Nonlinear Strength Research Articles

Numerical Analysis of Electrohydrodynamic Flow in a Circular Cylindrical Conduit by Using Neuro Evolutionary Technique

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a circular cylindrical conduit with an ion drag configuration. The phenomenon was modelled as a nonlinear differential equation. Furthermore, an application of artificial neural networks (ANNs) with a generalized normal distribution optimization algorithm (GNDO) and sequential quadratic programming (SQP) were utilized to suggest approximate solutions for the velocity, displacements, and acceleration profiles of the fluid by varying the Hartmann electric number (Ha2) and the strength of nonlinearity (α). ANNs were used to model the fitness function for the governing equation in terms of mean square error (MSE), which was further optimized initially by GNDO to exploit the global search. Then SQP was implemented to complement its local convergence. Numerical solutions obtained by the design scheme were compared with RK-4, the least square method (LSM), and the orthonormal Bernstein collocation method (OBCM). Stability, convergence, and robustness of the proposed algorithm were endorsed by the statistics and analysis on results of absolute errors, mean absolute deviation (MAD), Theil’s inequality coefficient (TIC), and error in Nash Sutcliffe efficiency (ENSE).

Rayleigh wave propagation in nonlinear metasurfaces

We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe, analytically and numerically, the effects of nonlinear interaction force and energy loss on the dispersion of Rayleigh waves. We develop closed-form expressions to predict the dispersive characteristics of nonlinear Rayleigh waves by adopting a leading-order effective medium description. In particular, we demonstrate how hardening nonlinearity reduces and eventually eliminates the linear filtering bandwidth of the metasurface. Softening nonlinearity, in contrast, induces lower and broader spectral gaps for weak to moderate strengths of nonlinearity, and narrows and eventually closes the gaps at high strengths of nonlinearity. We also observe the emergence of a spatial gap (in wavenumber) in the in-phase branch of the dispersion curves for softening nonlinearity. Finally, we investigate the interplay between nonlinearity and energy loss and discuss their combined effects on the dispersive properties of the metasurface. Our analytical results, supported by finite element simulations, demonstrate the mechanisms for achieving tunable dispersion characteristics in nonlinear metasurfaces.

Effect of pyrocarbon interphase texture and thickness on tensile damage and fracture in T‐700™ carbon fiber–reinforced silicon carbide minicomposites

AbstractIn this paper, T‐700™ carbon fiber–reinforced silicon carbide (C/SiC) minicomposites with pyrocarbon (PyC) interphase with different textural microstructure and thickness were fabricated using the chemical vapor infiltration method. The interface properties (i.e., textural microstructure, thickness, hardness, and modulus) were obtained through multiple testing methods (i.e., Raman spectroscopy, X‐ray diffraction, scanning electron microscopy, and nanoindentation tests). Relationships between the deposition temperature and residence time with the texture type (i.e., low, medium, and high texture) were established. Uniaxial tensile experiments were conducted for C/SiC minicomposites with different PyC interphases to characterize the composite's internal damage evolution and fracture. Relationships between the composite's tensile nonlinear damage evolution, fracture strength and strain, PyC interphase texture, and thickness were established. The composite's tensile strength and fracture strain were the highest for the C/SiC minicomposite with medium‐high texture PyC interphase. For the C/SiC minicomposite with the same texture interphase, the composite's tensile strength and fracture strain were affected by the coating thickness. The higher the thickness of the coating, the lower the composite's tensile strength and fracture strain.

Examining the Effects of Suction and Nonlinear Strength Envelopes on the Stability of a High Plasticity Clay Slope

Slope failures in high plasticity clay deposits are common occurrences in many parts of the world. In western and central Alabama, expansive Prairie clays are commonly found, and shallow slope failures have occurred in both fill and cut slopes containing these high plasticity clays. The objective of this study was to examine the effects of suction and the use of nonlinear strength envelopes on the embankment stability of a section of highway AL-5. The testing program consisted of fifteen ring shear tests performed using a Bromhead Ring Shear Device. The results of the tests were used to develop both linear and nonlinear fully softened and residual strength envelopes. The saturated strength envelopes are then used in a limit equilibrium slope stability analysis with and without the effects of suction. The results show stability (factor of safety >1) for all cases except the residual friction angle without suction. Given these results, large slope failures are unlikely to occur in this area, but surficial failures and deformations due to creep may be possible. These results demonstrate the importance of considering the effects of suction and nonlinear strength envelopes when examining the potential for shallow slope failures in high plasticity clays.

Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity

We establish uniform error bounds of time-splitting Fourier pseudospectral (TSFP) methods for the nonlinear Klein–Gordon equation (NKGE) with weak power-type nonlinearity and O ( 1 ) O(1) initial data, while the nonlinearity strength is characterized by ε p \varepsilon ^{p} with a constant p ∈ N + p \in \mathbb {N}^+ and a dimensionless parameter ε ∈ ( 0 , 1 ] \varepsilon \in (0, 1] , for the long-time dynamics up to the time at O ( ε − β ) O(\varepsilon ^{-\beta }) with 0 ≤ β ≤ p 0 \leq \beta \leq p . In fact, when 0 > ε ≪ 1 0 > \varepsilon \ll 1 , the problem is equivalent to the long-time dynamics of NKGE with small initial data and O ( 1 ) O(1) nonlinearity strength, while the amplitude of the initial data (and the solution) is at O ( ε ) O(\varepsilon ) . By reformulating the NKGE into a relativistic nonlinear Schrödinger equation, we adapt the TSFP method to discretize it numerically. By using the method of mathematical induction to bound the numerical solution, we prove uniform error bounds at O ( h m + ε p − β τ 2 ) O(h^{m}+\varepsilon ^{p-\beta }\tau ^2) of the TSFP method with h h mesh size, τ \tau time step and m ≥ 2 m\ge 2 depending on the regularity of the solution. The error bounds are uniformly accurate for the long-time simulation up to the time at O ( ε − β ) O(\varepsilon ^{-\beta }) and uniformly valid for ε ∈ ( 0 , 1 ] \varepsilon \in (0,1] . Especially, the error bounds are uniformly at the second-order rate for the large time step τ = O ( ε − ( p − β ) / 2 ) \tau = O(\varepsilon ^{-(p-\beta )/2}) in the parameter regime 0 ≤ β > p 0\le \beta >p . Numerical results are reported to confirm our error bounds in the long-time regime. Finally, the TSFP method and its error bounds are extended to a highly oscillatory complex NKGE which propagates waves with wavelength at O ( 1 ) O(1) in space and O ( ε β ) O(\varepsilon ^{\beta }) in time and wave velocity at O ( ε − β ) O(\varepsilon ^{-\beta }) .

Nonlinearity enhancement and photon blockade in hybrid optomechanical systems.

The nonlinear optomechanical coupling is an attracting characteristic in the field of optomechanics. However, the strength of single photon optomechanical coupling is still within weak coupling regime. Using the optomechanical coupling to achieve strong nonlinear interaction between photons is still a challenge. In this paper, we propose a scheme by employing optomechanical and spin-mechanical interactions to enhance the nonlinearity of photons. An effective Hamiltonian is derived, which shows that the self-Kerr and cross-Kerr nonlinearity strengths can be enhanced by adjusting the classical pumping or enhancing the spin-mechanical coupling strength. In addition, we investigate the potential usage of the nonlinearity in the photon blockade. We demonstrate that the single and two photon blockades can occur in two super modes.

Nonlinear mechanical response and residual tearing strength of flexible composite sheet with single edge-crack under uniaxial tension

The paper seeks to probe nonlinear mechanical response and residual tearing strength of flexible composite sheets. Uniaxial tensile tests are conducted on flexible composite sheets containing single edge-cracks with different crack lengths, nonlinear beach chair-like curves of load versus displacement are measured and failure modes including instantaneous rupture and progressive tearing are observed. New constitutive model is proposed to depict nonlinear curves of load versus displacement of flexible composite sheets with single edge-cracks, and novel formulations are then derived to determine nonlinear fracture toughness and alternation crack size for predicting residual strength and failure mode. Predictions are in good agreement with experimental results, demonstrating the practical and effective use of proposed models.

Airy–Gaussian vortex beams in the fractional nonlinear-Schrödinger medium

We address the propagation of vortex beams with the circular Airy–Gaussian shape in a ( 2 + 1 )-dimensional optical waveguide modeled by the fractional nonlinear Schrödinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of peak intensity in the focal plane on the corresponding Lévy index α , with a strong maximum at α ∼ 1.4 . Effects of the nonlinearity strength, the ratio of widths of the Airy and Gaussian factors in the input, as well as the beams’ vorticity on the autofocusing dynamics are explored. In particular, multiple autofocusing events occur if the nonlinearity is strong enough. Under the action of azimuthal modulational instability, an axisymmetric beam may split into a set of separating bright spots. In the case of strong fractality (for α close to one), the nonlinear beams self-trap, after the first instance of autofocusing, into a breathing vortical quasi-soliton. Radiation forces induced by the beams’ field are considered too, and a capture position for a probe nanoparticle is thus identified.

