Acta Mechanica最新文献

Unconventional elastoplasticity models, whether in small strain or finite strain regimes, have been developed to accurately depict material responses under diverse loading conditions. Due to the unrealistic and unphysical predictions of certain existing models in such scenarios, the proposing and refining of time integration schemes becomes imperative. This paper introduces a novel numerical implementation for the subloading surface model, an unconventional approach, within the framework of finite strain elastoplasticity. The proposed method is based on intermediate configurations in hyperelastoplasticity, utilizing dual multiplicative decompositions. Additionally, detailed calculations of partial derivatives, which are essential for the time integration scheme, are provided. Compared to recently published papers, the proposed time integration scheme is simpler in terms of the number of equations, unknown variables, and partial derivatives. The implementation is demonstrated through the solution of simple shear and tension/compression deformations, incorporating kinematic and combined hardenings for various materials including metals and polymers. Results are compared with available data from literature and experimental findings. The presented examples demonstrate a good agreement between the results under different conditions.

This paper presents a novel model for analyzing the behavior of a generalized photo-microelongated thermoelastic semiconductor system that incorporates hydrodynamic and poroelastic effects. Motivated by the need to understand semiconductor dynamics under coupled mechanical, thermal, and photonic stimuli for advanced technological applications, the study develops a one-dimensional (1D) framework using Laplace transformation to derive analytical solutions. Numerical computations and graphical representations illustrate the evolution of critical physical quantities such as carrier density, temperature distribution, displacement, pore water pressure, and stress functions, emphasizing the influence of time progression, relaxation parameters, and microelongation effects. The results highlight the unique contributions of hydrodynamic and poroelastic interactions, providing insights into semiconductor behavior at microscales. This comprehensive analysis advances the understanding of semiconductor materials, offering potential applications in photonic devices, energy systems, and thermal management technologies while providing a theoretical framework to predict material behavior under diverse external stimuli, minimizing the need for costly experiments.

Piezoelectric materials have been extensively used as energy collector due to their excellent character of environmental vibration energy conversion. However, the existing piezoelectric energy collector model is not suitable for complex multi-layered beam structures. The objective of this paper is to explore the dynamic response and piezoelectric patch energy harvesting of four-layered beams with single unimorph piezoelectric patch subjected to multiple moving loads, and the governing equations are derived by using Hamilton’s principle. The effects of structural lamina parameters and piezoelectric patch parameters of four-layered beams with single piezoelectric patch on dynamic response and optimal energy harvesting are investigated. A detailed parametric analysis of the structural lamina and piezoelectric patch of the four-layered beam model is conducted, and the optimality of energy harvesting parameters of the layered beam is discussed. It is found that the dynamic central deflection of layered beam and output voltage are quite related to the geometrical and physical parameters of each functional layer including the fiber orientation angles. The dynamic central deflection of layered beam is not sensitive to the piezoelectric patch, and so it is suitable of introducing the piezoelectric patch to produce the electric power. The optimum energy harvesting efficiency of the layered beam is also discussed in detail.

This paper intends to explore the effects of cracks characteristics on free vibration behavior of functionally graded plates and shells by means of Lagrangian formulation in conjunction with the variational principle on the basis of three-dimensional theory of elasticity. The discretization of the equation of motion is achieved by using a four-noded 3D tetrahedral finite element taking into account the normal component of the displacement field in the thickness direction. The material properties of the plates and shells are assumed to vary continuously and smoothly in the thickness direction according to a general four-parameter power-law distributions in terms of volume fractions of the constituents. The consistency and reliability of the present formulation is demonstrated through several numerical tests, by comparing the obtained natural frequencies with the existing results from the literature. Three numerical examples, including the vibrational response of functionally graded rectangular and annular plates, as well as, cylindrical shells under different crack positions, orientations and lengths are studied and presented. Parametric studies on crack characteristics, geometric and material parameters are explored in deep. It was demonstrated that the crack orientation, length and positions, additionally to material characteristics of FGM structures have a significant impact on vibrational behavior of cracked FGM plates and shells, which must be considered in the structural design and performance of functionally graded plates and shells.

Wave propagation through a saturated frozen soil layer sandwiched by two elastic soil half-spaces is investigated in this paper. The saturated frozen soil layer in the middle consists of a saturated three-phase medium of solid, liquid and ice, which is considered isotropic. Due to the presence of the three-phase medium, three types of longitudinal waves and two types of shear waves exist in saturated frozen soil. The concept of state vector is introduced. The state transition differential equation is derived based on the reduction of order of the motion equations, and the state transfer matrix is obtained by solving the state transition differential equation. By introducing the interface conditions between saturated frozen soil and elastic soil, the state transition matrix is simplified, and redundant state vectors are eliminated to establish the relationship between the incident wave, reflection wave and transmission wave. Two cases (incident P wave and incident SV wave) are considered, and the reflection and transmission amplitude ratios varying with the incident angle are calculated. The results indicate that the incident wave frequency, porosity, saturation and cementation parameters have a substantial influence on the reflection and transmission. This study provides a new research perspective for controlling the propagation of elastic waves in saturated frozen soils.

