Continuum Mechanics and Thermodynamics最新文献

We review the tools used in the inverse scattering transform, focusing primarily on their computational aspects. As an example, we discuss the Toda’s chain, an apparently simple nonlinear discrete system, to illustrate the various steps of the process. We chose this naturally discrete nonlinear system to avoid the additional errors that can arise from discretizing a differential equation whose continuum limit represents the problem under consideration. Furthermore, the homogenized Toda’s chain is equivalent to the renowned Korteweg–de Vries equation and also resembles the equally famous Fermi–Pasta–Ulam–Tsingou problem. Given that the Toda’s chain serves as a prototype for nonlinear systems with known analytical solutions, it provides a valuable test case for numerical procedures. Our main goal is to outline the various steps of the inverse scattering transform, with particular attention to numerical aspects, including the reconstruction of soliton shapes.

We employ a model of a special type of continuum that possesses both translational and rotational degrees of freedom. We formulate differential equations describing the behaviour of this continuum by using the spatial description with a moving observation point. Next, we reduce these differential equations to the form convenient for the comparison with Maxwell’s equations and introduce electrodynamic analogues of mechanical quantities. In doing so, we arrive at Maxwell’s equations that have exactly the same form in the case of moving media and in the case of motionless media. We also obtain the constitutive equations that coincide with the Lorentz equations and the constitutive equations that coincide with the Minkowski equations.

The major functions of eukaryotic cells can be significantly affected by mechanical stimuli. A common limitation of approaches to the study of cell mechanics is the lack of consideration of the microscopic structural features of the cytoskeleton which, among other things, influence the inelastic behavior. In this paper we develop a statistically based thermodynamic description of the cytoskeleton to simulate finite deformation of the cell. It is proposed statistical-thermodynamic approach to use order parameters to describe the orientation of microfilaments and the sliding of the actin bundles of the cell cytoskeleton. A form of the free energy is obtained as a function of these parameters, temperature and shear stress. Besides, there was found the dependence on the free energy on the structural parameter playing the role of the “effective temperature” and characterizing the structural susceptibility of the cytoskeleton. Following the complete system of objective constitutive relations of the cytoskeleton, the cell shear deformation was studied. The “critical” dynamics was ascertained in characteristic ranges of the structural parameter as a form of the orientation and microshear collective modes.

This research presents an innovative spatiotemporal nonlocal model designed to analyze the behavior of a thermoelastic micropolar medium under laser irradiation. The model incorporates phase-delay heat conduction theory, enabling a more accurate depiction of thermal and mechanical responses, particularly in nanoscale materials. By accounting for both spatial and temporal nonlocal interactions, the model effectively addresses size-dependent phenomena, which are essential for understanding the behavior of micropolar materials. These nonlocal effects consider how the surrounding environment and the material’s previous responses influence its current behavior, thereby enhancing the model’s precision and real-world relevance. The integration of phase-delay theory facilitates the characterization of non-Fourier heat conduction, which is critical for accurately modeling material behavior under brief laser pulses. Moreover, the phase delays capture the time-lagged responses of materials to sudden thermal inputs, a vital consideration in applications involving laser heating. The study includes graphical representations that illustrate the impact of key parameters, such as micropolarity, phase delay, and the nonlocal index, on the material’s mechanical behavior with respect to distance. This analysis enhances understanding of spatial variations in stresses, displacements, and mechanical properties of micropolar elastic materials under laser heating.

Thermal shock testing is a crucial method for evaluating the quality and lifespan of thermal barrier coatings, which are widely used in the aerospace and power generation industries. Currently, these tests are predominantly conducted under static conditions, which do not fully replicate real operational environments. In this study, we aimed to assess the strength and quality of thermal barrier coatings under dynamic conditions and to collect data on temperature distribution, supported by experimental analyses. To achieve this, a specialized test setup was designed, coating applications were performed, and lifetime tests were conducted. In addition to the test results microscopic examinations of the coatings were performed. The findings reveal that static tests do not accurately reflect the effects observed under dynamic operating conditions. Furthermore, the damage occurred significantly faster in the dynamic tests than in the static tests. These results highlight the necessity of dynamic testing for a more reliable assessment of thermal barrier coatings.