Friction-damage coupled models and macroscopic strength criteria for ice-saturated frozen silt with crack asperity variation by a micromechanical approach

This paper aims to present physical friction-damage coupled models and derive macroscopic nonlinear strength criteria for ice-saturated frozen silt. Two material scales are considered here. The material at the mesoscale is composed of a frozen silt matrix and embedded mesocracks. At the microscale, the frozen silt matrix is composed of elastic mineral grains and elastic ice crystals. Considering this microstructure, for the ice-saturated frozen silt, the plastic deformation is related to frictional sliding along the mesocracks, and damage is due to the propagation of mesocracks. We obtain the effective elastic properties with a two-step linear Mori-Tanaka homogenization procedure. For the second homogenization step, we deduce the macroscopic stress-strain relations and local thermodynamic forces associated with damage and plasticity. Then, an energy release-based damage criterion is developed to capture the evolution of damage, and a friction sliding criterion with an associated/nonassociated local plastic flow rule is introduced to describe the rate of plasticity. The friction sliding criterion considers the variation of surface asperities of mesocracks as a result of pressure melting and damage evolution. In this context, associated/nonassociated multiscale friction-damage models are established. Furthermore, associated/nonassociated macroscopic nonlinear strength criteria as inherent parts of the corresponding multiscale models are derived under a large range of compressive stresses. For application, a semi-implicit local numerical algorithm of the multiscale models is developed. The accuracy of associated/nonassociated multiscale models is assessed by comparing their numerical simulations with conventional triaxial compression (CTC) tests. Although the associated multiscale model correctly predicts the nonlinear strength behavior and axial deformation of the Lanzhou frozen silt under CTC tests with different temperatures, it fails to quantitatively reproduce volumetric deformation. Nonassociated multiscale model predictions with experimental data of volumetric deformation are significantly improved compared to the associated multiscale model.

Multiaxial fatigue damage and reliability assessment of aero-engine compressor blades made of TC4 titanium alloy

This paper discusses the multiaxial fatigue damage and reliability evaluation of aero-engine compressor blades using an improved strength degeneration scheme based on Chaboche damage model combined with stress-strength interference (SSI) approach. Firstly, the multiaxial proportion and non-proportion fatigue tests of TC4 (Ti-6Al-4V) alloy under a series of loading paths are carried out. The nonlinear fatigue damage calculation and life prediction of TC4 alloy is described by combining the Chaboche nonlinear damage criterion and critical plane method with proposed damage control parameter. Secondly, a nonlinear strength degradation model based on accumulative damage is further developed, and it is proved that the model can get greater precision under different loading conditions. Finally, a revised time-varying reliability model is established by viewing mechanical characteristic of compressor blade set as interconnected system with variant load component on each blade. According to the results of Monte Carlo simulation, the proposed revised model has a better prediction precision, with the error controlled less than 5%.

Numerical and experimental modeling of geomechanical behavior of partially saturated soils

The Barcelona Basic Model (BBM) has been implemented in a finite difference-based computer program to simulate the behavior of unsaturated soils subjected to wetting. The BBM implementation was verified using analytical solutions, and the proposed model has been used to simulate the response of a compacted embankment under complete saturation and suction induced conditions. Numerical analyses indicate that considerable amount of total and differential settlements could develop at the top surface of the embankment. BBM is executed into FLAC2D extending a defined module for modified Cam Clay (MCC) and has been set up an analytical solution for suction-dependent stress and strain. Evaluating the effect of anisotropy and nonlinear apparent tensile strength in unsaturated soils, a modification to BBM formulation has been proposed and optimized by developing numerical analyses to reduce the size of elastic region of loading collapse (LC) curve. Then, an experimental study in the literature is investigated by utilizing comparative curves from BBM and modified BBM indicating well agreement with natural circumstances. As a result of the work presented in this research, finite difference codes with BBM and modified BBM has the capability of simulating the real behavior and is operational being applied to problems associated with earthen structures in unsaturated or partially saturated of expansive soils as a three-phases medium.

