Continuum Mechanics and Thermodynamics最新文献

A thermo-elastic continuum model for a mass-in-mass metamaterial is suggested. An influence of thermal conduction on the harmonic wave behaviour is studied using an asymptotic dispersion relation analysis. It is found that the position and the size of the band gap is not affected by the thermal effects. Numerical simulations are performed on boundary excitation of thermo-elastic waves using both the harmonic and constant temperature excitations. Mutual influence of the strain and thermal waves give rise to oscillatory or monotonically decaying wave profiles.

A thermodynamically consistent continuum modeling framework is developed to investigate the transient thermo-mechanical response of rotating bi-directional functionally graded (BD-FG) discs as a result of a friction heating regime from a gray cast iron (GCI) brake pad. The disc gradation is through-thickness from the ceramic phase (({Al}_{2}{O}_{3})) at the inner surface to the metallic shear phase (GCI) at the outer surface, where friction takes place. Hence, the effects of material inhomogeneity can be analyzed in terms of heat conduction and mechanical deformation. The transient thermal field follows the Fourier law for the heat conduction mechanism, where the outer surface of the disc experiences a constant and uniform heat flux and the inner surface is adiabatic. The structural response is achieved through a quasi-3D refined zigzag theory where transverse shear deformation and non-uniform temperature distribution through the thickness can be described. Geometric nonlinearity is achieved using Von-Kármán-type kinematic relations, and nonlinear governing equations are established using an energy-based variational principle. The system of equations is discretized using the differential quadrature method for both spatial and temporal solutions, with time-domain problems solved using Newmark integration. Numerical results reveal the effect of functional gradation, rotational inertia, and thermal boundary conditions on the nonlinear bending performance of the disc. The work provides a predictive approach for the design of high-performance thermally loaded FG rotating structures subjected to complicated loading histories.

This study presents a novel thermo-viscoelastic model for analyzing the thermal and mechanical behavior of nanoscale viscoelastic materials subjected to non-Gaussian laser radiation and magnetic fields. By integrating memory-dependent derivatives (MDDs), the Moore Gibson Thompson (MGT) heat conduction equation, and nonlocal elasticity theory, the model addresses limitations inherent in traditional heat transfer approaches such as Fourier-based methods and Green Naghdi type III formulations that overlook size-dependent effects, memory behavior, and finite thermal wave propagation. The framework incorporates MDDs to capture historical deformation, nonlocal elasticity to represent long-range atomic interactions, and MGT equations to ensure finite thermal wave speeds. Additionally, tensorial relaxation functions and customizable kernel functions enhance the accuracy of time-dependent thermo-mechanical response predictions. The governing equations are solved using Laplace transform techniques for a one-dimensional viscoelastic semi-infinite domain exposed to laser heating and an external magnetic field. Numerical simulations, based on the properties of Plexiglas, demonstrate the model’s superior accuracy in predicting displacement, temperature, and stress distributions compared to classical and fractional models, particularly under extreme conditions. This innovative approach provides a robust tool for designing durable nanomaterials with applications in nanoelectronics, creep-resistant polymers, biomechanical prosthetics, and aerospace composites. It establishes a scalable and physically consistent framework for tackling critical challenges in next-generation nanotechnology and engineering.

This study presents a novel thermoelasticity framework that extends classical elasticity theory by integrating spatial and temporal nonlocality through a Klein–Gordon-type isotropic elasticity model. The proposed approach incorporates internal length and time scales alongside conventional thermoelastic properties to more accurately capture the dynamic behavior of nanostructures. Thermal diffusion is modeled using the dual-phase-lag (DPL) heat transfer theory, while nonlocal constitutive relations are developed with a dynamic kernel function to account for nonlocal interactions. The model analyzes transverse vibrations of axially moving Euler–Bernoulli (EB) thermoelastic nanobeams subjected to axial forces and external excitations. Numerical simulations and parametric studies reveal the significant influence of axial velocity, nonlocal effects, phase-lag parameters, and external loads on vibrational response. The findings highlight the critical role of nonlocal parameters in governing system stability and performance, offering valuable insights for designing advanced nanostructures in dynamic environments.

Melting of metallic nanostructures such as nanoparticles and nanowires has been extensively studied particularly using atomistic simulations and thermodynamic relations for melting temperature. In addition, continuum modeling due to its capabilities has recently received attention for modeling of melting at nanoscale. In this work, melting of copper nanowires is investigated using a phase field model as a continuum model. Axisymmetric model is used to effectively solve the combined Ginzburg–Landau and elasticity equations in order to capture the melting process. The obtained melting temperature shows a nonlinear reduction as the radius decreases and stands between two known thermodynamic relations. The premelting temperature is found slightly below the melting temperature for the radii of (Rge 3text{nm}) while is significantly lower than it for (R<3text{nm}). The obtained melting temperature also shows a nonlinear reduction as the length decreases. Also, the obtained MT is averagely 3.5% larger than the melting temperature from the thermodynamic relation for the lengths of (L<80text{nm}); and this difference reduces for lower radii. The melting mechanism differs for radii smaller than the solid-melt interface width where the interface propagates only along the nanowire length and not radially. Having studied different thermodynamic driving forces of melting, the transformation strain driving force is found the dominant mechanical term while thermal strain practically shows no impact on the melting temperature for (R>3text{nm}). The obtained melting temperature well matches the start temperature of melting from the existing molecular dynamics simulations for (Rge 2text{nm}).

