Acta Mechanica最新文献

Microring gyroscopes are promising candidates for inertial navigation systems due to their exceptional performance, robustness in harsh environments, and relatively low cost, which makes them well suited for applications such as self-driving car navigation systems. Previous models of ring gyroscopes often relied on the assumed mode method and low-order multi-elements finite element analysis (FEA) to predict gyroscope performance, while simplifying the geometry for ease of computation. In this paper, a modeling approach that uses higher-order curved beam finite elements is proposed. This approach leads to a clear relation between the gyroscope’s dynamic performance and its geometric parameters. Consequently, this approach allows the gyroscope designer to decide the performance of the gyroscope by using one geometric parameter and it leaves a room for him to select material properties and other dimensions based on other design considerations. The dynamic performance is measured by the scale factor, which is directly proportional to the Coriolis constant. The proposed approach is validated by comparing its results with finite element simulation software, demonstrating an estimation error of less than 5% over a specific design range. The proposed method not only improves the accuracy of gyroscope modeling but also offers a straightforward approach to modeling more complex gyroscopes, such as multi-ring gyroscopes, without significantly increasing formulation complexity.

It is known that inserting the position vector ({x}) into the divergence theorem yields simple expression for the volume integral, and leads to the possibility to evaluate the expression by integration over the surface. This can be applied for providing the volume or the center of a volume as well, which is identical to the entire mass or the center of mass for constant density of a material body. It is shown that the entire idea can be extended to the calculation of the mass moment of inertia tensor. As a side product, the area moment of inertia tensor is discussed as well. All expressions are developed in a coordinate-free representation. Using, for example, triangulation techniques, simplified approaches can be derived for nearly arbitrary volumes and areas. Thus, the numerical treatment on the basis of triangulation is provided as well. Examples and coding will demonstrate the outcome of the results indicating a simple implementation. However, an inherent consequence of the discretization is the emergence of non-symmetric inertia tensors. This issue is discussed as well.

Since thermoelastic damping (TED) plays a pivotal role in miniature structural elements, accurate simulation of this thermomechanical behavior can significantly ameliorate their functionality. A key aspect of precisely modeling the thermoelastic performance of small-scale structures is incorporating the impact of size in both mechanical and thermal analyses. In this work, the nonlocal theory (NT) and the nonlocal dual-phase-lag (NDPL) heat transfer model are utilized to develop a new size-sensitive formulation for TED in ultra-small rotating rectangular cross-sectional rings. To accomplish this, the governing equations for motion and heat transfer are derived in the first place according to the NT and NDPL model. Following this, the complex frequency (CF) approach is applied to define damping, leading to a single-term formula for TED. The numerical analysis includes multiple cases to appraise the effects of key parameters, particularly the scale factors in the NT and NDPL model, on TED. Results suggest that the NT and NDPL model have a crucial role in determining TED, particularly when the ring’s size approaches the structural or thermal characteristic lengths, making this influence undeniable.

In this work, an attempt is made for the first time to present the axial vibration of non-local rods made of a polymer matrix reinforced with short fibers under the influence of a magnetic field and an elastic medium. This paper examines the influences of small-scale based on the non-local theory and a transverse magnetic field on free axial vibration of short-fiber-reinforced nanorods embedded in an elastic medium for the first time in the literature and prefers the finite element method. Using the Lorentz magnetic force derived from Maxwell’s relation, the equation of motion for the non-local axial vibration of the short-fiber-reinforced nanorods subjected to the transverse magnetic field and embedded in an elastic medium is constituted. Then, a size-dependent finite element formulation of embedded and magnetically affected short-fiber-reinforced nanorods is posed based on the weighted residual method. The dimensionless frequencies of clamped–clamped and clamped-free embedded short-fiber-reinforced nanorods are calculated by using the finite element method based on various arguments such as mode number, fiber properties, non-local parameter, magnetic parameter, magnetic field strengths’ ratio and elastic medium. The changes in frequencies due to the effects of these arguments are presented with a number of figures and tables and a detailed discussion is carried out.

This study proposes a novel computational method, the plane wave expansion/finite element (PWE/FE) method, to solve the governing equations of PC beams under multi-physics field coupling across multiple scales. The proposed method integrates the theoretical foundations of the plane wave expansion and finite element methods, exploiting the structural periodicity to decompose the displacement field. By incorporating Bloch's theorem, the approach is implemented using the partial differential equation module in COMSOL Multiphysics 6.2, a widely used finite element software. Rigorous validation through comparative numerical simulations and experimental measurements confirms the method's accuracy. By way of example analysis, it is found that an increase of one order of magnitude in the height of the beam will correspondingly increase the frequency band where the bandgap is located by one order of magnitude, and the applied voltage required to change the bandgap frequency band needs to be increased by several orders of magnitude. The PWE/FE analysis reveals significant dependencies of bandgap properties in piezoelectric PC and nanoscale PC structures on three key factors: piezoelectric coupling coefficients, size-dependent effects at the nanoscale and dimensional parameters.

We investigate the propagation behavior of Rayleigh waves in a composite system composed of nonlocal micropolar thermoelastic materials. The structure under study consists of an initially stressed, rotating, nonlocal transversely isotropic micropolar thermoelastic layer placed over a similar rotating half-space. Our theoretical formulation is grounded in nonlocal elasticity theory combined with micropolar thermoelasticity utilizing both the Lord–Shulman (L–S) and Green-–Lindsay (G–L) generalized thermoelastic models. We derive the constitutive and governing equations leading to a closed-form expression for the Rayleigh wave dispersion equation. To solve the resulting seventh-order secular equation we develop a robust numerical scheme involving initial root estimation, convergence enforcement and stability checks to ensure accurate computation of phase velocities. The model is validated with the pre-established results under both L–S and G–L theories. Numerical results reveal the effects of nonlocality, initial stress, rotation and layer thickness on phase velocity, attenuation and specific loss. Graphical analyses demonstrate the strong dependence of wave characteristics on these parameters providing deeper insight into Rayleigh wave behavior in advanced anisotropic thermoelastic media with implications for geophysical exploration and high-performance engineering applications.

