International Journal of Applied Mechanics

Piezoelectric materials are widely applied in electronic components due to their ability to couple electric and mechanical fields. For the piezoelectric thin plate as a pressure sensor, we extend the modified first-order piezoelectric plate theory to explore the nonlinear solution of electric potential and discuss the relevant regulation mechanisms. Based on the piezoelectric effect, the electric potential generated by deformation is not linear with thickness. A quadratic function of electric potential across thickness is introduced. However, the electric potential on upper and lower electrodes is an unknown constant, which can be determined by the nonlinear complementary equation based on the Gauss theorem. It is shown that the nonlinear results of electric potential are consistent with outcomes by the three-dimensional finite element method. Furthermore, relevant regulation mechanisms are discussed on electric potential, including supported conditions, plate thickness, and load area. In addition, the influence of load locations on the electric potential response is analyzed. It is expected that these findings will be instructive to the structural design of piezoelectric pressure sensors.

The application of the discrete element method (DEM) to continuous medium problems is becoming increasingly widespread. In this work, a parallel computing method with multiple time steps based on overlapping particles is proposed. The domain decomposition method (DDM) with overlapping particles method is used to increase the speed up and shorten the computation time and meet the consistency requirements during data transmission. The multi-time-step method (MTSM) is adopted to tackle the matching of asynchronous step boundary. Data are exchanged at the boundaries in each subdomain with a message passing interface (MPI). The computational efficiency of different step ratios in both serial and parallel computing is studied respectively. Numerical examples show that the DEM can effectively handle large structure deformation problems, and provides a shorter calculation time than that of the finite element method (FEM). The DEM with multiple time steps in different subdomains effectively reduces the computation time than that with a single time step in the entire domain. Under fixed step ratio conditions, using parallel computing can save more time than serial computing. This work develops ideas for expanding the application of DEM for large engineering problems.

Machine learning has sparked significant interest in the realm of designing mechanical metamaterials. These metamaterials derive their unique properties from microstructures rather than the constituent materials themselves. In this context, we introduce a novel data-driven approach for the design of an orthotropic cellular metamaterials with specific target properties. Our methodology leverages a Bézier curve framework with strategically placed control points. A machine learning model harnesses the positions of these control points to achieve the desired material properties. This process consists of two main steps. Initially, we establish a forward model capable of predicting material properties based on given designs. Then, we construct an inverse model that takes material properties as inputs and produces corresponding design parameters as outputs. Our results demonstrate that the dataset generated using the Bézier curve-based strategy shows a wide range of elastic distributions. Describing the geometry in terms of design parameters, rather than pixel-based figures, enhances the training efficiency of the networks. The dual-network training approach helps avoid contradictions where specific elastic properties may correspond to various geometric designs. We verify the prediction accuracy of the inverse model concerning elastic properties and relative density. The presented approach holds promise for accelerating the design of cellular metamaterials with desired properties.

An analysis of the dynamic response and damage assessment of partially confined metallic cylinders under transverse air-blast loading is presented in this paper. The examination of the blast shock wave load distribution and the consequences of standoff distances on the plastic deformation of cylinders was conducted with meticulous attention in the experimental testing. The charges of TNT were determined to have masses of 16.3 kg and 29.5 kg, while the distances at which they were placed from the target varied between 1.5 m and 4.25 m. Three unique deformation modes were found to exist in the unilaterally supported cylinder, all of which were directly connected to the distribution of the blast load. In order to obtain an improved understanding of the dynamic behaviors exhibited in cylinders, a finite element simulation model was utilized and subsequently validated using an examination of the experimental results. The assessment of shock wave damage was conducted by utilizing the residual deformation of the metallic cylinder as an equivalent characterization under lateral blast shock wave loading. The duration of the positive pressure zone of the shock wave was determined to be between one-fourth and ten times the vibration period of a unilaterally supported cylinder, indicating that the P-I (overpressure-impulse) criterion could be utilized for damage evaluation. The incorporation of the P-I criterion was subsequently employed to evaluate the detrimental consequences, taking into consideration the radial distribution of residual deformation identified in metal cylindrical shell constructions subjected to lateral blast shock wave loading. This research contributed to a better comprehension of the dynamic behavior of partially confined metallic cylinders subjected to lateral blast loading and highlights the significance of the P-I criterion for evaluating and mitigating the damage effects in such scenarios.

