Continuum Mechanics and Thermodynamics最新文献

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.

Functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAM) have attracted much attention due to their excellent negative Poisson’s ratio properties. Research on the vibration characteristics of FG-GOEAM cylindrical shells remains insufficient. To fill this gap, this work systematically investigates the free vibration behavior of FG-GOEAM cylindrical shells under different temperature profiles using first-order shear deformation shell theory. There are three common types of temperature profiles: uniform temperature rise, linear temperature rise, and sinusoidal temperature rise. Temperature correction functions for LTP and STP conditions are established by taking the geometrically neutral surface temperature of each layer of the shell as a proxy for the overall temperature of that layer. To accurately characterize the effects of thermal effects, a thermal strain energy analysis model is introduced in this work. The material parameters were determined based on a micromechanical model assisted by genetic programming. The governing equations are derived by Hamilton’s principle and solved by Navier’s method. After validating the model, this work investigates the effects of key parameters on the vibration characteristics of the FG-GOEAM cylindrical shell. The numerical results of this work are expected to provide a theoretical basis for the structural optimization and innovative design of FG-GOEAM cylindrical shells.

This paper is concerned with modeling inertia effects in materials. We propose elasticity-inertia models incorporating a novel element called inerter, which exhibits the property of equivalent inertia. Different from the existing works that capture inertia effects by strain gradients, the proposed models directly model general inertia effects by inerters. The stress-strain relationships of the proposed models are represented by spring-inerter networks, which resemble viscoelastic models represented by spring-dashpot networks. It shows that in the constitutive equations and dynamic equations of the proposed models, strain acceleration terms or micro-inertia terms can be easily and directly obtained without adding terms or using operator transformations. The dispersion and vibration properties of the proposed models are derived analytically. The discretization methods are presented as well for obtaining numerical solutions of the proposed models. The proposed elasticity-inertia models provide a very natural way in capturing inertia effects, offering an alternative perspective for modeling inertia effects in materials.

This study proposes Chebyshev polynomials-based different shear deformation theories to analyse the buckling, bending, and free vibration behaviours of axially loaded functionally graded (FG) curved beams for the first time. The Chebyshev-third-order shear deformation theory satisfies the condition of eliminating shear stress at the bottom and top surfaces of the FG curved beam without requiring a shear correction factor. Furthermore, this theory can be simplified to the first-order shear deformation and classical beam theories. The material characteristics of the FG curved beam exhibit variability through its thickness by a power law distribution. The governing equations are derived from Lagrange’s equations. The Ritz method, utilising polynomial shape functions based on the Fibonacci sequence, has been developed to solve the problem. FG curved beams with four boundary conditions are examined, including simply-supported, clamped-free, clamped-simply supported, and clamped-clamped. Numerical examples are carried out to assess the accuracy and efficacy of the present theory. Additionally, the study elucidates the behavioural patterns of FG curved beams regarding various parameters such as boundary condition, slenderness ratio, curvature, and power-law index. The findings of this study serve as a benchmark for future research endeavours. Moreover, they have the potential to enhance the design and optimisation of FG curved beams across a diverse array of engineering applications.

We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo-Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions.