Mechanics of Solids最新文献

This study examines the mechanical behavior of ultra-high-molecular-weight polyethylene (UHMWPE) under three-point bending at a low strain rate, with a particular focus on evaluating the influence of its distinct tensile and compressive properties on its bending response through finite element analysis. The tensile and compressive stress-strain characteristics of UHMWPE were experimentally determined at a strain rate of 5 × 10⁻³ s^–1, complemented by three-point bending tests conducted at a constant loading speed of 0.05 mm/s. To predict the flexural behavior of UHMWPE, two finite element models were constructed using the SAMP-1 material model in LS-DYNA: one incorporating the Von-Mises yield surface, which assumes similar material behavior in tension and compression, and the other employing the Drucker-Prager yield surface, which accounts for dissimilar material behaviors between tension and compression. Results of the numerical analyses revealed substantial discrepancies between the predictions of the Von-Mises and Drucker-Prager models, with the latter offering a more precise prediction of the flexural response of UHMWPE, thereby underscoring the critical importance of accounting for dissimilar material behaviors to achieve enhanced predictive accuracy.

Recently, there has been a significant increase in the interest of researchers to application of strong pulsed electromagnetic field for healing both macrocracks and microdefects in metallic materials. The healing here is meant as the restoration of the continuity of the material by joining (welding) the edges of cracks (both macro- and micro-sizes). Complete healing of cracks by exposure to the pulsed electromagnetic field is a very complex task, and the choice of the electric pulse action mode that leads to full healing of specific cracks in the samples is of a purely experience based. At the same time, different researchers for healing similar macrocracks in the same metal often use the pulse parameters, such as the maximum induced current density and pulse duration – differing by several orders of magnitude. It is because of such excessively wide range of the pulsed electromagnetic field effects, the results of experimental observations of macrocracks healing phenomenon in plates and strips do vary a lot, and also the discussions occur regarding the mechanism of such healing. In addition, the selection of the optimal mode of electric pulse action if made purely empirically – by the method of successive approximations, is very tedious and ineffective. In the present work, based on a simple analytical model, an attempt is made to limit the above-mentioned very wide range of modes of current pulses on macrocracks in plates and strips, as well as on internal microdefects in the material, which still would lead to their healing. In the proposed range of modes, we propose to select rather not the several parameters of the pulse, as was done previously, but selecting just one – the specific electromagnetic energy dissipated in the material at one pulse (energy of the pulse). The value of this energy depends on the physical properties of the material and on the electromagnetic energy intensity factor at the crack tip. The energy intensity factor concentration coefficient turns out to depend only on the geometry of the crack and the sample (or the mutual arrangement of microcracks in it). The obtained dependence is proposed to be used to adjust the pulse parameters in the process of crack healing (reducing its length or increasing the radius of curvature at the tip or the distance to the free boundary). Thus, using this dependence, it is possible to set the optimal mode of electric pulse action. Comparison of analytical estimates with experimental data for cracks in metals and alloys confirms the validity of the assumptions made in the model, as well as the possibility of further development and practical application of the proposed approach.

This study investigates the propagation of Love-type waves in a piezoelectric layer and non-local elastic orthotropic layer resting on a microstructural couple-stressed half-space. Analytical solutions to the governing equations yield mechanical displacement and stress components. By applying relevant boundary conditions, dispersion equations for Love-type wave propagation are derived. Special cases are compared to the classical Love-type wave dispersion equation to validate the results. Numerical simulations and graphical illustrations demonstrate the significant influence of nonlocal elasticity, initial stress, piezoelectric constant, dielectric constant, thickness ratio, couple tension, and imperfection parameters on Love-type wave phase velocity, considering perfect and imperfect interfaces under electrically short conditions. This research provides valuable insights for designing efficient piezoelectric devices, sensors, and energy harvesting systems.

The paper considers a mathematical model of stress distribution in the yeilding zone near the tip of a normal tensile crack (mode I crack) in a perfectly plastic solid under plane stress conditions. The von Mises yield criterion is adopted. Based on the formal statics formularion of the problem (indepentently of kinematical equations), exact formulas are obtained for calculating stresses within the plastic zone localized near the tip of the crack. A comparison of the exact results obtained in the article with the results of a numerical analysis of stress distribution given by Hutchinson in 1968 is presented.

In the present paper, harmonic waves propagating in 3D isotropic viscoelastic media are analyzed using the fractional derivative Scott-Blair model, Kelvin-Voigt model, Maxwell model and standard linear solid model. It is known that only the first and second Lamé constants, or the bulk and shear moduli, appear in Hooke’s law for three-dimensional media, but not Young’s modulus or Poisson’s ratio. This indicates that the bulk and Lamé operators are the most intrinsic operators to express stress in terms of strain when studying wave propagation in 3D viscoelastic media. That is why in the present paper, the emphasis is made on the comprehensive analysis of time-dependent operators for Lamé parameters. In so doing, the fractional derivative models are utilized for defining the time-dependent modulus of the P-wave, which governs the velocity of the longitudinal wave. Asymptotic values of the wave velocities, their coefficients of attenuation and logarithmic decrements have been found for the case of absence of bulk relaxation.

Predicting the formation of shear bands is important for understanding the damage mechanisms of sands. Whereas the accuracy of strain localization predictions strongly relies on the selection of the constitutive model. In this paper, the generalized non-coaxial plastic flow theory proposed by Hashiguchi is firstly used to release the coaxiality limitation of the three-dimensional state-dependent dilatancy model of sand, and to establish the non-coaxial constitutive model of sand. In order to further accurately describe the characterization of the strength of the sand as a function of the angle of deposition (direction of principal stresses), the original anisotropic state variables were corrected using an interpolating function. After that, a series of plane strain simulations were carried out for Toyoura sands under different depositional angles and confining pressures. The results show that the established constitutive model can accurately capture the stress-strain relationship before bifurcation, reflect the variation pattern of the peak stress ratio of the sand with the deposition angle, and substantially improve the prediction of the bifurcation axial strain and the shear band inclination. On the other hand, it is proved by mathematical derivation that the non-coaxial stress rate tangent to the yield surface in the deviatoric plane is essentially composed of four orthogonal stress rate components.

The article is devoted to the design of an equi-strength rotating cylinder under conditions of plane or generalized plane strain. Both solid and hollow cylinders are investigated. The problem statement is based on the equations of the linear theory of elasticity. The lateral surfaces of the cylinder are assumed to be traction-free. It is supposed that Young’s modulus is an unknown function of the radial coordinate, and the other physical and mechanical parameters of the material are constant. The dependencies of Young’s modulus are established, at which the desired stress state is achieved in the cylinder. As such a state, a constant hoop stress, a constant difference between the hoop and radial stress, and a constant linear combination of the hoop and radial stresses are considered.

A numerical method for calculating the relaxation of residual stresses in a solid cylinder with a series of periodically located semicircular notches after advanced surface plastic hardening under creep conditions during thermal exposure has been developed and implemented based on the finite element method. The capabilities of the method and the results of its application are illustrated on surface-hardened cylinders made of EI698 alloy with a radius of 3.76 mm and a single notch of radius 0.1; 0.3; 0.5} mm and a series of 3, 5, and 7 periodically repeating notches of the same type with a radius of 0.1 and 0.3 mm. Relaxation of residual stresses for all calculation variants using the law of steady-state creep at T = 700°C on a time base of 1000 h is investigated. A comparative analysis of calculation data for a smooth cylindrical sample and cylinders with notches is performed. It is shown that when a single notch of 0.1 mm radius is applied after hardening of the cylinder, residual circumferential and axial compressive stresses along the depth from the bottom of the notch are comparable, and sometimes even higher, than for a smooth sample, and when notches are applied, the radius of which is greater than the thickness of the hardened layer, the values of these components are significantly lower. For a series of notches, the circumferential and axial residual compressive stresses are significantly reduced, decreasing nonlinearly from the extreme notches of the system to the central one. During creep during thermal exposure, relaxation of residual stresses occurs, but their value, although decreasing (in absolute value), retains a negative sign over time. This result is a positive factor in assessing the performance of surface-hardened cylinders with defects such as semicircular notches under high-temperature creep conditions. The calculation results are illustrated by numerous graphs and tabular data regarding the kinetics of residual stresses.

Challenges related to the flight safety and efficiency of supersonic aircraft call for the development of novel design concepts. To address this need, a project focused on the design of a supersonic aircraft wing is proposed. A wing based on special lattice structures is examined, and its performance is evaluated against conventional structural configuration. The analysis is supported by the sizing optimization. Various formulations of optimization problem are investigated to establish how different parameters and constraints affect the results. The effect of geometric nonlinearity is discussed for the identification of buckling modes associated with significant wing deflection. The results demonstrate that the proposed lattice structure satisfies the strength criteria based on maximum equivalent von Mises stress and exhibits higher stiffness compared to the conventional structural scheme. Moreover, the lattice configuration ensures fail-safety by localizing the damage to individual lattice cells, thereby preventing catastrophic global failure of the primary structure.

In this work, a three-dimensional (3D) finite element model is developed to investigate the coupled thermal, mechanical and the white layer formation phenomena during electromechanical treatment (EMT) of AISI 1045 annealed steel. White layer is frequently mentioned as specific kind of martensitic structure (untempered martensite). However, through SEM study it was shown that the white layer which is formed during the EMT has a nonuniform ultra-disperse structure which has nothing to do with the conventional martensite. The results of numerical based thermal analysis show that alternating current during the EMT leads to repetitive temperature variations in the surface layer. As a consequence, a regular inhomogeneous structure is formed with alternating fragments of the white layer and self-tempered zones with the initial structure. It was found that the white layer has a dominant effect on the residual stress distribution. The calculation results show that longitudinal residual stress at the surface varies depending on the white layer volume fraction. More detailed analysis indicates that the stress state close to biaxial compression is formed in the regions corresponding to white layer fragments. In the areas with a lower white layer volume fraction two principal stresses are compressive, and the last one with the highest absolute value is tensile.