In this paper, the possibility of using piezoelectric elements to create a prestress state in a plate and a shallow shell leading to a change in the natural frequencies is demonstrated numerically and experimentally. Strains in the thin-walled structure are determined using the non-linear relations based on the Reissner–Mindlin theory, which are linearized with respect to the state with a small deviation from the initial equilibrium caused by the inverse piezoeffect. A mathematical formulation of the dynamics problem is based on the variational principle of virtual displacements, taking into account the prestress state. The solution was developed by the finite element method. The validity of the obtained results is confirmed by comparing the natural frequencies and mode shapes of a rectangular plate with a piezoelectric element obtained numerically and experimentally at different values of electrical voltage. A series of calculations has been carried out to analyze the influence of the elasticity modulus, length, thickness, curvature of the shallow shell and voltage on the spectrum of natural frequencies of vibration. It was found that the effectiveness of using this technique decreases with increasing stiffness of the structure as a whole.

Nanowires (NWs) play a crucial role across a wide range of disciplines such as nanoelectromechanical systems, nanoelectronics and energy applications. As NWs continue to reduce in dimensions, their mechanical properties are increasingly affected by surface attributes. This study conducts a comprehensive examination of nanomechanical models utilized for interpreting large deformations in the bending response of silicon NWs. Specifically, the Heidelberg, Hudson, Zhan, SimpZP and ExtZP nanomechanical models are explored regarding their capability to predict the elastic properties of silicon NWs with varying critical dimensions and crystal orientations. Molecular dynamics simulations are employed to model silicon NWs with unreconstructed surface states. The calculation of intrinsic stresses and the methodology for quantifying surface properties, including surface stresses and surface elasticity constants, are carried out using atomistic modeling. The findings reveal significant disparities of up to 100 GPa among nanomechanical models in interpreting a singular force-deflection response obtained for a silicon NW. Inadequate consideration of surface and intrinsic effects in nanomechanical modeling of NWs leads to substantial variability in their mechanical properties. This investigation yields valuable insights into the surface characteristics of silicon NWs, thereby enhancing our understanding of the essential role played by nanomechanical models in the intricate interpretation of mechanical properties at the nanoscale.

This paper explores the use of carbon fiber-reinforced elastomeric skins for advancing flexible morphing wing technologies, highlighting exceptional 1D morphing capabilities. The study focuses on synthesizing a specially engineered elastomer-based skin with a zero Poisson’s ratio, achieved through precise formulation and fabrication onto unidirectional carbon fiber. Poisson’s ratio of the 1D skin is confirmed to be zero via image analysis. Micro-CT tomography evaluates carbon fiber quality and voids under varied prestretch conditions, revealing proportional increases in void sizes. X-ray tomography also provides insights into void distribution and morphology during pre- and post-cyclic stretching. The innovative approach enables seamless 1D morphing, achieving an impressive 200% stretch with a slight increase in actuation force and hysteresis loss percentage. Inspired by continuum mechanics, the proposed “Exp-ln-ln” framework accurately models the loading–unloading stretching of the skin. An extensive parametric investigation assesses key parameters, advancing fiber-reinforced elastomeric materials for aerospace morphing skins.

Quasi-zero stiffness vibration isolators (QZSI) can effectively resolve the contradiction between the load bearing and the vibration isolation for low-frequency vibration systems. The three-spring QZSI is a classical QZSI. However, constrained by its geometrical relationship, the working stroke of the QZSI is limited, and the isolation performance will deteriorate when the displacement response is significant. To solve this question, the shape memory alloy (SMA) damper, characterized by lower secondary stiffness, partially replaces the positive-stiffness spring of the three-spring QZS isolator to widen its effective working stroke, which forms a novel SMA-QZSI. Based on a piecewise linear constitutive model of SMA, a theoretical model of the force–displacement relationship of SMA-QZSI is established. Subsequently, the approximate analytic amplitude–frequency response equation of the non-smooth nonlinear SMA-QZSI system under harmonic excitation is obtained by the average method and verified numerically. In addition, the effects of mechanical parameters of SMA springs and external excitation parameters on mechanical behaviors and low-frequency isolation performance of the SMA-QZSI isolator are discussed. Finally, the static and dynamic experiments of SMA-QZSI are conducted to verify its force–displacement relationship and isolation performance. The results show that the proposed SMA-QZSI has remarkable low-frequency vibration isolation performance.

