International Journal of Applied Mechanics

This study numerically investigated the behavior of a Newtonian droplet impacting a heated porous surface. In this regard, a two-phase finite volume code was used for laminar flow. The time adaptive method was applied to enhance the accuracy of results and better convergence of the solving process. Also, the dynamic grid adaptation technique was adopted to predict the liquid-air interface precisely. The results were first validated against experimental data at different Weber numbers. Then the effect of variations in the droplet temperature was investigated on the spreading factor. The obtained results revealed that the rise in droplet temperature led to an increase in the maximum spreading diameter due to the reduction in the effects of viscosity, density, and surface tension. In the next step, the effects of droplet impact on the hydrophilic and superhydrophobic surfaces with the porosities of 20–80% were evaluated. The obtained results revealed that the increase in the surface porosity caused a decrease in the droplet diameter during the impact time. Also, at high surface porosity values, the decline in the contact angle influence on the droplet dynamic behavior was observed.

Origami-inspired structures have found many innovative applications in engineering fields. The expressive volume changes intrinsically related to their geometry is very useful for different purposes. Nevertheless, the mathematical description of origami structures is complex, which makes the design a challenging topic. This work deals with the use of reduce-order models for the origami description. A cylindrical origami structure with waterbomb pattern, called origami stent, is of concern. A reduced-order model (ROM) is developed based on kinematics and symmetry hypotheses. Afterward, a finite element analysis (FEA) is developed based on a nonlinear bar-and-hinge model. Numerical simulations are carried out evaluating the ROM validity range. Rigid and non-rigid situations are investigated showing that ROM is able to be employed for origami description.

An improved time integration scheme is proposed for linear and nonlinear dynamics. The proposed scheme has two free parameters which control numerical dissipation and accuracy effectively. Basic properties including spectral stability, algorithmic accuracy, algorithmic damping, period elongation and overshooting behavior are investigated. The influences of algorithmic parameters on these properties are quantified. The effectiveness of the proposed scheme for linear and nonlinear dynamics is evaluated through some numerical examples. Analytical and numerical results demonstrate that the proposed scheme has the following significant characteristics: (1) desirable accuracy can be obtained for various linear and nonlinear problems, when compared with other effective schemes; (2) for nonlinear problems, new scheme also shows good performance; (3) the proposed scheme has simple formulation and good compatibility for various dynamic problems, and thus, is a promising candidate for practical analysis.

Rubbing is an important problem in machinery industry which occurs when a rotating element hits a stationary part. This rotor-to-stator rub may result in the catastrophic breakdown of the machine. In this work, the phenomenon of rotor rubbing is analyzed from the perspective that the signal analysis tools that are in use today to detect this defect emphasize or highlight particular aspects of the studied phenomenon. So, sometimes it is necessary to use more than one tool to deepen the understanding of the problem. For this purpose, laboratory tests were performed on a rotor system with a rubbing mechanism, while mechanical vibrations were measured with an accelerometer and a data acquisition system. Experiments were carried out for fixed rotor speed, and for run-up and run-down rotor speed conditions. The analysis approach included various processing tools to study their capabilities in rubbing detection: Root Mean Square (RMS), Fourier transform, Wavelet transform and Hurst exponent. Fixed rubbing conditions show similar results for RMS and Hurst exponent on the information obtained. For variable run-up and run-down rotor speed conditions, the Hurst exponent shows predictability, a fact that can be used for rub detection. However, the Wavelet and Fourier Transforms operated in a very distinct way. Although both transforms give frequency information, Fourier transform results in a more detailed frequency analysis, while the Wavelet transform can give time localization of the rubbing phenomenon.

In this paper, the thermo-acoustic behavior of a rectangular panel fully immersed in a compressible fluid at rest is investigated. A boundary element method (BEM) has been employed taking into account the Kirchhoff–Helmholtz (K-H) integral equation for the acoustic pressure and with the fluid-plate interface boundary condition the acoustic pressure jump over the panel is calculated. The thermal effects are considered regarding in the form of a uniform increment of temperature of the panel and are analyzed in order to prevent the buckling phenomena. The deformation modes of the panel correspond to the vacuum case. Applying a collocation method for the panel equation, the natural frequencies are obtained. The effects of several geometric parameters regarding different thermal loads on these frequencies are evaluated. Furthermore, the influence of the wave number for different temperatures of the panel on the acoustic damping ratio is evaluated, as well as the acoustic radiation efficiency for the different modes. The verification of the method is proven with other works.

This paper explores the high-accuracy analysis of bending and frequency response of the sandwich cylindrical shell with functionally graded (FG) carbon nanotubes reinforced composite (FG-CNTRC) face-sheets and polymeric core under the effect of initial axial stress and various mechanical loading based upon the three-dimensional theory of elasticity for various sets of boundary conditions. The sandwich structure is composed of multilayers with uniformly dispersed carbon nanotubes (CNT) in each fictitious layer of face-sheets, but its weight fraction changes layer-by-layer along the thickness direction. With the aid of compatibility conditions, the sandwich structure with three layers is modeled. Analytical bending and frequency solutions are obtained for simply supported shells. Also, the state-space based differential quadrature method (SS-DQM) is employed to determine the bending and frequency response of the sandwich cylindrical shell by considering various boundary conditions. The bending response of the sandwich cylindrical shell is obtained under the impact of various mechanical loadings. The influences of several parameters, such as initial stress and various mechanical loadings are investigated on the bending and frequency of the structures. The results of the presented study can be served as benchmarks to assess the validity of the conventional two-dimensional theory.