Power-law creep, where the creep strain rate follows a power-law relationship with time, is ubiquitous in crystalline materials. However, this behavior typically exhibits multi-stage characteristics in amorphous materials due to the intrinsic structural and dynamic heterogeneity. In this study, we systematically performed high-temperature creep experiments on a Pd₂₀Pt₂₀Cu₂₀Ni₂₀P₂₀ metallic glass. It is found each stage in multi-stage creep is governed by different deformation mechanisms, influenced by factors such as temperature, stress, and structural relaxation. Experimental results indicate that increasing temperature causes the power-law creep behavior to change from two stages to three stages, while increasing stress does not alter this behavior. After cyclic creep, the power-law creep behavior reverts from three stages to two stages. Based on the quasi-point defect theory, we propose a creep constitutive model that includes the contribution of structural relaxation to creep behavior in the generic metastable materials. Theoretical modelings show creep response is primarily driven by two deformation mechanisms: the activation of inherent deformation units (shear microdomains), which dominate the early stage of creep; and the mechanism related to structural relaxation, with atomic correlations significantly influenced by temperature and aging conditions. The constitutive model reveals the factors influencing the power-law creep and clarifies the intrinsic mechanism underlying the transition from two stages to three stages. These mechanisms align with the thermal and mechanical effects observed in the experiments.

Harmonicity principle is a strategy of reducing stress concentration around holes or inclusions in an elastic solid for given external far-field loading, and the use of this principle would lead to optimal shapes of the holes or inclusions that minimize the stress concentration in the solid in certain common situations (such shapes are commonly referred to as ‘harmonic shapes’). In this paper, we follow this principle and focus on identifying the harmonic shape of a macroscale fluid inclusion embedded in a soft elastic solid under plane deformation for a remote biaxial loading. Considering that the soft solid usually undergoes relatively large deformations and therefore the fluid pressure-induced traction acting on the surrounding solid would experience a directional change during deformation, we particularly incorporate such a directional change in the identification of the harmonic shape of the inclusion. We show that as opposed to the classical harmonic shape for a fluid inclusion (corresponding to the case in which the surrounding solid is relatively stiff and the directional change in the fluid pressure-induced traction during deformation is neglected), the modified harmonic shape identified here remains still elliptical but occupies a different aspect ratio. Basically, the modified harmonic shape features its dependence on the magnitude of the remote loading for a fixed ratio between the two components of the loading. We input the classical and modified harmonic shapes, respectively, into the large-deformation finite element model of a fluid inclusion in a soft hyperelastic Neo-Hookean solid, and confirm from the numerical simulations that the modified harmonic shape is indeed more accurate than the classical counterpart in meeting the initial harmonicity principle. We present also a few numerical examples to illustrate the differences between the current modified solution and the classical counterpart in determining the aspect ratio of the harmonic shape as well as corresponding internal pressure.

Impact-contact events can significantly degrade structural integrity, making it important to evaluate how protective structures respond under such conditions. This study illustrates a novel boundary element method (BEM) for analysing the elastodynamic behaviour of cellular structures subjected to low-velocity impact. The proposed method builds on the conventional BEM for solving the transient analysis of anisotropic elastic materials in two dimensions and the contact constraint relations of elastodynamic impact-contact problems. By leveraging these relations, the impact-contact BEM can accommodate various impact-contact situations, e.g. when the indentation depth is prescribed and the initial velocity is given. Previous studies demonstrated that bone-inspired cellular structures (BCS) have superior mechanical performances and higher impact resistance than conventional honeycomb and auxetic structures. This paper further investigates the impact-contact behaviour of BCS materials under impact-contact conditions. The reliability and applicability of the proposed method are validated through comparisons with results obtained using the finite element method (FEM) in a commercial software. With the provided numerical results, the parametric studies of BCS under impact loads are further studied and discussed. These provide valuable insights and help deepen our understanding of the elastodynamic impact-contact responses of BCS under impact-contact situations.

Dual-phase (DP) steels, characterized by a ferrite/martensite microstructure, have garnered significant industrial attention due to their superior mechanical properties. This study develops a crystal plasticity (CP) model for DP steels, incorporating ferrite grain boundaries (GBs) and ferrite/martensite phase boundaries (PBs). The GBs and PBs are characterized by introducing a relationship between plastic shear rate and slip resistance. Utilizing real microstructures of DP steels, the study investigates the influence of GBs and PBs on the work-hardening behavior of DP steel samples with varying compositions and heat treatment processes during loading. CP models for nanopolycrystalline DP steels with grain sizes of 80, 200, 300, and 500 nm, as well as DP steels with PB percentages of 3.2%, 5.3%, 8.6%, and 14%, are established to systematically study the strengthening mechanisms of GBs and PBs. The results demonstrate that the consideration of GBs and PBs enhances the accuracy of the CP model in predicting stress–strain responses. Defects arising from the GBs and PBs improve the material’s resistance to deformation. High-stress fields tend to form at the intersection of homophase and heterophase boundaries due to microstructural differences. Under different grain size conditions, the strengthening effects of GBs and PBs exhibit a superposition effect, with the strengthening effect of GBs being more pronounced than that of PBs. Furthermore, during plastic deformation, PBs absorb more strain energy, modulating the macromechanical properties of DP steel by locally storing and subsequently releasing energy into phases with a higher elasticity modulus.