Continuum Mechanics and Thermodynamics最新文献

The exact, resultant equilibrium conditions for irregular shells reinforced by beams along the junctions are formulated. The equilibrium conditions are derived by performing direct integration of the global equilibrium conditions of continuum mechanics. New, exact resultant static continuity conditions along the singular curve modelling reinforced junction are presented. The results do not depend on shell thickness, internal through-the-thickness shell structure, or material properties of shell and beam elements. In this theoretical approach, the beam’s kinematics is represented by the elastic Cosserat curve. Kinematically, the six-parameter model of shell structures coincides with the Cosserat curve model of the beam. The presented method can be easily applied to cases of connection of three or four shell elements with the reinforcement along the junction.

This research investigates the effects of thermodynamic and kinetic parameters on simulated Fe(_{{2}})O(_{{3}})–2Al thermite reaction propagation. For that, a full-factorial design was applied. Five parameters were investigated: mixture density (A), thermal conductivity (B), specific heat (C), activation energy (D), and pre-exponential factor (E). Among these factors investigated, the activation energy, the specific heat, and their two-factor interaction had by far the highest percentage contribution of effects in the five responses observed: burning velocity, thickness of the reaction zone, peak temperature, ignition temperature, and ignition delay. Higher activation energy and specific heat resulted in a slower and thicker reaction propagation wave that required a longer time to ignite and reached a lower peak temperature. However, while activation energy affected the ignition temperature positively, the specific heat presented a negative effect. The remaining parameters had less pronounced effects but were significant in all five responses. Moreover, regression models of burning velocity, thickness, and ignition delay responses were estimated, which allowed mapping effects on these responses through contour plots of the main two-factor interactions.

The granular shear-transformation-zone (STZ) model is an energy-based constitutive model for studying granular materials subjected to vibration. This paper provides a detailed analysis of the thermodynamic foundation of the granular STZ model and applies it to investigate the mechanism of vibration-induced shear resistance reduction (ViSRR) in granular soils. Firstly, using the principles of thermodynamics, an energy conversion equation for a mechanical-energy-governed granular soil system is derived, accounting for vibration energy, configurational energy, strain energy, and contact energy dissipation. Then, by incorporating the critical state concept from soil mechanics, the energy conversion function is used to develop the evolution law of configurational temperature, one of the three governing functions of the granular STZ model. The analysis shows that ViSRR is influenced by the rate of strain energy development and the input rate of vibration energy, and that a limitation in soil deformation during vibration is necessary for ViSRR to occur. Furthermore, the contact energy dissipation arising from inelastic contact deformation and particle collisions contributes to enhancing a granular soil’s shear resistance by absorbing part of the external energy applied to the soil.

A higher-grade theory of non-ferromagnetic thermo-elastic dielectrics which incorporates the local mass displacement, the heat flux gradient, polarization inertia, and flexodynamic effects is developed. The process of local mass displacement is associated with changes in material microstructure. Using the fundamental principles of continuum mechanics, electrodynamics, and non-equilibrium thermodynamics, the gradient-type constitutive equations are derived. Due to accounting for the polarization inertia, the rheological constitutive equation for the polarization vector is obtained. In the balance equation of linear momentum, an additional term with the second time derivative of the polarization vector appears in comparison with the classical theory. This term controls the influence of the dynamic flexoelectric effect on the mechanical motion of dielectric solids. The propagation of a plane harmonic wave is analyzed within the context of the developed theory. It is shown that the theory allows for capturing the experimentally observed phenomenon of high-frequency dispersion of a longitudinal elastic wave. The theory may be useful for modeling coupled processes in nanodielectrics and heterogeneous polarized systems.

Phase transformations play a key role in numerous coupled natural processes, and they are important for many industrial applications. However, the kinetics of phase transformations in coupled chemo-mechanical systems undergoing large mechanical deformations still needs to be better quantified. Here, we study the phase transformation kinetics of a two-phase binary mixture using the diffuse interface approach. We couple a Cahn–Hilliard type model with a mechanical model for a compressible viscous flow. The bulk compressibility is a nonlinear function of the pressure, and the shear viscosity is a nonlinear function of the concentration. The mechanical coupling is achieved by employing a pressure-dependent mechanical mixing term in the equation for the Gibbs energy. We derive a dimensionless system of equations which we solve numerically with a pseudo-transient method using conservative finite differences for discretization. We perform numerical simulations in 1D and 2D model setups considering far-field simple shear and pure shear. For a chemo-mechanically coupled system, we show that the velocity of the phase boundary is a linear function of the degree of metastability and, hence, confirm the hypothesis of “normal growth.” A stronger mechanical coupling and a larger volumetric effect of the chemical reaction result in lower phase boundary velocities. The 2D results show a significant impact of the mechanical coupling and the far-field deformation on the orientation and kinetics of the phase transformations. Under far-field simple shear and pure shear in 2D, the phase transformations generate string-like patterns. The orientation of these patterns is controlled by the applied far-field deformation and orientations differ by 45 degrees between simple shear and pure shear.