This work presents a comprehensive theoretical framework for flexoelectric materials by incorporating higher-order strain gradient and polarization gradient effects into the constitutive modeling. Using an extended strain gradient elasticity (SGE) approach, coupled with a generalized Toupin-like variational formulation, we derive governing equations, balance laws, and boundary conditions based on an enriched internal energy density function. Analytical solutions, expressed in terms of modified Bessel functions, provide key insights into the role of higher-order gradients in influencing displacement, polarization, and electric fields. The study highlights the critical impact of size effects on flexoelectric response, revealing that reducing material thickness enhances sensitivity and energy conversion efficiency. Furthermore, numerical simulations validate the theoretical model and demonstrate its applicability in the design of nanoscale flexoelectric sensors and energy harvesters. These findings establish a robust theoretical foundation for optimizing nanoscale electromechanical devices, with potential applications in biomedical sensors, structural health monitoring, and energy-efficient electronics.

This innovative study presents a novel framework for analyzing the axial dynamic response of a rotating thermoelastic nanobeam subjected to a moving load, marking a significant advancement in the field of nanoscale mechanics. By integrating the Klein-Gordon nonlocal theory with an innovative internal time scale parameter, the research derives governing equations that effectively capture nonlocal effects. The application of Hamilton’s principle in conjunction with Euler-Bernoulli beam theory ensures precise modeling, while the dual-phase lag (DPL) framework accounts for thermoelastic properties without energy dissipation, incorporating both internal length and time scale parameters. The use of the Laplace transform method to solve the resulting partial differential equations demonstrates a robust analytical approach. A detailed numerical example highlights the effects of nonlocal parameters, rotation, and load speed on axial dynamic deflection, stress, and temperature distribution, with graphical results validating the model’s accuracy against previous studies. This study sets a new standard for modeling complex nanoscale systems and provides valuable insights into their dynamic behavior.

The current technological development has put forward higher requirements for the multifunctionality of materials and structures. This study delves into the bandgap attributes of a zigzag connection (ZC) lattice metamaterial, capable of being constructed through the mirroring or rotation of basic units. This metamaterial exhibits nearly zero thermal stress when subjected to thermal expansion deformation. Through a comprehensive analysis and comparison of three distinct arrangements, the rotational symmetrical quadruple cell emerges as the optimal choice. Subsequently, the investigation explores the influence of various geometric dimensions, constituent materials, and additional parameters on the bandgap. The findings elucidate the exceptional bandgap characteristics of this configuration, coupled with its ability to accommodate tailored thermal expansion coefficients and minimize thermal stress. By judiciously selecting materials and refining structural design, the study envisages the attainment of multiple objectives in thermal expansion properties and bandgap modulation. Such endeavors hold promise for enhancing the tunability and multifunctionality of the metamaterial, thereby advancing its utility across diverse applications.

This study presents a generalized photo-thermoelastic model for solid semiconductor media subjected to photoacoustic excitation within the framework of multi-temperature theory. The model captures the complex interactions among optical, thermal, and elastic waves, offering a more realistic representation compared to traditional single-temperature approaches. The governing equations are formulated by coupling the photoacoustic source with multi-temperature thermoelasticity, accounting for separate thermal responses associated with thermodynamic and conductive temperature fields. Analytical solutions are obtained using the normal mode analysis technique, allowing for detailed evaluation of the main physical field distributions. Comparative simulations highlight the differences in wave behavior under multi-temperature theories. The results show that the hyperbolic and two-temperature models outperform classical models in capturing sharp thermal gradients, delayed thermal wavefronts, and stronger stress and displacement responses. These findings confirm the importance of advanced thermal theories in improving the design and reliability of semiconductor-based photonic and optoelectronic devices.