Mechanics of Materials最新文献

This paper studies the tractive rolling nanocontact occurring between an exponentially graded coating-substrate structure and a circular rigid indenter. Employing the framework of Steigmann–Ogden surface elasticity, it models the surface effects inherent in the nanocontact of graded coatings. The contact area is assumed to comprise a central stick zone bounded by two distinct slip zones. Central to the investigation is the utilization of the nonclassical Flamant solution, which serves as the foundational framework for deriving integral equations governing the continuity of both vertical and tangential displacement gradients. Utilizing Gauss–Chebyshev quadratures, the paper discretizes and collocates these integral equations, along with the force equilibrium conditions and shear traction smooth condition at the leading side stick/slip transition point. An iterative algorithm is then developed to tackle the resultant algebraic system, particularly concerning the discretized contact pressure and friction traction. The paper rigorously validates its proposed solution method and numerical algorithm against existing literature results, showcasing their accuracy and reliability. Moreover, it conducts extensive parametric studies to unravel the effects of various parameters, such as surface material properties, coefficient of friction, inhomogeneity index, and thickness of the exponentially graded coating. These analyses uncover the significant role of surface effects in shaping contact pressure, frictional traction, stresses, subsidence distributions, and stick–slip zones. Notably, the inclusion of surface effects is found to reduce maximum stress and subsidence while inducing a shift of the stick region towards the rolling direction. The parametric exploration of graded coating properties also offers insights into tailoring nanocontact responses for gradient nanostructures.

Grain boundaries (GBs) significantly affect the mechanical properties of metals and alloys. In this study, we investigated using molecular dynamic simulations the migration behavior of Σ25 (710), Σ5 (310), and Σ37 (750) [001] symmetric tilt GBs in CoCrCuFeNi multi-principal element alloy (MPEA) and Cu samples subjected to shear deformation. In Cu, the migration of the GBs exhibits a coupled migration pattern, consistent with the Cahn model; while in MPEA, the migration pattern varies with GB angle and temperature. Both Σ25 (710) and Σ37 (750) GBs, along with higher temperatures, induce GB roughening and continuous migration in the MPEA samples. Further investigation to the effects of GB angle and temperature was conducted through microstructure evolution tracing and quantitative analysis. A model was developed to describe the temperature-dependent continuous GB migration and average flow stress in MPEA samples with Σ25 (710) or Σ37 (750) GBs. This work can help understand the mechanical behavior of GB in MPEA and provide valuable insights for the development of high-performance materials.

This article investigated the impact of intergranular hydride precipitation on the mechanical behavior of zirconium (Zr) bi-crystals using molecular dynamics (MD)-based simulations. Uniaxial tensile tests were conducted to explore the effects of hydride precipitation on symmetric and asymmetrical tilt grain boundaries (GBs) of Zr with [0 $\bar{1}$ 10] as the tilt axis. The stress-strain curves and deformation governing mechanism of bi-crystalline Zr were analyzed using the MD-based simulations in conjunction with the COMB force field. Misfit stress and tensile stress degradation induced by hydride precipitation were evaluated to understand their correlation with GB misorientation angles. Hydride precipitation induced the residual stresses in the vicinity of GB plane and mitigates the overall mechanical properties. It was predicted from the simulations that GBs with low misfit stress develop a lower mismatch between the lattice of Zr and hydride precipitate. Consequently, the effect of hydride on the tensile strength gets nullify. In contrast, the effects of hydrides are more pronounced on the tensile strength of Zr containing low-energy GBs in conjunction with high-misfit stress. The study further reveals that intergranular hydride precipitation causes the hydride embrittlement effect in Zr bicrystals, which intensifies with large size hydride precipitate. These findings contribute to an atomistic-level understanding of intergranular hydride-induced embrittlement and its correlation with Zr grain boundary orientation.

