Continuum Mechanics and Thermodynamics最新文献

The phenomenon of buckling of a nonlinearly elastic hollow circular cylinder with dislocations under the action of hydrostatic pressure is studied. The tensor field of the density of continuously distributed dislocations is assumed to be axisymmetric. The subcritical state is described by a system of nonlinear ordinary differential equations. To search for equilibrium positions that differ little from the subcritical state, the bifurcation method is used. Within the framework of the model of a compressible semi-linear (harmonic) material, the critical pressure at which the loss of stability occurs is determined, and the buckling modes are investigated. The effect of edge dislocations on the equilibrium bifurcation is analyzed. It is shown that the loss of stability can also occur in the absence of an external load, i.e., due to internal stresses caused by dislocations.

Previous studies showed that electric fields could change the boiling point and vapor pressure of the vapor–liquid equilibrium (VLE) state of pure substances and mixtures. This is an important feature in controlling the separation of mixtures. In this paper, based on the principle of phase equilibrium, together with the formulas of chemical potential including the effect of electric field and the dielectric pressure, the Raoult’s law was extended to include the effect of electric field to describe VLE of a mixture under an external electric field. The effects of electric field on VLE can be calculated by combining the extended Raoult’s law and the Dalton’s law of partial pressure, and then, the effect of electric field on the relative volatility can also be calculated. Numerical calculations showed that the effects of an electric field on VLE depend on both the magnitude and the direction of the electric field, and the effects become obvious until the field strength is greater than 10(^{7}) V/m. When the direction of the electric field is parallel to the gas–liquid interface, the vapor pressure decreases; the equilibrium temperature, the mole fractions of the volatile component, and the relative volatility increase. While, when the direction of the electric field is perpendicular to the gas–liquid interface, the opposite changes in these properties appear. The shifting of the equilibrium curves caused by the electric field indicates that the electric field can cause the vapor–liquid phase transition and change the amount of the phase material.

In this paper, we study the blood flow through blood vessels of various radii (including the case of variable cross section as well as modeling the blood flow through venae and arteries). Two approaches are discussed in order to mimic the dependence of blood viscosity on red blood cells aggregation, which changes with the shear rate and position inside the vessel: Two microstructural parameters together with empirical constitutive equations as a characteristic of aggregation are proposed, namely the microinertia as well as the volume fraction of blood particles (erythrocytes, platelets and leukocytes). Consequently, the Navier–Stokes system of equations for an incompressible fluid is supplemented by a constitutive equation for the moment of inertia in one case and for the volume fraction in another. The problems are solved numerically by the finite volume method for vessels of various geometries in spatial description. A comparison with experimental data for a narrow capillary shows the efficiency of the proposed constitutive equations for describing blood flow. Also, velocity profiles are obtained on the basis of compiled empirical formula for various sections of a blood vessel of variable radius. In addition, the flow through vessels of the human circulatory system, such as the inferior vena cava and the carotid artery, are studied.

This work presents the development of a two-way coupled flexoelectric plate theory starting from a 3D gradient electromechanical theory. The gradient electromechanical theory considers three mechanical length scale parameters and two electric length scale parameters to account for both mechanical and electrical size effects. Variational formulation is used to derive the plate governing equations and boundary conditions considering Kirchhoff’s assumptions. A computationally efficient (C^2) continuous non-conforming finite element is developed to solve the resulting plate equations. To assess the accuracy of the non-conforming finite element framework, the results are compared with Navier-type analytical solution for a simply supported flexoelectric plate. The finite element framework is also validated with experimental results in the existing literature for a passive micro-plate. The results show excellent agreement with both analytical and experimental results. Furthermore, computational efficiency of the non-conforming element is compared with the standard conforming element, which contains greater degrees of freedom and continuity across all elemental edges. It was observed that the non-conforming element is almost twice as fast as the conforming element without a significant loss of accuracy. The 2D finite element formulation is subsequently used to analyze the size-dependent response of flexoelectric composite plates operating in both sensor and actuator modes. Various parametric studies are performed to analyze the effect of boundary conditions, length scale parameters, size of the plate, flexoelectric layer thickness ratio, etc., on the response of flexoelectric plate-type sensors and actuators. It is found that the effective electromechanical coupling increases in a flexoelectric plate at microscale (due to the size effects), and it is higher than standard piezoelectric materials for plate thickness (h le 8,{{upmu }})m.

