Continuum Mechanics and Thermodynamics最新文献

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.

An important part for material modeling is the consideration of electromagnetic fields. In this paper, we add them to Hamilton’s principle for mechanical and thermal fields. We begin with a brief introduction to the electric and magnetic limit cases, which allows a non-relativistic formulation. After introducing the thermodynamic fundamentals, we present the Hamilton functionals for the limit cases from which we derive our governing system of equations by applying Hamilton’s principle of stationary action. In order to be able to describe the microstructure as well, we also consider general internal variables. After the derivation of the equations for the dominant fields, we show how to obtain the secondary fields. For both limit cases we show an example where the dominant electromagnetic field and the mechanic field are coupled by material properties.

Understanding and accurately quantifying thermoelastic damping (TED) in micro/nanoresonators is a major step in designing them to work well. Empirical and theoretical evidence suggests that classical elasticity theory (CET) and the Fourier heat equation break down when applied to structures with minuscule dimensions. This research presents an innovative framework to approximate TED value in miniature circular plates by leveraging both the frequency and energy-based approaches commonly applied in TED studies. The model incorporates the modified couple stress theory (MCST) and Moore–Gibson–Thompson (MGT) heat equation to enhance accuracy beyond the constraints of classical formulation at ultra-small scales. Non-classical constitutive relations and heat equation are firstly derived. Next, the MGT heat conduction equation is solved to determine the temperature distribution within the plate. In conclusion, TED is analytically formulated using two distinct approaches of frequency and energy. The agreement between these two approaches in yielding identical TED expressions reinforces the accuracy of the computations and the credibility of the developed model. The discussion in the numerical results section highlights the influence of essential parameters, especially the characteristic constants of the MCST and MGT model, on TED. The results indicate that while MCST reduces TED and the MGT model increases it, the classical framework, grounded in CET and the Fourier model, predicts a higher TED than the non-classical framework proposed in this study. This suggests that the reduction caused by MCST outweighs the increase due to the MGT model.

The paper considers a time-iterative approach, to solve a classical 2D problem of hydromechanics for a viscous fluid flow around a circle. Using the boundary integral equation method and special Green’s function outside the cylinder, a closed system of integral representations is obtained, to determine the perturbed values of the stream and vorticity function in the flow region. The solution is constructed as a trigonometric series of sines, in which the number of harmonics doubles with each time iteration. As a result, a time-iterative method is constructed, on the basis of which the stream and vorticity functions are calculated.