Continuum Mechanics and Thermodynamics最新文献

Effect of the external surface layer on the phase transition (PT) between the low pressure phase and high pressure phase (HPP) in a NiAl bicrystal is investigated. Using a phase field model, the external surface layer is included, within which the elastic properties and surface energy are properly distributed. After resolving a stationary layer, the coupled phase field and elasticity equations are solved to capture the HPP evolution. Residual stress concentrator is included as a shear band representing an inelastic shear strain. Due to the small grain size, the surface layer can influence the stress distribution and consequently, the critical inelastic shear strain (gamma _{cr}) for the HPP growth. Above a certain applied pressure, the surface layer width ({Delta }_{{xi }}) shows no effect on (gamma _{cr}), e.g., (P=10) GPa for the grain size of L (=) 20 nm. For lower pressures, (gamma _{cr}) increases as pressure reduces. Due to the interplay of size addition by the surface layer and size reduction by the transformation strain, (gamma _{cr}) reduces versus ({Delta }_{{xi }}) and then increases for larger ({Delta }_{{xi }}). For smaller grain sizes, the surface layer effect is promoted as it is imposed to a larger transformation work. The lowest (gamma _{cr}) is obtained for (P=19) GPa, in good agreement with the theoretical pressure of 20 GPa. Combining the external shear on pressure adds an extra shear term to the transformation work, which allows for the relaxation of the shear band and results in a nonlinear reduction of the PT pressure versus applied shear.

Material modeling for micromorphic continua (in the sense of Eringen and Suhubi [IJES, 1964]) of combined viscoelastic-viscoplastic constitutive nonlinearity is developed, for application to some geomaterials and other granular materials, and is recast in a compact energetic formulation via “granular micromechanics.” Under the granular mechanics homogenization paradigm, potentials and pseudo-potentials for viscoelastic viscoplasticity are scale-bridged by averaging discrete grain-contact interactions over a representative granular assemblage. As a critical feature of the proposed multiscale method, higher-order kinematics are considerably simplified by employing a microstructural length scale in conjunction with Taylor-series expansion. In distinction to prior micromorphic micromechanics, our discrete-to-continuum scale-bridging embeds a volume constraint to weakly enforce mean-field definitions in the representative assemblage by the method of Lagrange multipliers: analogous to the classical three-field reformulation of a mixed interpolation space for nonlinear finite elements’ selective integration. As subsequently demonstrated, volume-constrained reformulation renders micromorphic modeling constitutively appropriate for viscoelastic viscoplastic particulate materials. As a consequence, coupled pressure- and rate-sensitive dissipative phenomena - i.e., of combined viscoelasticity and Drucker–Prager viscoplasticity– -become microstructurally sensitive and algorithmically advantageous, utilizing numerical methods in bound-constrained optimization.

The current investigation deals with the deformation of a non-homogeneous thermoelastic half space under hydrostatic initial stress for the Green–Naghdi model III. The medium is supposed to be rotating with a constant angular velocity. The non-homogeneous properties of the material are along the x-direction. At the first instance, the problem has been solved analytically to obtain stress and displacement components. Further, the numerical values of these expressions are evaluated using a computer program for a particular medium. The numerical values obtained are then presented graphically to show the effect of initial stress parameter and non-homogeneity parameter on the quantities.

An analogy is drawn between version of non-equilibrium thermodynamics a distribution-based containing an additional thermodynamic first-passage time parameter, nonequilibrium statistical operator method and extended irreversible thermodynamics with flows as an additional thermodynamic parameter. Thermodynamics containing an additional thermodynamic first-passage time parameter maps to extended irreversible thermodynamics. Various conditions for the dependence of the distribution parameters of the first-passage time on the random value of energy, the first thermodynamic parameter, are considered. Time parameter relaxation time (tau ) of extended irreversible thermodynamics is replaced by the average first-passage time. Expressions are obtained for the thermodynamic parameter, the conjugate of the first passage time through the entropy change, and for the average first passage time through the flows.

The purpose of this study was to evaluate the possibility of using mechanical spectroscopy to determine the strength of tool coatings from their lifespan. Mechanical spectroscopy with the determination of the index tan(delta ) (internal friction) was used as the research method. Samples were coated with lamellae composed of WC-6wt% Co cemented carbides. The specimens measured 1.0 mm, 3.0 mm, and 40.0 mm, created using a conventional industrial liquid phase sintering procedure. The original powder consisted of cobalt with traces of chromium and vanadium, and submicron WC grains. The tools tested included carbide cutting tools, and the workpieces were steel alloys. Comparative results showed that coated tools had significantly improved tool life and durability. The relationship between the coating and tool life was evident, providing a practical approach for predictive and non-destructive analyses of coatings on tool durability for composite and finely structured materials.

