Acta Mechanica最新文献

Interface cracks are an important structural defect across various engineering domains. Based on Bak’s model, this paper explores the scattering problem of an interface crack between a 1D hexagonal quasicrystals (QCs) coating and an elastic substrate under harmonic plane waves. The Fourier transform method has been used to obtain the Cauchy singular integral equations (CSIEs) of the second kind in which the unknown variables are the dislocation density functions. The Jacobi polynomials have been used to reduce the CSIE into a system of linear algebraic equations. By taking the limit of the stress field near the crack tip, dynamic stress intensity factors (DSIFs) and crack opening displacements (CODs) are obtained. Finally, numerical results investigate the DSIFs for various wave types, material combinations, crack sizes, incident angles, and coupling coefficients of the phonon-phason field. The research findings provide valuable insights into using integral equation methods to address practical engineering issues related to crack detection and prediction.

The increase of Al percentage x transforms the crystalline structure of (FeCoNiCrMn)_100-xAl_x high-entropy alloys (HEAs) from single face-centered cubic (FCC) phase to FCC + body-centered cubic (BCC) two phase, which affects subsequent mechanical properties. Therefore, it is necessary to develop a constitutive model that can establish the relationship between microstructure and macro-mechanical properties. In the current study, Mori–Tanaka homogenization method is adopted to describe the evolution of microstructure with increasing Al concentration, which assumes that BCC inhomogeneity is embedded in FCC matrix as a reinforcement phase. A dislocation density-based crystal plasticity theory is employed to simulate the plastic deformation of both FCC and BCC phases. By coupling the influence of Al concentration into the constitutive model, the model is able to predict the plastic deformation of the FCC phase. The multi-scale constitutive theory, implemented into subroutine, is applied to describe the tensile behavior of HEAs. The numerical simulation matches well with the experimental data. The proposed model can accurately predict the tensile deformation of (FeCoNiCrMn)_100-xAl_x HEAs and provide valuable theoretical guidance for optimizing the mechanical performance of HEAs by adjusting the proportion of the components.

The paper investigates models of electrostriction by following a new approach though within the basic laws of continuum mechanics. Three general requirements are considered. Firstly, in a three-dimensional setting the balance of angular momentum implies a symmetry condition for the Cauchy stress tensor, the electric field and the electric polarization. By checking the thermodynamic consistency it is observed that constitutive equations with a separate dependence on the deformation gradient and the electric field does not satisfy the symmetry condition. Instead the symmetry is shown to hold for variables involving jointly the deformation gradient and the electric field or the polarization. This scheme in turn is found to satisfy both the thermodynamic consistency and the objectivity principle. Next electrostriction is examined by determining the deformation of an isotropic elastic solid induced by an electric field. Furthermore, it is shown that a proper dependence on the polarization or on the electric field results in elongations or contractions just as it is observed in real materials.

Uncertainty propagation and quantification analysis in nonlinear systems are among the most challenging issues in engineering practice. Probabilistic analysis methods, based on the statistical information (i.e., mean and variance) of random variables, can account for uncertainties in the dynamical analysis of nonlinear systems. The statistical information of responses obtained by the Polynomial chaos expansion (PCE) method for nonlinear systems with random uncertainties deteriorates as the time history increases. Thus, the significant difficulty arises in analyzing the stochastic responses and long-term uncertainty propagation of nonlinear dynamical systems. To solve this problem, this paper proposes the PCE-HHT method by embedding a classical signal decomposition technique named Hilbert–Huang transform (HHT) in the PCE. Firstly, the HHT technique decomposes the multi-component response of a nonlinear system into a sum of several single vibration components and a trend component. Secondly, the PCE employs Hermite polynomials to approximate the instantaneous amplitudes and phases of each vibration component and the trend component, thereby establishing a coupled model of the system response, which can be used to determine the mean and variance of the dynamical response. Finally, considering parameter uncertainties in the Duffing–Van der Pol oscillator, the rigid double pendulum, and the spatially rigid-flexible crank-slider mechanism, the effectiveness of the PCE-HHT method is validated. Numerical results demonstrate that the PCE-HHT method exhibits desirable computational accuracy in the long-term random dynamical analysis of nonlinear systems.

In this study, a novel theory, called the modified nonlocal strain gradient theory, is established for the analysis of functionally graded nanoplates. This theory integrates the nonlocal effects through classical stress tensors, the deviatoric part of the symmetric couple stress tensor, dilatation gradient and deviatoric stretch gradient tensors. This combination ensures compatibility for investigating a wide range of structures, from nano- to macro-scales. Some comparative studies are performed to establish the precision and reliability of the proposed theory in specific cases. Furthermore, a massive parametric study is organized to illustrate the influence of several coefficients on the bending, free vibration and buckling behaviors of the functionally graded nanoplates. The proposed theory provides a robust theoretical foundation for future investigations into various small-scale structures situated within multi-physical environments. This establishing approach not only enhances the understanding of micro- and nanoscale mechanics but also paves the way for advanced applications in mechanical engineering.