Finite element method (FEM) is a powerful tool to predict the properties and reveal the mechanisms of metal-matrix composites (MMCs) with very complex architectures and novel microstructures. Recent studies have demonstrated the effectiveness of network reinforcement architectures on simultaneous strengthening and toughening. Here, as a key factor in modeling network architecture, the critical microstructure size was studied via FEM. We found that a critical microstructure size of 23 $\mu$m (cell count $\sim$20) existed in the FEM model, beyond which the crack deflection may be feasibly induced from particle-rich to matrix regions, leading to crack propagation in the ductile matrix cells and thus high strength and elongation. While, with cell size 20–23 $\mu$m in SiC/6061Al model, the composite strength and elongation remained intact, implying that the maximal microstructure size is 23 $\mu$m for effective network architecture simulations.

Topology optimization (TO) is becoming an essential part of designing new or modifying current parts to improve their properties. A typical problem of TO in structural applications is minimizing compliance with volume (mass) constraints. TO is often complemented by additive manufacturing which allows the printing of complex geometries. Resulting geometries are dependent on the used method, most of the time it is the finite element method. The exported geometry from the optimization procedure, however, tends to have a lot of sharp edges, which causes problems with stress distribution, aesthetics and manufacturing (even if it is additive manufactured). The aim of this paper is to review, apply smoothing techniques on the surface of bodies, Laplacian and Taubin smoothing, and compare the results of smoothing. To fulfill this aim, we developed a smoothing procedure and evaluated the criteria of smoothed-out polymer geometries.

Metal cutting is an important process in industrial manufacturing. Using the mechanical quantities of metal cutting to optimize process design is helpful to improve productivity. However, it is expensive to obtain these quantities due to the complexity of the cutting process, including material nonlinearity, geometric nonlinearity, state nonlinearity and their interactions. In this paper, a prediction model is constructed by combining machine learning (ML) and simulation data to quickly acquire multi-difficult-to-obtain metal cutting mechanical quantities to solve this problem. First, Adaptive Smoothed Particle Hydrodynamics (ASPH) is used to generate a simulation dataset of 2000 metal cutting cases. Based on the simulation data, six machine learning (ML) methods are employed to establish two prediction models, single-task learning and multi-task learning, to predict the mechanical quantities of metal cutting. The experimental results demonstrate that the ML method can predict abundant reference data efficiently after understanding the relationship between simulation parameters and mechanical quantities from simulation data, which is expected to replace some similar and repetitive simulation work. The Multilayer Perceptron (MLP) model under the multi-task setting provides the best prediction performance, fastest prediction time efficiency, and stable model behavior. Additionally, input erasure experiments reveal that the prediction of maximum equivalent plastic strain is significantly affected by particle spacing, and cutting speed plays a vital role in predicting maximum velocity. This work highlights the promotion of the data-driven ML method in quickly obtaining abundant reference data for the metal cutting process, and provides an auxiliary means for process optimization.

In this study, the effects of freeze–thaw cycles and cyclic impacts on frozen soil were systematically investigated. With an increase in the number of freeze–thaw cycles, the peak stress of frozen soil decreased until a stable state was achieved. Moreover, subjecting frozen soil to an increased number of cyclic impacts led to notable alterations in mechanical characteristics, including peak stress, critical strain and dynamic elasticity modulus. Both the freeze–thaw cycles and cyclic impacts were identified as primary damage mechanisms in understanding frozen soil degradation processes. Damage resulting from these impacts conformed to the Weibull distribution pattern. Damages induced by freeze–thaw cycles, individual impacts and cyclic impacts were integrated into the Zhu–Wang–Tang viscoelastic model (ZWT model). Relying on principles of elastic mechanics, the role of confining pressure on frozen soil was examined and subsequently integrated into an improved ZWT model. To evaluate the model’s effectiveness, its predictions were compared with experimental results.