Continuum Mechanics and Thermodynamics最新文献

Motivated by the abundance of fractals within the natural world, the present study deals with a novel extension of classical thermoelasticity to fractal materials by formulating a generalized vector calculus in non-integer dimensional spaces. Fractal media, characterized by complex geometries and anomalous transport behavior, are modeled as continua with non-integer mass dimensions. We develop a comprehensive thermoviscoelastic diffusion framework that incorporates nonlocal elasticity, fractional-order derivatives, and a three-phase-lag heat conduction model. The physical system considered is an infinitely extended Kelvin–Voigt viscoelastic medium with a cylindrical cavity subjected to time-dependent thermal and chemical boundary conditions. The governing equations are transformed into the Laplace domain and solved analytically, with time-domain solutions obtained via Zakian numerical inversion. Numerical simulations reveal the significant influence of fractal geometry, nonlocal effects, and fractal operators on temperature distribution, stress evolution, and diffusion behavior. These findings offer valuable insights for the design of advanced materials and nanoscale systems where classical models fall short.

In the framework of Extended Irreversible Thermodynamics and in agreement with the second law of thermodynamics, in this paper we derive a heat-transport equation which generalizes the classical Fourier law and contains non-local and non-linear contributions related to the heat flux. In order to delve mainly into the possible influence of the non-linear effects on the heat transfer at nanoscale, only meant as the direct consequence of the non-linear terms appearing in the heat-transport equation, we focus on the longitudinal propagation of heat flux in a thin layer in steady states. The analysis is performed by also employing enhanced boundary conditions which allow to account for the phonon-boundary scattering. A comparison with the results arising from another non-local and non-linear proposal of heat-transport equation is performed as well.

This paper presents a meshless numerical approach to the heat conduction analysis of multi-directional functionally graded materials (FGMs) with non-uniform boundary conditions (BCs) and heat sources. A novel three dimensional (3D) Chebyshev spectral approximation scheme is proposed to discretize and approximate the spatially varying material properties and boundary conditions. Without meshing, a simple and unified discrete governing equation is derived for 2D and 3D transient heat conduction problems of multi-directional FGMs. A series of numerical experiments are performed to validate the convergence and accuracy of the method, considering various FGMs, non-uniform BCs and heat sources. The results converge rapidly and agree well with analytical solutions and finite element simulation results. The advantage of this method is that it can handle non-homogeneous material with non-uniform BCs and heat loads without meshing, and is independent of the laws of material gradients and variation of BCs and heat sources, and has a consistent form in 2D and 3D problems.

This study investigates the influence of non-local thermal stresses on the mechanical behavior of fiber-reinforced poro-viscoelastic structures, utilizing the Lord-Shulman (L–S) model to incorporate thermal relaxation effects. The research employs normal mode analysis to derive and analyze the governing equations and boundary conditions, which integrate the Lord-Shulman heat conduction law and constitutive relations for viscoelastic porous materials. The study explores the effects of key parameters, such as relaxation time, porosity, and viscoelastic properties, on heat propagation and the thermo-mechanical response of the structures. Analytical solutions for the governing equations are obtained through normal mode analysis, yielding explicit expressions for critical physical quantities, including stress components, displacements, and temperature distributions within the material domain. These analytical results are then numerically evaluated for a specific material, with the findings presented graphically to illustrate the influence of the studied parameters. Additionally, the predictions of the Lord-Shulman (L–S) theory are compared with those of the classical heat conduction (C–T) theory, both in the absence and presence of viscous parameters, highlighting the differences and implications of the two approaches. This work provides valuable insights into the thermo-mechanical behavior of fiber-reinforced poro-viscoelastic structures under non-local thermal stresses.

We discuss the correspondence between discrete and continuum models of one-dimensional (1D) elastic structures. We propose positive definiteness as a consistency condition for continuum models. As a result, generalized continuum models may be required, as simple (Cauchy-type) continuum models may be insufficient. This theory is illustrated by a few physical examples.

