Continuum Mechanics and Thermodynamics最新文献

The main relations of the two-dimensional of asymmetric elasticity theory are considered. The matrix for the fundamental solutions of these equations is constructed. In the context of two-dimensional asymmetric elasticity, the volume potential, also called logarithmic potential, is obtained, which is the analog of the volume potential, from the abstract theory of singular integral equations. In the same context, the single-layer and double-layer surface potentials are obtained, which are also analogous to the surface potentials from the classical theory of equations of integral type. For the first and the second inside problems with values to the limit are deduced the specific system of integral equations of singular type. Similar for the two outside problems with values to the limit. It is demonstrated that the index of the equations of the integral type, previously defined, is null, for all four systems of singular integral equations.

This study utilizes the nonlocal strain gradient theory (NSGT) to establish a generalized, size-dependent thermoelastic framework for transversely isotropic piezo-thermoelastic (PTE) microbeam under the Euler-Bernoulli beam theory. The model incorporates two different length-scale parameters, viz. nonlocal elasticity and strain gradient effects to characterize microscale structural behavior. To address thermal lagging phenomena, the heat conduction equation is derived based on the Moore-Gibson-Thompson (MGT) framework, which introduces memory-dependent derivatives over a variable time interval. By employing coupled Laplace transform and finite Fourier sine integral methods, analytical solutions for thermoelastic distributions (e.g., deflection, bending moment, thermal moment) are derived for a simply supported microbeam. The Laplace-domain solutions are obtained via Fourier inversion, and their time-domain counterparts are reconstructed using the Zakian’s algorithm. Numerical simulations based on PZT-5A material investigate the influence of kernel functions on heat transport behavior and evaluate the performance of the proposed nonlocal strain gradient model against classical formulations. The results demonstrate a strong sensitivity of physical responses, such as thermal moment and deflection to time delay parameter, revealing the potential for controllable vibration damping. Overall, the study offers valuable design insights for microscale beams in MEMS/NEMS applications, bridging advanced theoretical modeling with practical optimization strategies.

This paper presents a comprehensive study of exact wave solutions within the framework of coupled theory (CT) thermoelasticity, incorporating temperature dependence. We employ tauthorhe method of improved modified extended tanh-function (IMETF) to derive analytical solutions for the governing equations that account for the interaction between thermal and mechanical fields in materials. The temperature-dependent characteristics of materials are considered, which significantly influence the thermoelastic behavior under various loading conditions. The proposed method enhances the conventional tanh-function approach by allowing for more complex wave structures, thereby we obtained of a broader range of exact solutions featuring distinct free parameters, involving hyperbolic,exponential, Jacobi elliptic, dark soliton, compice dark-singular soliton, rational, and polynomial solutions. The results reveal valuable insights into the propagation of waves in thermoelastic materials. In addition, some of the results for stress tensor components, displacement components, and temperature are shown as graphical visualizations.

Magnetic Pulse Welding (MPW) is an innovative solid-state welding technology that uses high-speed electromagnetic forces to achieve defect-free joints without melting the base materials. This paper presents a comprehensive numerical investigation into MPW for industrial applications, focusing on plates and tubular components. By leveraging coupled electromagnetic and mechanical models developed in COMSOL MULTIPHYSICS, this research explores critical parameters affecting weld quality, such as material properties, geometries, air gaps, and energy levels. The simulations demonstrate that Al/Al plate welding achieves complete joint formation within (10 mu s) at a discharge current density of (3.2 times 10^{11} A/m^3), while dissimilar joints such as Cu/Al and Ti/Al require up to (12.5 mu s) and (47 mu s) respectively. In tube welding scenarios, similar material combinations (Al/Al) showed successful bonding within (20 mu s), while dissimilar pairs (Mg/Al and Cu/Al) required significantly more time and higher energy input. Weldability maps and deformation analysis confirm that air gap and coil geometry substantially impact welding time and joint quality. These results underline MPW’s potential for cost-effective, high-speed, and sustainable manufacturing in aerospace and automotive sectors.

Determining the limiting behavior of discrete systems with a large number of particles in Statistical Mechanics is crucial for developing accurate analytic models, especially when addressing multistability and multiscale effects. Typically, one considers the so called thermodynamical limit or the continuum limit. The guiding principle for selecting the correct limit is to preserve essential properties of the discrete system, including physical attributes such as the interplay between enthalpic and entropic contributions, the influence of boundary conditions, and possible other energetic contributions such as interface effects. In this sense, an important role is played by the fundamental constants. Selecting appropriate rescaling factors for the Planck and Boltzmann constants, according to the specific limit considered, is a key theoretical concern. Despite the importance of this problem, the existing literature often lacks clarity on how different rescalings affect model accuracy. This work aims to clarify these issues by examining classical lattice models – particularly those that exhibit multistable behavior – and by proposing suitable limit rescalings to retain the discrete model’s material response when the number of particles increases.