A continuum theory of pantographic lattices, based on second-grade elasticity, is presented. The proposed model is able to describe the mechanical behavior of a type of material structure made up of multiple layers of pantographic sheets connected with a third family of fibers. Thus, these materials are characterized by an orthogonal pattern of fibers that can bend, stretch and twist. Numerical experiments illustrate the predictive potential of the model when the material is subjected to different types of mechanical loads, including compression, torsion and two kinds of bending. Analyzing the material responses for these various tests makes it possible to reveal unusual deformation patterns characteristic of such “pantographic blocks.” Numerical simulations using the finite element method are intended to assist in designing an experimental program using 3D-printed specimens made of different materials.

Depleted uranium (DU) and tungsten heavy alloys (WHA) are commonly used as kinetic energy projectiles penetrators due to their excellent properties such as remarkably high density and strength which significantly affect their armor penetration capabilities. This article presents the results of laboratory and field tests of the new WHA sinter which summarize the results of a development project intended to increase the strength of the above-mentioned sinters used in the production of kinetic ammunition. The alloy with the composition W91–6Ni–3Co was used for the tests. The obtained alloy was subjected to cold swaging deformation with reduction of 25%. The parameters of individual technological processes were determined based on previous research. These studies concerned the impact of the degree of cold swaging deformation on the mechanical properties of the 91W–6Ni–3Co alloy. The above-mentioned work presents the results of UTS test, Charpy impact strength measurement, hardness and microhardness measurement, and the results of WHA microscopic observations in two states: after heat treatment and the final state after cold swaging deformation with reduction of: 25%. The next purpose of the research was to check the strength and functioning of the new WHA rods used in 120 mm sub-caliber projectiles. This examination was crucial for the completion of this research project, and its results enabled a synthesis of laboratory results and experimental tests.

In this present study, we intend to obtain a new criterion for the analyticity of a complex function. More exactly, we will deduce some concrete restrictions that must be performed by a function that is complex, is defined on the disc centred at the origin that has radius 1 (hereinafter referred to as the unit disc), which, in addition, is continuous on this disc, including its border, to be analytic on the open unit disc. After that, as applications, we will deduce the Schwartz–Villat’s formula in this context, and we will obtain the known Joukowski’s function.

The shear constitutive model of soils plays a key role in the stability analysis of slopes. In this work, a statistical damage-based shear constitutive model for soils and its parameter determination method are proposed. An improved Weibull distribution function is introduced to calculate the damage variable. The shear test results of the slip band soils of the three gorges reservoir area in China are used to validate the proposed model. Quantitative indexes such as coefficient of determination, mean absolute percentage error and mean square error confirm that the accuracy of the proposed model is higher than that of an existing model. Compared with the existing model, the proposed model can better describe the experimental curve of shear stress vs. shear displacement in the post-peak stage. To analyze slope stability, a displacement-dependent transfer coefficient method is proposed by combining the proposed shear constitutive model with limit equilibrium theory. A case study demonstrates that the soil deformation at both ends of the slide mass is in the strain softening state first as the external load increases, and the resisting segment of the slide mass is located in its middle position. For a specified factor of safety, by considering the strain softening behavior in the proposed method, the computed allowable displacement of the slope is reduced at most by approximately 27% to that using the existing method neglecting the characteristics. The displacement-dependent transfer coefficient method reflects the progressive failure mode of the slope and can easily determine the displacement mapped to a factor of safety varied with the slope stress state.

Developing a technology that increases the service life of valve seats in CNG/LNG-powered vehicles requires the appropriate selection of material and its application technology. Commercially used valve seat materials show accelerated wear under operating conditions, especially in natural gas vehicle engines. The authors developed a new material and technological concept to protect the valve seat in CNG/LNG-powered vehicles. Two materials were used in the research: Stellite 6 alloy and Fe(_{3})Al intermetal. A commonly used material for valve seats of combustion engines is Stellite 6. The Fe(_{3})Al is the new proposed material coating for the protection of the valve seats of internal combustion engines. The article compares the abrasive wear resistance of these materials. The abrasion tests were performed on a T-11 pin-on-disc tester, and the counter-sample was steel S235JR. The test conditions were similar to those prevailing during the operation of the valves in the head of the internal combustion engine, without the influence of temperature. The results indicate that the Fe3Al intermetallic compound is characterised by a lower coefficient of friction and wear intensity than Stellite 6. The results of exploitation tests confirm that the Fe(_{3})Al phase is a prospective material to be used as a protective material on the valve seat of vehicles. The authors made a mathematical model for the wear of the newly created surface layers and proposed hypotheses regarding the wear mechanisms of these layers.