The structural complexity of high-tech industries is often compromised by a combination of thermal, mechanical, and geometric weaknesses. New generation materials and engineering the structure of materials are among the techniques that engineers employ to eliminate these effects. In this study, a comprehensive analysis solution is derived using Lekhnitskii’s complex variable approach with the use of general mapping functions, the concept of functionally graded materials (FGMs), and holomorphic functions in the form of Laurent series. This general solution is used for the thermoelastic analysis of perforated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with polygonal hole. A refined-calibrated rule of mixtures is used to approximate the material property of FG-CNTRC plates according to gradational changes in direction of thickness and available molecular dynamics simulations results. After validation of present analytical solution results with finite element analysis results and available mechanical analysis of composite plates results, stress and moment resultants due to remoting heat flux-mechanical loading is studied. The effect of FG-CNTRC material properties, heat flux condition, and four parameters affecting the shape of the polygonal holes has been investigated. During the present parametric analysis, the results clearly show that the parameters related to the FG-CNTRC material properties, flux conditions, and hole geometry each provide a reliable tool for designers to influence the stress and moment resultants to minimize undesirable stresses. This general formulation is able to calculate thermoelastic parameters (thermal and mechanical parameters, separately) for the generalized problems of the FGM plate or composite laminates with a polygonal hole.

In this study it is approached a linear model for the mixture of two Cosserat bodies having pores. It is formulated the mixed problem with initial and boundary data in this context. The main goal is to show that the coefficients that realize the coupling of the elastic effect with the one due to voids can vary, without the mixture being essentially affected. In a more precise formulation, this means that a small variation of the coefficients in the constitutive equations of the two continua causes only a small variation of the solutions of the corresponding mixed problems, that is, the continuous dependence of the solutions in relation to these coefficients is ensured. The considered mixture model is consistent because all estimates, specific to continuous dependence, are made based on rigorous mathematical relationships.

The paper focuses on the effect of damage on the bone remodeling process. This is a crucial, although complex, aspect. A one-dimensional continuous deformable body is employed to model living bone tissue. The model incorporates the bone functional adaptation through an evolution law for an effective elastic modulus driven by mechanical feedback via a mechano-transduction diffusive signal. This type of information transduction, i.e., diffusion, is essential for the model to take into account remodeling in the case of minor injury or pathology-affected regions where there is no signal production. In addition, the model is able to also take into account potential tissue damage that may evolve over time according to a suitable evolution law. To illustrate the capability of the model to describe the mentioned complex coupled phenomena, numerical tests have been performed encompassing high external loads causing the onset of damage and cyclic loading for healing. The numerical simulations carried out via finite-element analyses yield insights into the mechanisms of bone remodeling, with the final goal of aiding clinical decisions and implant designs for bone health and repair. Overall, a key aspect of the paper is to highlight the feasibility of modeling the evolution in bone elasticity arising from the combined effect of damage and remodeling.

In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors.

Stochastic equations of hydrodynamic theory of plasma are presened. The article shows that for transfer processes in liquid and gas, on the one hand, and in plasma, on the other hand, there exist sets of stochastic differential equations for substantial quantities based on the equality of measures between deterministic motion and random motion. It is shown that the application of these stochastic equations makes it possible to obtain new theoretical solutions for the occurrence of turbulence also for a plasma as a result of its heating in an external electric field instead of only for a classical gas, as it was proved previously. Theoretical solutions for the conductivity of turbulent plasma during its heating in an external electric field are considered. At a first time taking into account the turbulence parameters theoretical relations for the electron drift velocity and corresponding relations for electron mobility, for the frequency of electron collisions, and for the Coulomb integral are obtained. All theoretical relations are applied to calculate the conductivity during the turbulent heating of plasma in an electric field. Here experiments with hydrogen plasma are being considered. The theoretical explanation of the cause for the existence of a constant conductivity in the field of strength (E = 0.6-19) V/cm and its fall at (19<E<100) V/cm is given. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data at the electric-field strength in the turbulent region (E = 0.6-100) V/cm and in the region (E < 0.6) V/cm.The equation for the critical electric-field strength is presented.