Theoretical and Applied Mechanics Letters最新文献

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.

In this paper, by applying theoretical method to the governing equations of compressible viscous flow, we derive the theoretical formula of the boundary dilatation flux (BDF) on a flexible wall, which generalizes the most recent work of Mao et al. (Acta Mechanica Sinica 38 (2022) 321583) for a stationary wall. Different boundary sources of dilatation are explicitly identified, revealing not only the boundary generation mechanisms of vortex sound and entropy sound, but also some additional sources due to the surface vorticity, surface angular velocity, surface acceleration and surface curvature. In particular, the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted, namely, the product of the surface velocity divergence $\left({\nabla }_{\partial B}·U\right)$ and the vorticity-induced skin friction divergence $\left({\nabla }_{\partial B}·{\tau }_{\omega }\right)$. The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures. Therefore, by properly designing the surface velocity distribution, the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.

The present study is focused on the constitutive modeling for the mechanical behavior of rubber reinforced with filler particles. A filler-dependent energy density function is proposed with all the continuum mechanics-based necessities of an effective hyperelastic material model. The proposed invariant-based energy function comprises a single set of material parameters for a material subjected to several modes of loading conditions. The model solution agrees well with existing experimental results. Later, the effect of varying concentrations of filler particles in the rubber matrix is also studied.

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled, but several essential issues remain that strongly affect the performance. Two problems are studied in the current research: (1) the processing of the Reynolds stress tensor and (2) the coupling method between the machine learning model and flow solver. For the Reynolds stress processing issue, we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress. Then, the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis. An adaptive regularization term is employed to enhance the representation performance. For the coupling issue, an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow. The results have high consistency with the direct numerical simulation true values, which proves the validity of the current approach.

In this work, the evolution of melt pool under single-point and single-line printing in the laser engineered net shaping (LENS) process is analyzed. Firstly, the basic structure of the melt pool model of the LENS process is established and the necessary assumptions are made. Then, the establishment process of the multi-physical field model of the melt pool is introduced in detail. It is concluded that the simulation model results are highly consistent with the online measurement experiment results in terms of melt pool profile, space temperature gradient, and time temperature gradient. Meanwhile, some parameters, such as the 3D morphology and surface fluid field of the melt pool, which are not obtained in the online measurement experiment, are analyzed. Finally, the influence of changing the scanning speed on the profile, peak temperature, and temperature gradient of the single-line melt pool is also analyzed, and the following conclusions are obtained: With the increase in scanning speed, the profile of the melt pool gradually becomes slender; The relationship between peak temperature and scanning speed is approximately linear in a certain speed range; The space temperature gradient at the tail of the melt pool under different scanning speeds hardly changes with the scanning speed, and the time temperature gradient at the tail of the melt pool is in direct proportion to the scanning speed.

When using the projection method (or fractional step method) to solve the incompressible Navier-Stokes equations, the projection step involves solving a large-scale pressure Poisson equation (PPE), which is computationally expensive and time-consuming. In this study, a machine learning based method is proposed to solve the large-scale PPE. An machine learning (ML)-block is used to completely or partially (if not sufficiently accurate) replace the traditional PPE iterative solver thus accelerating the solution of the incompressible Navier-Stokes equations. The ML-block is designed as a multi-scale graph neural network (GNN) framework, in which the original high-resolution graph corresponds to the discrete grids of the solution domain, graphs with the same resolution are connected by graph convolution operation, and graphs with different resolutions are connected by down/up prolongation operation. The well trained ML-block will act as a general-purpose PPE solver for a certain kind of flow problems. The proposed method is verified via solving two-dimensional Kolmogorov flows (Re = 1000 and Re = 5000) with different source terms. On the premise of achieving a specified high precision (ML-block partially replaces the traditional iterative solver), the ML-block provides a better initial iteration value for the traditional iterative solver, which greatly reduces the number of iterations of the traditional iterative solver and speeds up the solution of the PPE. Numerical experiments show that the ML-block has great advantages in accelerating the solving of the Navier-Stokes equations while ensuring high accuracy.

A mass-rod-disk system consisting of an oscillating mass attached to a rigid rotating disk by an elastic rod is designed to study rigid-flexible coupling mechanism. Suppose the rod is lightweight and has enough stiffness, the theorems of linear momentum and angular momentum are applied to the mass-rod-disk system based on the kinematic description of the system. With respect to two deflections of the mass and one angular velocity of the system, a group of nonlinear differential equations are established where the tangential inertial force, centrifugal force, Coriolis force as well as the moments of additional inertial forces take important effects on the dynamic response. For the sake of description, these three types of inertial forces mentioned before are referred to as additional inertial forces in this paper. The horizontal deflections of the mass and the angular velocity of the disk rotating about a fixed-axis are numerically solved for the prescribed external torque. The oscillating trajectory of the mass is deeply influenced by the additional inertial forces, meanwhile the dynamic fluctuations of the angular velocity and rotary inertia of the system are strongly affected by the mass oscillation.

Hybrid nanofluids have attracted burgeoning attention owing to their outstanding capacity to improve heat transfer. The influence of velocity and temperature slip parameter and nanoparticls' (NPs') volume fraction on a vertical plate in the existence of suction has been explored in this work. The investigation's controlling partial differentiation equations were transformed into a conventional differential equation mechanism using resemblance modifications. Equations were then solved employing the fifth-order Runge-Kutta method. The skin coefficient of friction, temperature, and temperature gradient all rise when the volume percentage of NPs increases from 0 to 2%. Furthermore, a rise in the temperature slip variable was linked to a drop in the Nusselt number (heat transfer).The Nusselt number increased 0.15% and 5.63% respectively when the velocity slip parameter enhanced from 0 to 5 and the NPs volume percentage were increased from 0 to 1.5%. Furthermore, an increase in the temperature slip from 0 to 3 inflated the x-direction skin friction coefficient 8.2%, while inflation in the velocity slip from 0 to 5 was associated with a decline in the x-direction skin friction coefficient 95%.

Holding an object by clamping force is a fundamental phenomena. Layered or laminated architectures with internal sliding features are essential mechanism in natural and man-made structural system. In this paper, we combine the layered architecture and clamping mechanism to form a multilayered clamper and study the clamping force with internal friction. Our investigations show that the clamping force and energy dissipation are very much depend on the number of layers, its geometry and elasticity, as well as internal friction. The central goal of studying the multilayered clamp is not only to predict the clamping force, but also as a representative case to help finding some clue on the universal behaviours of multilayered architectures with internal friction.