Continuum Mechanics and Thermodynamics最新文献

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).

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.