This paper proposes a theoretical model for the description of tension-compression cyclic plasticity of gradient nanostructured (GNS) metals. The gradient grain size effect is considered by introducing the Hall–Petch relation for local yield stress and strain hardening. With the experimentally measured grain size distribution profile, the average axial stress can be calculated for cylindrical GNS metal specimens. The model was verified using experimental data obtained from 316L stainless steel treated by surface mechanical rolling treatment (SMRT). Moreover, the corresponding strain energy for cyclic plasticity can be calculated from the constitutive equations, providing an energy-based approach to explain the fatigue life of gradient 316L stainless steel.

Chemically-responsive amorphous shape-memory polymers (SMPs) can transit from the temporary shape to the permanent shape in responsive to solvents. This effect has been reported in various polymer-solvent systems. However, limited attention has been paid to the constitutive modeling of this behavior. In this work, we develop a fully thermo-chemo-mechanical coupled thermodynamic framework for the chemically-responsive amorphous SMPs. The framework shows that the entropy, the chemical potential and the stress can be directly obtained if the Helmholtz free energy density is defined. Based on the entropy inequality, the evolution equation for the viscous strain, the temperature and the number of solvent molecules are also derived. We also provide an explicit form of Helmholtz free energy density as an example. In addition, based on the free volume concept, the dependence of viscosity and diffusivity on the temperature and solvent concentration is defined. The theoretical framework can potentially advance the fundamental understanding of chemically-responsive shape-memory effect. Meanwhile, it can also be used to describe other important physical processes such as the diffusion of solvents in glassy polymers.

A coupling convected particle domain interpolation based implicit material point method (ICCPDI) is developed in this paper for the long-time consolidation and dynamic problems of fully saturated porous media involving massive deformation. In the method, the implicit formulas based on the u-p form governing equations are derived to overcome the time step size limitation within the conventional explicit method and in turn improve the computational efficiency particularly for consolidation problems. Then, the CPDI technique is adopted to eliminate the numerical noises occurring while material points crossing cell boundaries in the massive deformation of solid skeleton. Moreover, an extended material point penalty method is proposed to effectively treat the boundary constraints in the coupled system by avoiding introducing an auxiliary boundary layer. Numerical simulation results of several representative examples demonstrate the accuracy and efficiency of the proposed ICCPDI method to predict the consolidation and dynamic responses of saturated porous media with massive deformation.

A controlled surface wrinkling pattern has been widely used in diverse applications such as stretchable electronics, smart windows, and haptics. Here, we focus on hexagonal wrinkling patterns because of their great potentials in realizing anisotropic and tunable friction and serving as a dynamical template for making non-flat thin films through self-assembling processes. We employ large-scale finite element simulations of a bilayer neo-Hookean solid (e.g., a film bonded on a substrate) to explore mechanical principles that govern the formation of hexagonal wrinkling patterns and strategies for making nearly perfect hexagonal patterns. In our model, the wrinkling instabilities are driven by the confined film expansion. Our results indicate robust hexagonal patterns exist at a relatively small modulus mismatch (on the order of 10) between the film and substrate. Besides, the film expansion should not exceed the onset of wrinkling value too much to avoid post-buckling patterns. By harnessing the imperfection insensitivity of one dimension sinusoidal wrinkles, we apply a sequential loading to the bilayer structure to produce the nearly perfect hexagonal patterns. Lastly, we discuss the connection between the simple bilayer model and the gradient structures commonly existed in experiments.

Dynamic methods for identifying a model of a nonlinearly elastic deformable body are considered. By the effective phase velocities of longitudinal and transverse waves propagating along and across the axis of the compressed bar, it is possible to determine five elastic constants of the second and third orders included in the model relations. Calculation formulae are obtained and an example of determining the dependence of phase velocities on the preliminary deformation for polyamide 6 is given. The influence of preliminary deformations on polar diagrams of wave velocities is investigated.

Multi-crack propagation is investigated mainly by experimental measurement and little by theoretical prediction. The classical fracture criteria can better predict tensile fracture under arbitrary loading conditions (pure tensile, pure shear and mixed-mode), but have difficulty in predicting shear fracture. In this paper, Mode I and Mode II SIFs of branch-cracks initiated by the original cracks were calculated by the complex function and superposition method, and a new theory of multi-crack propagation was established based on the criterion of maximum tensile-shear SIF ratio. Theoretical results of two collinear cracks under uniaxial compression show that the cracks initiate more easily at $\alpha =30^{\circ }$ (the crack inclination angle) than other angles. Coalescence of branch-crack only occurs at $\alpha =45^{\circ }$ with the maximum crack propagation length. Peak stress $(P^{\mathrm{\text{un}}})$ reaches minimum when $\alpha \approx \phi$ (inner friction angle of rock), and the larger the $\alpha$, the closer to the compressive strength of rock the $P^{\mathrm{\text{un}}}$. Mechanism of the crack initiation and propagation are all Mode I under uniaxial compression. Uniaxial compressive test results of red sandstone (the rock material is assumed to be homogeneous) pre-cracked specimens agree well with predicted results of the crack initiation, stable and unstable propagation, which can prove the validity of the new multi-crack propagation prediction method.