Continuum Mechanics and Thermodynamics最新文献

In this paper, we are following the plane time-harmonic waves propagation in an entire linear thermoelastic space, knowing the wavelength. Concerning the thermodynamic response, we fit the dual phase-lag model, while the effect of porosity on elasticity is given by Cowin–Nunziato theory. We obtain two shear waves and five longitudinal waves as: quasi-elastic wave, quasi-microrotational wave quasi-micropolar wave, quasi thermal mode, quasi-phase-lag thermal mode. The purpose of numerical simulations and of graphs is to identify the influence of connection between thermoelasticity, microrotation and porosity.

How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provide two answers, which are similar but not identical, and are compared in this article. They are compared both analytically and numerically on several levels of description, varying in the amount of detail. Namely, a reduction to a more common one-momentum setting is shown, where the effects of the second momentum translate into diffusive fluxes. Both SHTC and GENERIC can thus be interpreted as a method specifying diffusive flux in standard theory. The GENERIC equations, stemming from the Liouville equation, contain terms expressing self-advection of the relative velocity by itself, which lead to a vorticity-dependent diffusion matrix after the reduction. The SHTC equations, on the other hand, do not contain such terms. We also discuss the possibility to formulate a theory of mixtures with two momenta and only one temperature that is compatible with the Liouville equation and possesses the Hamiltonian structure, including Jacobi identity.

In this paper, a new beam Euler–Bernoulli finite element for the transverse static bending analysis of cracked slender strip tapered footings on an elastic two-parameter soil is presented. Standard Hermitian cubic interpolation functions are selected to derive the closed-form expressions of complete stiffness matrix and the load vector. The efficiency of the proposed finite element is verified on an example with several width tapering variations of a simple cracked footing with the results of governing differential equation. Another novelty of this study is improved bending moment functions with included discontinuity conditions at the crack location. These functions now accurately describe the bending moments in the vicinity of the crack of the finite element.

After defining the fractional (varLambda )-derivative, having all the prerequisites for corresponding to a differential, the fractional (varLambda )-strain has already been established. Furthermore, only globally variational principles are allowed in the context of fractional analysis. Hence, balance laws, yielding the various field equations in (Lambda )-fractional continuum mechanics, are derived, allowing corners in their fields. The basic balance laws of mass, linear and rotational momentum, and energy conservation with jump conditions are derived in the context of (Lambda )-fractional analysis.

Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occurring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behavior. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution.

This paper explores the interplay of surface and bulk elasticity on the evolution of surface relief within nanosized thin-film coatings, driven by the relaxation of misfit stresses through surface diffusion mechanism. The proposed theoretical approach incorporates the constitutive equations of surface elasticity theory developed by Gurtin and Murdoch into the Asaro–Tiller–Grinfeld model of morphological instability, which takes into account the stress sensitivity of the local gradient in chemical potential driving mass transport along the perturbed surface. Linear stability analysis, based on the solution of the linearized evolution equation representing the amplitude change of surface perturbation with time, predicts the conditions leading to the early growth of surface topological defects. These conditions depend on factors, such as the initial shape and wavelength of the surface undulations, misfit stresses, tension at the surface and interface, and the elastic properties governing the deformation of the surface, interface, film, and substrate.

The effectiveness of multi-barrel rocket systems on today’s battlefields is strongly dependent on the reliability of operation and, hence, proper action of all components, especially rockets and propellants. Therefore, the properties of the solid rocket propellants used in the rocket motors must be determined with an efficient and reliable tool providing repeatable results. The article presents the results of a thermomechanical analysis of solid double-base rocket propellant used in multi-barrel rocket systems. One of the recommended methods for testing solid rocket propellants is dynamic mechanical analysis. Mechanical properties such as the dynamic storage modulus ((E^prime )), the dynamic loss modulus ((E^{prime prime }),) and the tangent tan((delta )) of the phase shift angle ((E^{prime prime }/E^prime )) were measured with the use of the TA Instruments DMA Q 800 device, in a temperature range of − 100 to (+)100 (^circ ) C with the use of different frequencies of applied force and heating rates. Special attention was devoted to determining the glass transition temperature following the STANAG 4540 standardization agreement, as well as the influence of testing parameters on the obtained experimental results. Dynamic mechanical analysis has proven to be an effective method for the evaluation of key properties influencing rocket motor behavior.

We study the homogenization of an elastic material made of an elastic matrix in contact with highly contrasted three-dimensional elastic rigid fibres with circular cross section. The interaction between the matrix and the fibres is described by a local interface adhesion law. Assuming that the Lamé constants in the fibres and the stiffness coefficient of the adhesive have appropriate orders of magnitude, we derive a class of deformation energies involving second gradient functionals, third gradient functionals, and a functional energy associated with inner torsion.

When the surface roughness is comparable to the surface separation in a hydrodynamic thrust bearing, the effect of the surface roughness should be considered. In the condition of low bearing clearances such as on the scales of 1 nm and 10 nm, normally not only the surface roughness but also the physically adsorbed layer on the bearing surface should be simultaneously considered in evaluating the bearing performance. The present paper presents the numerical calculation results of the surface roughness influences on the hydrodynamic pressure and carried load of the inclined fixed pad thrust bearing with low bearing clearances when the effect of the adsorbed layer is incorporated. It is shown that the influence of the surface roughness is strongly dependent on the adsorbed layer and it is significantly increased with the increase in the interaction strength between the fluid and the bearing surface when the bearing clearance is low. For a weak fluid-bearing surface interaction, the results are close to those obtained from the classical hydrodynamic theory indicating the increase in the hydrodynamic pressure and carried load of the bearing with the increase in the surface roughness, while for the medium or strong fluid-bearing surface interactions, this surface roughness effect is much stronger. The results reveal the new mechanism in the studied model of the bearing regarding the coupled effects of the surface roughness and the physically adsorbed layer on the bearing surface.

The paper presents research on identifying a biomechanical parameter from a theoretical model of changes during osteoarthritis. In vitro experiments were carried out on quasi-3D chondrocyte cultures seeded on corn-starch hydrogel materials and subjected to mechanical stress on a designed and constructed stand. The results were adapted to a mathematical model and calculated on a simplified two-dimensional specimen. Numerical simulations have been performed to illustrate the growth of bone spurs. The observed changes of variables which determine osteophytes are qualitative and more correlated to the real-life observations.