This study presents an innovative analytical model to estimate the overall energy dissipation in damped Euler–Bernoulli beams with uniform and non-uniform (stepped) cross-sections. The novelty lies in proposing a closed-form expression for an envelope function that closely matches the energy dissipation profile obtained from the time-domain response. Importantly, the study unveils a non-intuitive finding, which states that the rate of energy decay predominantly depends on the configuration (orientation) of the stepped beam. Both strain rate-dependent viscous damping and velocity-dependent viscous damping components are considered in the governing equations. An analytical formulation is developed to obtain the wave-number-dependent damped frequencies and damping ratios using the free-wave approach. The coefficient of energy decay, governing the envelope function, is expressed in terms of the damping ratios, natural frequencies, mode participation factors, and the ratio of flexural rigidities. Moreover, this study presents the experimental validation of the analytical formulation by estimating the settling times from free vibration tests on 3D-printed stepped beams with different configurations and further quantifies the damping coefficients of the stepped beam by applying the nonlinear least squares method to fit the peaks in the experimentally acquired acceleration response. The close agreement between analytical and experimental results establishes the accuracy and applicability of the proposed model for transient vibration mitigation.

Assessing the collective impacts of external loading and void pressure on the mechanical behavior of porous media presents a significant challenge due to its inherent heterogeneity and complex multi-physical field coupling mechanisms. This study addresses this challenge by developing a novel multiscale hydraulic-mechanical modeling framework to investigate the structural response of water-saturated asphalt pavement under sequential coupling hydro-mechanical loading. The framework comprises three key components. Firstly, incorporating an upscaling homogenization approach to establish the linkage of material properties between different scales; secondly, developing a downscaling transfer procedure to transfer the structural response across scales for insight into its multiphysics mechanisms; and finally, proposing a new sequential coupling algorithm in multiscale simulations for comprehensive multi-field coupling calculations. The primary outcomes of this study demonstrate that asphalt concrete (AC)-graded pavements are susceptible to “down-top” cracks under hydro-mechanical loading, while open graded friction course (OGFC)-graded pavements have the potential to develop both “top-down” and “down-top” cracks. In AC-graded pavements, increasing the hydraulic head reduces stress concentrations, while in OGFC-graded pavements, changes in the permeability coefficient have a lesser impact on mechanical response. At the mesoscopic level, tensile stress concentrations in the asphalt mortar decrease significantly at higher temperatures. Furthermore, the OGFC-graded RVE model exhibits higher tensile stresses in the asphalt mortar compared to the AC-graded RVE model.

A computational homogenization analysis is performed on three-dimensional representative volume elements (RVE) that contain two distinct populations of voids, to demonstrate the influence of the interaction between cavities. RVEs are constructed as cubic elastic perfectly-plastic matrices embedding two families of spherical voids, and subjected to dynamic loading under homogeneous kinematic boundary conditions. Multiple microstructure models are considered by varying the number, position, and size of voids to evaluate the micro-inertia contribution to the overall macroscopic stress. Velocity fields within numerical RVEs are investigated to reveal the interaction of voids and their key role in the dynamic macroscopic response of the porous material. Based on numerical simulation results, a homogenization analytical model considering void interaction is proposed to describe the mechanical behavior under dynamic loadings. This model relies on adjusting the strain rate level at the boundary of unit cells composing the porous material. Comparison between our numerical and analytical results with those obtained using the classical Taylor homogenization scheme highlights the limitations of the Taylor model in the case of porous materials under dynamic loading.

We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our approach is based on the Phase-Field Crystal (PFC) model, which describes the microscopic atomic density in crystals at diffusive timescales, naturally encoding elasticity and plasticity effects. In its amplitude expansion (APFC), a coarse-grained description of the mechanical properties of crystals is achieved. We introduce surface PFC and surface APFC models in a convenient height-function formulation encoding deformation in the normal direction. This framework is proven consistent with classical aspects of strain-induced buckling, defect nucleation on deformed surfaces, and out-of-plane relaxation near dislocations. In particular, we benchmark and discuss the results of numerical simulations by looking at the continuum limit for buckling under uniaxial compression and at evidence from microscopic models for deformation at defects and defect arrangements, demonstrating the scale-bridging capabilities of the proposed framework. Results concerning the interplay between lattice distortion at dislocations and out-of-plane deformation are also illustrated by looking at the annihilation of dislocation dipoles and systems hosting many dislocations. With the novel formulation proposed here, and its assessment with established approaches, we envision applications to multiscale investigations of crystalline order on deformable surfaces.

