Continuum Mechanics and Thermodynamics最新文献

In this paper, a one-dimensional Timoshenko-like equivalent beam model, embedded in a 2D space, is developed to analyze the static response of a chiral metamaterial, first presented in Misra et al. (Contin Mech Thermodyn 32:1497–1513, 2020). This is a beam-like structure, here referred to as the ‘grain beam’, which is made of a periodic assembly of a grain-pair interconnected with solid bars, exhibiting chirality through shear and axial strains coupling. The derivation of the beam model is conducted within the framework of the direct one-dimensional approach, wherein the constitutive law is established through a suitable homogenization procedure, that relies on an energy equivalence between a cell of the periodic model and a segment of the solid beam. Based on the geometry of the interconnecting elements of a grain-pair of the microstructure, analytical as well as numerical approaches are developed to identify the constitutive parameters, the latter grounded on a FE analysis of the cell. The analytical identification procedure, which shed the light on the dependence of the elastic coefficients upon proper defined nondimensional parameters, as the cell aspect ratio and the slenderness of horizontal and vertical fibers, is shown to be effective in designing grain beams with targeted stiffnesses, chirality and macroscopic behavior. The linear static response of some grain beams, taken as case studies, is analyzed and the results obtained by the Timoshenko-like beam model and the FE analyses, these latter carried out on refined models of grain beams, are compared. The effectiveness of the beam model, its limits of applicability, and the associated error magnitude in describing the static behavior of grain beams are investigated and discussed.

This study examines the two-dimensional deformation of a functionally graded Green Naghdi (type-III) thermoelastic half-space under hydrostatic initial stress. The material properties of the medium are assumed to vary along two directions. Such type of problem has not been attempted earlier. Using the normal mode technique, analytical expressions for displacement components, temperature distribution, and force stress are derived. The numerical evaluation of these field variables reveals the impact of initial stress and material inhomogeneity on thermoelastic behavior. Graphical representations illustrate the variations in displacement and stress fields, emphasizing the intricate interplay between mechanical and thermal responses. These findings provide valuable insights for stress-strain analysis and the design of advanced engineering materials in thermoelastic applications.

The paper studies the problem of wave propagation through a multi-layered structure, which consists of a finite number of solid / fluid parallel layers of finite thickness. By considering the structure as a protective multi-layered barrier placed in a (scalar) fluid space to reduce the amplitude of the plane incident wave, we give an exact explicit analytical representation for the transmission coefficient, in the case of arbitrary finite number of layers and arbitrary values of their thicknesses. We demonstrate wave properties of the barrier for various types of the geometry, including the case of ultra-low frequencies.

This paper presents a theoretical investigation of a functionally graded hydro-poroelastic semiconductor material subjected to photo-thermoelasticity theory. The material properties, including thermal conductivity, elasticity, and porosity, are assumed to vary spatially following a functionally graded distribution. A one-dimensional problem is formulated to analyze the coupled interactions between the hydro-semiconductor medium’s thermal, mechanical, and electronic transport phenomena. The governing equations incorporate hydrodynamic effects, poroelasticity, and semiconductor carrier transport under the influence of thermal and photonic excitation. The Laplace transform technique is employed to obtain analytical solutions in main physical fields. Numerical results are derived using inverse Laplace transformation, and the effects of functionally graded parameters on wave propagation and heat transport are examined. Graphical analysis illustrates the impact of grading index and porosity on the material’s response. The results highlight the significance of functional grading in tailoring the behavior of hydro-poroelastic semiconductors for advanced technological applications, including optoelectronic devices, photodetectors, and thermal management systems.

The phase-field method is well established for simulating microstructure evolution in computational materials science, providing a numerically efficient tracking of interfaces and surfaces by means of an order parameter. The derivation of its evolution equation is usually based on a variational approach or a corresponding principle of virtual power. Both approaches consider the order parameter as an additional degree of freedom and assume a diffuse interface region from the outset. This work examines the interpretation of the order parameter as an internal state variable, instead of an additional degree of freedom, since it represents an observable rather than a controllable quantity. Furthermore, the phase-field method is considered as an approximation of the sharp interface theory of a continuum containing a singular surface. A Cauchy continuum with a material singular surface is considered as starting point. The evolution equation of the order parameter is derived consistently in the context of continuum thermodynamics by exploitation of the Clausius–Duhem inequality. In this context, the equation of heat conduction and the thermomechanical coupling is discussed regarding the diffuse interface region and the role of the latent heat due to phase evolution. Based on restrictions of the free energy, special cases of the evolution equation are presented. For a special case, the coincidence of the evolution equation obtained by the presented approach and the classical variational approach is demonstrated. Based on the presented approach, the classical Allen–Cahn/Ginzburg–Landau equation is obtained by assuming a spatially homogeneous temperature distribution.