In some laser-based applications, such as laser welding and surface hardening, it is significant to maintain the surface temperature at an elevated level for a certain period even after the laser is turned off. This study investigates the effect of a surface temperature-dependent absorption coefficient that may control the surface temperature in a specific period. The MGL theory is employed to analyse the effects of the surface temperature-dependent absorption coefficient in a nonlocal thermoelastic semi-infinite medium heated by a laser pulse. The volumetric absorption technique is used in the heating process for a medium whose surface is exposed to surface-dependent heat loss and is traction-free. The integral transformation method is used analytically to obtain a general solution for the problem and computationally to attain the inverse transformation. The results indicate that the absorption coefficient, which depends on the surface temperature, exhibits a temporal and spatial impact period. It significantly influences thermal waves, while its impact on elastic waves is minimal.

We present a study of the thermal susceptibility associated with the Guyer-Krumhansl (GK) equation. This model is analyzed within the framework of causal linear response theory, which enables a causal and non-local description of thermal transport. We demonstrate that the real and imaginary parts of GK’s thermal susceptibility satisfy the Kramers-Krönig relations. Notably, unlike electromagnetic and mechanical systems where dissipation is linked to the imaginary part, in this case, thermal energy dissipation is associated with the real part of the susceptibility. Finally, we establish the sum rules for thermal susceptibility, which impose constraints on the value of Cattaneo’s response time.

In continuum thermodynamics, models of two-phase mixtures typically obey the condition of pressure equilibrium across interfaces between the phases. We propose a new non-equilibrium model beyond that condition, allowing for microinertia of the interfaces, surface tension, and different phase pressures. The model is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible equations, and it possesses variational and Hamiltonian formulations. Finally, via formal asymptotic analysis, we show how the pressure equilibrium is restored when fast degrees of freedom relax to their equilibrium values.

Simulation of the mechanical behaviour of hybrid laser-arc welded joints is a critical issue in both academic and industrial communities. A key challenge lies in addressing the microstructural heterogeneity across different zones, which complicates accurate or even acceptable predictions. To overcome this challenge, a novel cross-scale methodology is proposed to precisely simulate the mechanical behaviour of laser-arc welded joints in aluminum 6061 alloy with filling material of 4043 alloy. To achieve this, the microscale plasticity of single crystals (SCs) with orientations of [10-1] and [31-2] is first investigated using micropillar compression testing. The results reveal that the yield strength of these SCs at small scales exhibits size independence, which contradicts previous literature. This phenomenon is attributed to strong solid solution strengthening and high dislocation density. Building on these findings, a micromechanics model is developed, integrating dislocation-based crystal plasticity theory and experimental results from micropillar compression testing This model successfully reproduces the mechanical behaviour of SCs at the microscale. Leveraging insights from crystal plasticity at small scales, a macroscale polycrystal model is constructed to simulate the mechanical behaviours of bulk materials. The predicted results for compressive and tensile mechanical behaviour at the macroscale demonstrate excellent agreement with experimental data. The physics and mechanisms governing the mechanical behaviour across scales are discussed in depth, drawing on results obtained from both experiments and simulations. Unlike traditional approaches that phenomenologically simulate the mechanical behaviour of welded joints, this novel methodology explicitly accounts for microstructural evolution. By bridging microscale and macroscale analyses, it provides new insights into the relationship between microstructure and mechanical properties in welded joints of aluminium 6061 alloy with filling material of 4043 alloy.

The multiscale analysis is presented for the elasticplasto-hydrodynamic lubrication in the rolling and sliding macroscale elastoplastic steel line contacts involving the surface thermal deformation in the condition of heavy loads and high rolling speeds by incorporating the effect of the physically adsorbed molecule layer on the contact surface. The calculation results show that even for a small slide-roll ratio, the severe frictional heating and the consequently resulting contact thermal deformation can cause the very low lubricating film thickness which is on the same scale with the adsorbed molecule layer thickness, in combination with the effect of the contact elastoplastic or fully plastic deformations. The stronger interaction between the fluid and the contact surface results in both the thicker adsorbed layer thickness and the higher lubricating film thickness in the contact for a given operating condition when the surface separation is reduced to be comparable to the adsorbed layer thickness at sufficiently big slide-roll ratios. The increase of the slide-roll ratio (S) drastically reduces the lubricating film thickness if (S> 0.01).