Piezoelectric metamaterials are a class of composite structural materials with a piezoelectric effect that achieve efficient coupling between electrical and mechanical energy through their unique microscopic design. Typically, the tailoring of cellular architectures paves the way for unlocking the potential to achieve unprecedentedly designed materials with specific properties. We have developed three different inverse design frameworks for metamaterials, using deep learning (DL) techniques and underpinned by Bayesian optimisation. These frameworks reveal precise one-to-many correlations between material properties and geometric parameters within the triple periodic minimal surface (TPMS) piezoelectric metamaterial. For the first time, we have introduced the Progressive Latin Hypercube Sampling (PLHS) method to the inverse design process of metamaterials, highlighting the effectiveness of uniform sampling to improve the efficiency of deep learning models. The conditional variational autoencoder (cVAE), the conditional generative adversarial network (cGAN) and the multilayer perceptron (MLP) are studied for comparative analysis. All three models incorporate an inverse design network and a feature predictor to construct a continuous latent representation of a large number of hybrid TPMS (H-TPMS). After extensive training, the models can generate various piezoelectric porous structures that accurately meet the required material property parameters. Our results demonstrate the high accuracy of cVAE in inverse design, with 98.92% agreement for piezoelectric values and 96.44% agreement for mechanical properties. The three inverse design frameworks show different generalisation capabilities, with cVAE performing best. This study thoroughly analyses the strengths and limitations of each model, providing valuable insights for researchers seeking inverse design recommendations.

A mathematical model for buckling analysis during the first lithiation of cylindrical crystalline silicon (c-Si) anode particles is presented using the finite deformation framework. A reaction–diffusion model that incorporates a reversible alloying–dealloying reaction (ADR) captures the lithiation in the expanding amorphous zone, while an addition reaction models the dynamics of the crystalline-amorphous silicon interface. A “movable” lithium part and an “immovable” lithium part make up the full lithium. In sharp contrast to the case of amorphous silicon (a-Si), the axial force evolution in c-Si is found to show two different peaks during the initial and final stages of lithiation, respectively. These peaks form the basis of two different buckling criteria, which, in turn, are shown to be sensitively influenced by the influx of lithium and a crucial size-dependent parameter. This framework gives an insight towards investigating the buckling phenomena for lithiation with an evolving amorphous silicon zone due to the interface movement, which is still absent in the present literature. Additionally, the present model enables us to obtain a quantitative and mechanistic insight into and capture the previous experimental observation that the mechanical stability of a cylindrical silicon particle may be improved by maintaining a crystalline silicon core inside the amorphous shell through controlled first lithiation. It is shown that such a crystalline-amorphous core–shell structure can be advantageous to more complicated designs involving carbon fiber as the core. It is thus hoped that this model will contribute towards improving the theoretical underpinnings of an improved design of mechanically robust electrodes for next-generation batteries.

The particle size effect on the overall thermoelastic behavior of a composite containing many identical spherical particles reduces with the specimen-particle size ratio (SPR). When SPR is large enough, the effective stiffness converges, and the homogenized properties can represent the composite. This paper addresses two challenging questions: How large of an SPR is enough to reach the convergent results for different loading conditions, and whether is the critical SPR obtained from a uniform loading condition applicable to a nonuniform loading condition? When a uniform load is applied to a composite beam, the elastic moduli and thermal expansion coefficients can be calculated from the material’s response. When the beam is subjected to pure or thermal bending, the deflection can be predicted by the heterogeneous or homogenized beams. The inclusion-based boundary element method (iBEM) is developed for high-fidelity simulation of many-particle systems. Given a volume fraction of particles, particle and beam size, and beam geometry, the local fields and the effective deformation are calculated for uniform and nonuniform loading conditions. The comparative study between a homogenized beam by the micromechanical approach and the numerical simulation of the heterogeneous particle system shows that a much larger SPR is required for thermal bending to reach a convergent result between the heterogeneous and homogenized beam. When the SPR is moderate, a cross-scale modeling method shall replace the micromechanical modeling to achieve accurate results.