Microstructural anisotropy plays a crucial role in determining the qualitative and quantitative mechanical properties of polymer foams. Moreover, their behavior at high strain rates remains an open question due to the limited studies on the topic, which poses a limit in the design of impact absorbing foam-made components (e.g., helmets). In this work we study the influence of microstructural anisotropy on the dynamic behavior of transversely isotropic closed cells polystyrene foams. We first produce isodensity foams with different degrees of microstructural anisotropy by using the gas foaming technique. We characterize the microstructure of the cells of the produced polystyrene foams by analyzing 2D images of the microstructure and computing the statistics of the shape indicators of the cells. We then characterize their dynamical behavior on split Hopkinson pressure bars at an average strain rate of 835 s^-1. Dynamic results are compared with quasi-static ones and confirm similar findings to the literature. We report a different strain rate sensitivity for the different foams. In particular, a higher sensitivity for foams when cells are aligned with the loading direction. Therefore, the strain rate sensitivity of the foam can be associated with the microstructural distribution of cell and the strain rate sensitivity of the base material.

Using the Stroh octet formalism, we study the problem of an elliptical incompressible liquid inclusion embedded in an infinite piezoelectric matrix under a uniform remote electromechanical loading. The liquid inside the inclusion can be electrically conducting, electrically insulating or isotropic dielectric. Closed-form solutions to the problem are derived. Furthermore, real-form expressions for the internal uniform electroelastic field of hydrostatic stresses, strains, rigid body rotation, electric fields and electric displacements within the liquid inclusion are obtained in terms of the generalized Barnett-Lothe tensors and the fundamental piezoelectricity matrix for the anisotropic piezoelectric matrix.

Pantographic metamaterials display distinctive mechanical behaviors arising from their mesostructure, which consists of two orthogonal families of fibers interconnected by hinges. Owing to this architecture, such lattices are naturally described within the framework of second-gradient continuum mechanics, since the bending of fibers contributes to the strain energy through the second gradient of the placement field. In this context, flexoelectricity, namely, the generation of electric polarization induced by strain gradients, represents a natural multiphysics coupling for this class of metamaterials. Numerical simulations are presented to illustrate the resulting electric field distribution in pantographic specimens subjected to bias-extension, compression, and shear loading conditions.

The present paper is an examination of the axisymetric oscillation problem in infinite and finite cylindrical shells supported by two circular frames and hinged at edges.The solution of the problem determining trapped frequencies and modes of an infinite length shell has been found. The conditions under which trapped modes of an infinite length shells become natural frequencies of the finite length shells are determined. It is shown that trapped modes become multiple natural frequencies of the second order of the finite length shell. The cylindrical shell localized modes corresponding to these frequencies are also presented. The peculiarity of such oscillations is their localization along the length of the shell. The investigations shows that the existence of the real discrete frequency above the cut-off frequency must be considered in the design of the engineering structures.

This study presents a modern framework for analyzing thermo-electro-mechanical vibrations in functionally graded piezothermoelastic rods subjected to a moving heat source. By integrating a Klein-Gordon-type spatiotemporal nonlocal elasticity model with the Moore-Gibson-Thompson (MGT) heat conduction theory and memory-dependent derivatives, the work advances the modeling of smart materials under transient thermal loads. The proposed model introduces intrinsic length and time scale parameters, enabling a more accurate depiction of wave propagation, thermal lag, and electromechanical coupling in graded media. Numerical simulations reveal the critical influence of nonhomogeneity, heat source velocity, kernel function formulation, and nonlocal parameters on displacement, temperature, stress, and electric potential distributions. The results demonstrate that material gradation and memory effects can be strategically tuned to enhance performance in sensing, actuation, and energy harvesting applications. This research contributes a robust analytical and computational framework for the design of next-generation smart structures, especially in aerospace, MEMS/NEMS, and thermal protection systems. Future extensions may include multidimensional geometries, nonlinear material behavior, and experimental validation to bridge theory with real-world engineering applications.