It is shown that the continuum limit of the metamaterial mass-in-mass model with additional attached mass describes not only the appearance of the additional band gap but also variations in the width and the position of the band gaps. These variations are governed by the key parameter—the stiffness ratio of the attached masses. Numerical study of periodic boundary excitation of the harmonic waves reveals suppression of the harmonic waves for the frequencies lying inside the both band gap areas. Also it is found that harmonic waves recover differently for the frequencies below and above the band gap values. The control mechanism is developed based on the abrupt variation of the stiffness ratio. It gives rise to the arising of phase shift of the wave, its suppression or recovery of the previously suppressed harmonic wave. Nonlinear long wavelength generalization of the model results in obtaining the model equation whose coefficients differ from those of the usual nonlinear mass-in-mass model. It gives rise to propagation of the localized wave with another amplitude and velocity.

We propose the governing equations for a pre-stressed poroelastic composite material. The structure that we investigate possesses a porous elastic matrix with embedded elastic subphases with an incompressible Newtonian fluid flowing in the pores. Both the matrix and individual subphases are assumed to be linear elastic and pre-stressed. We are able to apply the asymptotic homogenisation technique by exploiting the length-scale separation that exists between the porescale and the overall size of the material (the macroscale). We derive the novel macroscale model which describes a poroelastic composite material where the elastic phases possess a pre-stress. We extend the current literature for poroelastic composites by addressing the role of the pre-stresses in the functional form of the new system of derived partial differential equations and its coefficients. The latter are computed by solving appropriate periodic cell differential problems which encode the specific contribution related to the pre-stresses. The model in the first instance is derived in the most general scenario and then specified for a variety of particular cases which are associated with different macroscale behaviour of materials.

We study the spectral instability of supersonic solitary waves taking place in a nonlinear model of an elastic electrically conductive micropolar medium. As a result of linearization about the soliton solution, an inhomogeneous scalar equation is obtained. This equation leads to a generalized spectral problem. To establish instability, it is necessary to make sure of the existence of an unstable eigenvalue (an eigenvalue with a positive real part). The corresponding proof of instability is carried out using the local construction at the origin and the asymptotics at infinity of the Evans function, which depends only on the spectral parameter. This function is analytic in the right complex half-plane and has at least one zero on the positive real half-axis for a certain range of physical parameters of the problem in question. This zero coincides with the unstable eigenvalue of the generalized spectral problem.

The present contribution provides a classification of generalized continua constructed by a micromechanical approach, relying on an extension of the Hill macrohomogeneity condition. The virtual power of equilibrium for a micromorphic effective medium is derived from the microscopic Cauchy balance equations, highlighting the classical and higher-order macroscopic stress tensors. The so-called homogeneous displacement associated with the micromorphic effective medium is derived from variational formulations. It allows establishing the extended Hill macrohomogeneity condition that prevails for the micromorphic continuum, wherein the higher-order stress tensors arise as the static variables conjugated to the selected macroscopic degrees of freedom. Suitable projections of the introduced kinematic micromorphic variables into degenerated kinematic variables lead to various subclasses of generalized continua: microstretch, micropolar, couple stress, microdilatation, microstrain, microshear, and strain gradient. An asymptotic ranking of the formulated generalized continua versus a small-scale parameter is formulated in the last part of the paper to quantify their relative importance. The micromorphic homogenization scheme is validated by comparing the predictions of the homogenized response at the macroscale for a double shear test to a reference exact solution. The proposed micromorphic homogenization method remedy most of the limitations of the existing schemes of the literature.

The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, a computational homogenization scheme based on Mindlin (type II) strain gradient elasticity theory is developed here. The model is based on variational formulation with periodic boundary conditions, implemented in the open-source software FreeFEM to fully characterize the effective classical elastic, coupling, and gradient elastic matrices in lattice materials. Rigorous mathematical derivations based on equilibrium equations and Hill–Mandel lemma are provided, resulting in the introduction of macroscopic body forces and modifications in gradient elasticity tensors which eliminate the spurious gradient effects in the homogeneous material. The obtained homogenized classical and strain gradient elasticity matrices are positive definite, leading to a positive macroscopic strain energy density value—an important criterion that sometimes is overlooked. The model is employed to study the size effects in 2-D square and 3-D cubic lattice materials. For the case of 3-D cubic material, the model is verified using full-field simulations, isogeometric analysis, and experimental three-point bending tests. The results of computational homogenization scheme implemented through isogeometric simulations show a good agreement with full-field simulations and mechanical tests. The developed model is generic and can be used to derive the effective second-grade continuum for any 3-D architectured material with arbitrary geometry. However, the identification of the proper type of generalized continua for the mechanical analysis of different cell architectures is yet an open question.