In the present paper, a consistent model for non-isothermal viscoelastic fluid of Jeffreys type forming a horizontal layer heated from below is introduced and the stability of a vertical constant throughflow is analyzed. Planes delimiting the layer are assumed isothermal, rigid and permeable. Via linear analysis, it is proved that the strength of the vertical throughflow affects the number of modes leading to the onset of oscillatory instability and that motions originating at the onset of instability are oscillating in time for strong enough throughflows, regardless the impact of the fading memory behavior. Moreover, viscoelastic fluids with elastic properties are more likely to sustain oscillatory instability compared to more viscous ones, even though the Rayleigh number required for instability is higher. A sufficient condition for nonlinear stability of the throughflow has been obtained, by introducing a suitable (L^2)-norm.

In this work we investigate a novel class of electro-mechanical metamaterials. The main idea is to construct materials that possess the ability to withstand higher mechanical loads than usual. This is achieved by applying an electric field in such a way that the induced Maxwell stress (resulting from the electric field) counteracts the mechanical stress (resulting from external forces). Consequently, the overall load on the material is reduced. The solution of the minimization problem at the material point level results in a mathematical relation that involves the smallest eigenvalue of the mechanical stress tensor. Additionally, we evaluate the constrained cases allowing only tensile or compressive stresses, respectively, and consider the plane stress problem. We show numerical results for all cases and discuss to what extent a stress reduction is possible.

In this paper, on the basis of the linearized model of prestressed elastic body, we propose approaches to studying coefficient inverse problems (IP) of 3 types on the prestress identification based on vibration sensing. We present techniques for reconstructing the nature of residual stress state (RSS) inhomogeneity, based on a combination of projection, iterative and finite element (FE) approaches. The fundamentals of the approach to analyzing a sensitivity of dynamic characteristics of elastic bodies to RSS type under various probing modes are discussed. A series of computational experiments is carried out to analyze the influence of RSS parameters and material inhomogeneity on the dynamic response and to reconstruct various types of 2D prestress fields in cylinders and plates. In addition, we present some recommendations for the implementation of the most effective modes of combined probing loading, providing the best reconstruction of RSS of various types in the studied objects.

This paper investigates the post-buckling behavior of functionally graded porous (FGP) perfect/imperfect cylindrical shells under external pressure in a thermal environment. The properties of these porous cylindrical shells are assumed to be temperature-dependent, determined using the modified rule of mixture and Touloukian formulation. The governing equations are derived from classical shell theory and von Kármán-Donnell’s type of kinematic nonlinearity. The boundary layer theory of shell buckling, which accounts for nonlinear prebuckling deformations, large deflections in the post-buckling range, and initial geometric imperfections, is extended to FGP cylindrical shells. A two-step perturbation approach is employed to solve the post-buckling problem, determining the buckling loads and post-buckling equilibrium paths. Numerical parametric analysis, including three types of porosity distribution, is conducted to examine the effects of shell geometric parameters, material properties, and temperature rise on the post-buckling behavior of the FGP cylindrical shell. Numerical results indicate that the current method effectively and accurately resolves the problem, aligning with literature findings. It is observed that increases in geometric parameters related to length, radius-to-thickness ratio, porosity volume fraction, functionally graded volume fraction index, and temperature lead to a decrease in post-buckling load. Additionally, it is demonstrated that the porosity index significantly influences the post-buckling path of an FGP cylindrical shell.

The stability of composite structures are fundamental problems in continuum mechanics. In present study, considering piezoelectric and electrostrictive effects simultaneously, electro-induced nonlinear buckling and post-buckling characteristics of graphene platelets (GPL) reinforced functionally graded dielectric circular plates are examined. Firstly, equivalent dielectric constant and Young’s modulus of the intelligent composites with different GPL distribution patterns are calculated according to effective medium theory, in which the gradient characteristics, the imperfect combination between reinforcements and matrix, the interface electron tunnel and the Maxwell–Wagner–Silla polarization are considered. Then, the nonlinear displacement governing differential equations are derived according to von Kármán nonlinear plate theory and virtual work principle and solved by shooting method for different boundary conditions. The buckling critical voltage and post-buckling deflection-voltage path under various conditions are obtained. Finally, the effects of distribution pattern, gradient slope and geometrical dimension parameters of GPL, as well as interface phase size on the critical electrical parameters and post-buckling characteristics are examined by cross-scale analysis between micro and macro in detail. This research may offer theoretical guidance value for the engineering design of the intelligent structures.