the layer boundaries. It is established that the coincidence of the sums of the left and right derivatives at both boundaries is a necessary condition for eliminating negative values of the mass density in the continuous limit.

Evaporation of multiple sessile droplets deposited on an impermeable flat substrate is considered in the diffusion-limited isothermal regime, with particular emphasis on determining the total quasi-stationary vapor fluxes from the droplet surfaces. The proposed approximate solution is based on Kachanov’s approximation for the vapor concentration field in the semi-infinite air domain, expressed as a linear combination of solutions to single-droplet problems, with the coefficients determined by imposing appropriate Bubnov–Galerkin orthogonality relations to enforce the boundary conditions on the droplet surfaces. A comparison of the proposed modified Kachanov method with other approximate approaches is presented. The case of multiple thin circular sessile droplets is examined in detail.

We study the plane strain problem associated with two circular compressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation located at an arbitrary position. With the aid of the techniques of conformal mapping and analytic continuation, the boundary value problem is ultimately reduced to an infinite system of linear algebraic equations, which, when solved via truncation leads to the elastic field in the matrix and the internal uniform hydrostatic stress fields within the two circular liquid inclusions. In addition, an explicit expression for the image force acting on the edge dislocation is derived using the Peach-Koehler formula. Numerical results are presented to demonstrate the effect of the two liquid inclusions on the mobility and stability of the edge dislocation. The stiffening and hardening effect of the two liquid inclusions can be observed under certain circumstances.

The present paper investigates the effects of magnetic and micropolarity on the propagation of Lamb, Rayleigh and flexural waves in generalized magneto-piezoelectric thermo-microstretch material. The thermoelastic theory without energy dissipation is used and the secular equations of the Lamb waves for both symmetric and anti-symmetric modes of vibration in the medium of finite thickness subject to suitable boundary conditions are derived. At short wavelength limits, the secular equations reduce to that of Rayleigh waves due to the nature of a semi-infinite medium. The secular equation of the anti-symmetric vibration reduces to the secular equation of flexural waves for longer wavelengths comparable with thickness of the medium. The phase speeds and attenuation coefficients are computed numerically from these secular equations using Aluminum epoxy material and the results are presented graphically. The numerical results have shown the simultaneous existence of three modes of dispersion and attenuation for Lamb, Rayleigh and flexural waves. The effect of magnetic field intensity and micropolarity on the phase speeds and attenuation of the three modes are noted. The path of particle motion for all three modes of Lamb, Rayleigh and flexural waves are evaluated analytically and numerically at different depths of the medium. Some special cases are reduced from the current formulation to validate our results.

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.