Continuum Mechanics and Thermodynamics最新文献

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.

The problem of the influence of distributed dislocations on the equilibrium stability of a rectangular bar loaded with a longitudinal force is investigated. In the subcritical (unperturbed) state, the body experiences a finite plane inhomogeneous deformation. The dislocation density tensor depends on the coordinate measured along the bar thickness and has only one nonzero component corresponding to the distribution of edge dislocations. Within the framework of the compressible semilinear material model, the unperturbed state is defined as an exact solution to the equations of the nonlinear continuum theory of dislocations. Stability analysis is performed using the Euler bifurcation method, which consists in finding nontrivial solutions to the linearized homogeneous boundary value problem of the equilibrium of a prestressed elastic body. The influence of different types of dislocation distribution on the critical values of the longitudinal force and the form of stability loss of the bar is studied. It is established, in particular, that dislocations significantly affect the number of waves along the length of the bar, characterizing the form of stability loss.

We give an explicit description of the spectral closure for the three-dimensional linear Boltzmann-BGK equation in terms of the macroscopic fields, density, flow velocity and temperature. This results in a new linear fluid dynamics model which is valid for any relaxation time, thus providing an optimal hydrodynamic model for rarefied gas flow over a large range of Knudsen numbers. The non-local exact fluid dynamics equations are compared to the Euler, Navier–Stokes and Burnett equations. Our results are based on a detailed spectral analysis of the linearized Boltzmann-BGK operator together with a suitable choice of spectral projection.

The compaction process is often carried out in relation to transportation infrastructure. The process is complex since the soil is a heterogeneous environment. Adequate compaction is necessary to ensure the homogeneity and durability of the pavement. This paper presents a novel visual method for assessing soil compaction. A slow-motion camera (optical sensor) and tracking markers placed on the compaction plate, were used to determine the trajectory of the compactor’s movement. Based on this and the proposed energy criterion, it is possible to observe changes in soil compaction up to the desired level. Quality control of soil compaction was experimentally compared to the standard method. The experiments show that the visual method gives similar results to the standard one. The proposed innovative visual method allows for developing and optimizing the machine’s workload efficiency and enables online compaction level monitoring.