The same axis of rotation can be defined in different coordinate systems, leading to different form and different interpretation of the rotation matrix. This definition is particularly important in case of successive rotations due to the wide use of finite orientation parameters to define rigid- and flexible-body kinematics as well as deformation measures. As discussed in this paper, in case of successive rotations, the rotation axes can be defined using a single frame or multiple intermediate frames. As it is known, the single-frame method (SFM) and multi-frame method (MFM) lead to different order of multiplication of the rotation matrices. It is demonstrated that the coordinate system in which the rotation axis is defined determines the physical interpretation of the rotation matrix and deformation measures. In the SFM approach, the single frame can be global, cross section, or body frame. Nonetheless, the SFM sequence does not allow easy interpretation of the rotations as torsion and/or bending measures. In the MFM approach, on the other hand, the rotations are defined relative to intermediate frames; and such relative rotations can only be given physical interpretation as deformation measures in case of infinitesimal rotations. Such a physical interpretation is not valid in case of using noncommutative finite rotations. Regardless of which method (SFM or MFM) is used, the sequence of rotations cannot, in general, be reversed. Using Rodrigues formula with the analysis and results of this study, it is demonstrated that the noncommutativity problem is not attributed to the choice of the spatial orientation parameters but to the noncommutativity of the rotation matrices.

Based on the strong form of three-dimensional (3D) consistent couple stress theory (CCST), we develop a meshless differential reproducing kernel (DRK) point method for the static instability and free vibration behavior analyses of a one-directional nonhomogeneous microplate under simply supported conditions and subjected to uni- and bi-axial compression. By selecting the transverse stress and displacement components as primary variables and employing the double Fourier series expansion method, we obtain a set of Fundamental equations expressed in the thickness coordinate to address this issue. By incorporating the DRK interpolants into the Fundamental equations, we develop a meshless point method for analyzing the 3D size-dependent static instability and free vibration behaviors of the microplate. The accuracy and convergence rate of the meshless DRK point method are validated by comparing the solutions it produced with those obtained using a 3D approach documented in the Literature. The results demonstrate that the solutions obtained using our meshless DRK point method align excellently with the corresponding 3D solutions and converge rapidly. The effects of the aspect ratio, material length-scale parameter, length-to-thickness ratio, and inhomogeneity index are demonstrated to have a significant impact on the microplate’s natural frequency and critical load. Furthermore, the applicable range of the structure size for the CCST is recommended to be between 1× 10^–7 and 1 × 10^–3 m.

The backward-facing step (BFS) is an appropriate model for studying flow separation. In this study, controlling separation bubbles behind a curved edge BFS with plasma actuators was investigated experimentally in Reynolds numbers ranging from 17 × 10³ to 51 × 10³ (depending on step height). Smoke flow visualization experiments were conducted to analyze the flow pattern around a BFS in the presence of a plasma actuator. Pressure distributions were measured under a variety of situations and analyzed. Seven curved edges were created, with a radius of curvature ranging from 0 (a sharp edge) to 50 mm. The results reveal that the length of the separation bubble decreases as the radius of curvature increases. Another series of experiments were carried out for bigger radius of curvature, studying the location of the placed plasma. The location varies when the angle with respect to the center of curvature changes. Plasma actuators were mounted on the curvature at two different angles (0 and 20 degrees). Both plasma actuators were utilized simultaneously at angles of 0 and 20 degrees. The best results were obtained by putting two plasma actuators on curvature at the same moment, which results in lowering reattachment length. The separation bubble's length was also lowered by using a plasma actuator at a 20-degree angle according to the center of the radius of curvature.

This work aims to generalize the method of conditional moments (MCM), a statistical approach developed for classical elasticity, to the case of strain gradient elasticity and to evaluate the effective properties of random particulate composites within the simplified strain gradient elasticity theory. The problem of finding the effective constants is reduced to a system of stochastic differential equations based on the fundamental equations of linear elasticity, which are solved by the method of conditional moment functions. Closed-form expressions for the effective moduli of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities are derived. The effective properties obtained within strain gradient elasticity depend not only on the properties of constituents, their volume fraction, shape, and distribution of inhomogeneities, but also on their size, which is impossible in the frame of usual classical elasticity. As a numerical example, it is considered a special case of a composite with an isotropic matrix and randomly distributed spherical inhomogeneities, where the materials of the matrix and the inhomogeneities are second gradient media. Variation of the normalized bulk and shear moduli of the particulate composite material as a function of volume fraction of inhomogeneity and as a function of inhomogeneity size is evaluated, analyzed, and compared in the context of other theoretical predictions.