Existing pores play a significant role in structural materials used in structural members such as plates, shells, and beams. Numerous qualities expected from structural materials involving the lightweight, high stiffness-to-weight ratio, high strength-to-weight ratio, resistance to mechanical and thermal shocks, and thermal insulation can be satisfied by setting porosity distribution from one surface to another. The porosity distribution affects the Young’s modulus, shear modulus, and mass density of the material. However, there is a lack of study on the lateral-torsional buckling (LTB) behavior of porous orthotropic thin-walled beams with I-sections. To remedy this lack, this paper aims to analyze the lateral-torsional buckling (LTB) behavior of porous orthotropic thin-walled beams with I-sections subjected to a uniformly distributed load. Young’s modulus, shear modulus, and mass density are assumed to be varied in the height direction according to four different porosity distribution patterns. The governing differential equation system of the LTB problem, including the equation of the warping effect, is developed using the Virtual work principle based on classical beam theory. Galerkin’s method and an auxiliary function of simply supported boundary conditions are employed to obtain critical LTB load formulation. Additionally, the formulation is confirmed via comparing with existing literature. A parametric study is applied to investigate the influences of porosity coefficients, porosity distribution patterns, orthotropy, slenderness ratio, and geometrical characteristics on the LTB characteristics of porous beams. Parametric study indicates that critical LTB loads of orthotropic I-beams reduce as the web depth and porosity coefficients increase, and they increase with an increase in the orthotropy ratio, flange slenderness ratio, flange-to-web thickness ratio, and span of the beam. The buckling loads of the beam with the D1 pattern are higher than its perfect (D4) counterpart, so the D1 porosity pattern is the best choice to improve the bearing capacity of orthotropic I-beams. Also, the nonuniform porosity distributions (D1 and D3) increasing from origin to flanges enhance the lateral stability of I-beams because the flange has the maximum Young’s modulus. The novelty of this study lies in its comprehensive LTB investigation of orthotropic thin-walled beams with I sections exposed to specific effects, such as porosity and warping. These effects on the structural performance are highlighted to significant insights into the porous material design to improve engineering structures’ LTB resistance. This study enhances our understanding of composite materials and their application in structural stability analysis across various engineering fields.

We employ the Stroh sextic formalism for anisotropic elasticity and Muskhelishvili’s complex variable formulation for isotropic elasticity to derive a full-field closed-form solution to the two-dimensional problem of a non-planar Zener-Stroh crack lying along the interface of a rigid elliptical inhomogeneity embedded in an infinite anisotropic elastic matrix. The rigid inhomogeneity is treated as an isotropic elastic inhomogeneity with its shear modulus approaching infinity. A real-form expression for the rigid body rotation of the rigid elliptical inhomogeneity is obtained in terms of the two Barnett-Lothe tensors H and S for the matrix by imposing the condition that tractions are continuous across the entire elliptical interface.

The objective of this research is to develop an effective model for carbon nanotubes (CNTs)-reinforced cement composites by investigating effects of different microstructures on Young’s modulus of the composites. Different types of representative volume elements (RVEs) were developed, including aligned CNTs, random CNTs, random CNTs with curvature, random CNTs with agglomeration, random CNTs with agglomeration and curvature, random CNTs considering interphase between the cement matrix and CNTs, and random CNTs with agglomeration, curvature, and void. The influence of parameters was also studied by varying one of the parameters while keeping the others constant to study their individual effect on our model. The results revealed that the most effective model of predicting experimental results is the model with curved CNTs, incorporating agglomeration and void in the RVE. Developing an effective model for the mechanical properties of nanocomposite materials can help in designing and optimizing such materials to meet the requirements of various applications.

The study of finite size stress concentration in the design and implementation of piezoelectric semiconductor devices is crucial. A symmetric collinear cracks model is established for piezoelectric semiconductor with finite thickness dimensions. Considering two boundary conditions of stress and displacement, the dislocation density functions are introduced to obtain the distribution of the stress, carrier density, current density intensity and electric displacement. Two singular integral equation systems on which the boundary value problem depends are derived and solved numerically. Expressions for stress intensity factors, current density intensity factors and energy release rates are given. The results indicate that the distribution of current density, carrier density and electric displacement are all affected by the doping concentration of piezoelectric semiconductor. Mechanical load and electric load can affect the stress intensity factor and the current density intensity factor, which reflects that the existence of mechanical load and electric load can accelerate or slow down the growth of crack.

It is well known that the Lagrange–d’Alembert and Hamilton principles, which are widely used to derive the laws of motion for nonholonomic systems, are not equivalent and that, in some cases, the equations of motion derived from them differ. The aim of this paper is to illustrate these differences by comparing the solutions of the dynamic equations derived from these principles in a simple nonholonomic system.