We study the dynamics of subsonic solitary waves taking place in a nonlinear model of an elastic electrically conductive micropolar medium interacting with an external magnetic field. First, we perform the stability analysis using the concept of the Evans function. As a result of linearization about the soliton solution an inhomogeneous scalar equation is obtained. This equation leads to a generalized spectral problem to be investigated with the help of the Evans function, which depends only on the spectral parameter. This function is analytic and may have zeroes in the right half of the complex plane of the spectral parameter. These zeroes coincide with the unstable eigenvalues of the mentioned generalized spectral problem. For the case under consideration there are two modes decreasing at spatial infinity and we need to adopt the previously developed external form approach to construct the Evans function. Our stability results are confirmed with the direct numerical calculations of the evolution of solitary waves in question.

This work presents a parametric analysis of quadratic convection with heat production or absorption through an inclined surface. The flow dynamics of granular materials, such as metal ores, sand, and coal, have garnered considerable interest owing to their significance in technical problems. In several industrial processes, these materials undergo heating before processing and cooling after processing. The governing mathematical model accounting for quadratic convection and heat generation/absorption is developed from the continuum model. Two categories of boundary conditions have been examined for thermal distribution: fixed-temperature boundary conditions and heat-flux boundary conditions. The established governing equations are nonlinear; hence, a numerical method has been used to obtain the numerical solutions. The graphical representation of the impacts of volume fraction profiles, temperature distributions, and velocity distributions has been analyzed for all pertinent variables. The proposed work has practical applications in real-world physical systems, particularly in industrial processes involving granular materials like sand, coal, and metal ores in inclined chutes, rotary kilns, and packed bed reactors.

The objects of considerations are thin, linearly elastic, Kirchhoff–Love-type, circular, cylindrical shells of a heterogeneous microstructure, which is periodic in the circumferential direction and continuously slowly changing along the axial coordinate (composite shells with a space-varying periodic microstructure). Since macroscopic (averaged) properties of such shells are constant in the circumferential direction but smoothly slowly varying in the axial one (i.e. in the direction parallel to interfaces between constituents), then we deal with shells of a functionally longitudinally graded macrostructure. The aim of the contribution is to formulate and discuss a new, mathematical, averaged, non-asymptotic model for the analysis of selected dynamic problems for these shells. This, so-called, combined asymptotic-tolerance model is derived by applying both the consistent asymptotic and the tolerance non-asymptotic procedures, which are coupled together into a new modelling technique. The combined model equations derived here include coefficients constant in periodicity direction and continuously slowly changing along the axial coordinate. Since some of these coefficients depend on a cell size, then the model can be applied to study the effect of a microstructure size on the shells dynamics. Moreover, it makes it possible to analyse micro-dynamics of the shells independently of their macro-dynamics.

In the present paper, we study the problem of reflection of homogeneous plane waves from a free surface of generalized magneto micropolar thermoelastic using modified Ohm’s law and generalized Fourier law. There exist five coupled elastic waves propagating in such materials which are longitudinal, transverse, micropolar, thermal, and magnetically influenced waves. We have examined the analysis for an incident longitudinal wave at the free surface. The phase velocities of these waves are obtained analytically and numerically. Using appropriate boundary conditions, the amplitude and energy ratios corresponding to the reflected waves are obtained analytically and numerically. Magnetic and thermal effects on the reflected waves are examined, and we also confirmed the conservation law of energy in all cases.

The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and pioneering works of Helmholtz, Clausius, and Boltzmann have been reinstated as possible dynamical foundations of the (first part of the) Heat Theorem. The present paper follows the work of Wald et al., where black hole entropy was identified as a Noether charge. The adiabatic invariance of the thermodynamic entropy indeed invites a connection with Noether’s theorem, and has been the subject of various papers. Here we add the case of GENERIC, a macroscopic dynamics whose acronym stands for “General Equation for Non-Equilibrium Reversible-Irreversible Coupling”. Its evolution has two contributions: a dissipative part, which is of a generalized gradient descent form, and a Hamiltonian flow. We consider a quasistatic protocol for external parameters, and we embed GENERIC as the zero-cost flow for a Lagrangian governing the dynamical fluctuations. We find a continuous symmetry of the corresponding path-space action with the thermodynamic entropy as Noether charge, both in the Lagrangian and Hamiltonian formalisms. We make the calculations explicit through the example of an inertial probe with nonlinear friction.