Quasi-stable localized excitations in the β-Fermi Pasta Ulam Tsingou system

The lifetimes of localized nonlinear modes in both the $\beta$-Fermi-Pasta-Ulam-Tsingou ($\beta$-FPUT) chain and a cubic $\beta$-FPUT lattice are studied as functions of perturbation amplitude, and by extension, the relative strength of the nonlinear interactions compared to the linear part. We first recover the well known result that localized nonlinear excitations (LNEs) produced by a bond squeeze can be reduced to an approximate two-frequency solution and then show that the nonlinear term in the potential can lead to the production of secondary frequencies within the phonon band. This can affect the stability and lifetime of the LNE by facilitating interactions between the LNE and a low energy acoustic background which can be regarded as "noise" in the system. In the one dimensional FPUT chain, the LNE is stabilized by low energy acoustic emissions at early times; in some cases allowing for lifetimes several orders of magnitude larger than the oscillation period. The longest lived LNEs are found to satisfy the parameter dependence $\mathcal{A}\sqrt{\beta}\approx1.1$ where $\beta$ is the relative nonlinear strength and $\mathcal{A}$ is the displacement amplitude of the center particles in the LNE. In the cubic FPUT lattice, the LNE lifetime $T$ decreases rapidly with increasing amplitude $\mathcal{A}$ and is well described by the double log relationship $\log_{10}\log_{10}(T)\approx -(0.15\pm0.01)\mathcal{A}\sqrt{\beta}+(0.62\pm0.02)$.

Novel Model for Limit-Equilibrium Analysis of Slope Stability with a Nonlinear Strength Criterion

Slope stability has always been a concern of the geotechnical engineering community, and geotechnical scholars have continued to explore the reasonable failure mechanism of slopes and make the theoretical models of slope stability more reliable. This work established a novel model for limit-equilibrium (LE) analysis of slope stability with a nonlinear strength criterion. In this theoretical model, the thrust line of interslice force and corresponding increment are reasonably simplified. Then, the formula of normal stress on slip surface is derived by assuming the increment of normal interslice force. Meanwhile, strength reduction technology is applied to reduce the shear strength of the geotechnical body on the slip surface with slope factor of safety (FOS) to obtain shear stress on the slip surface. Thereafter, mechanical equilibrium conditions satisfied by the whole slope sliding body and newly introduced equation about increments of interslice force are used to solve LE stability of the slope. For stability analysis of a slope with a nonlinear strength criterion via a simple and feasible calculation process, an iterative loop solution strategy is adopted in the analysis. After comparison and analysis of several slope examples, the feasibility and rationality of the present method are verified. Moreover, the present method has high efficiency in terms of calculation speed.

Direct Search for Critical General Slip Surface of Slopes with Nonlinear Strength Envelope

Direct Search for Critical General Slip Surface of Slopes with Nonlinear Strength Envelope

Effective design and characterization of flutter-based piezoelectric energy harvesters with discontinuous nonlinearities

A comprehensive study on the design and nonlinear characterization of a two-degree of freedom piezoaeroelastic energy harvesting system with freeplay and multi-segmented nonlinearities in the pitch degree of freedom is explored and discussed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived and the unsteady representation based on the Duhamel formulation is employed to represent the aerodynamic loads. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay and multi-segmented nonlinearities before and after the linear onset of flutter. Such nonlinearities can be introduced to piezoaeroelastic energy harvesters for performance enhancement through the possible existence of subcritical Hopf bifurcation and aperiodic responses due to the grazing and grazing/sliding bifurcations. It is shown that the existence of discontinuous effects result in the possibility of harvesting energy at lower speeds than the linear onset speed of instability due to the activation of the subcritical Hopf bifurcation. Additionally, the increase of the strength of the multi-segmented nonlinearities leads to the existence of aperiodic responses with the presence of several bifurcations limiting the system's dynamics at low pitch angles with limiting stall issues. It is proved that an effective design with harvesting energy at low wind speeds can be carried out for wing-based energy harvesters by carefully selecting the linear stiffness of the pitch degree of freedom, gap and type of the multi-segmented discontinuity, and electrical load resistance.

Variation of Apparent Cohesion and Friction Angle Under Polyaxial Stress Conditions in Concrete

Amongst many mechanical properties, cohesion (c) and angle of internal friction (φp) are probably the most widely used rock and rock-like material strength design parameters. However, unlike Mohr-Coulomb (MC) failure criterion that assumes cohesion and friction angle are intrinsic material properties and are not affected by the applied stress level, the Hoek-Brown (HB) criterion predicts a continuous change of apparent cohesion and friction angle if the induced normal stress on the fracture plane changes. That is, at low values of normal stresses, the instantaneous angle of friction will be relatively large, whereas cohesion will be a small value. As the applied normal stress value on the fracture plane increases (moving ‘up’ the non-linear Hoek-Brown strength envelope), the angle of friction reduces, and the cohesion increases. This is an important result from the HB failure model and allows a more realistic estimate of shear strength to be made at low values of normal stress, preventing potential over-design problems. Nevertheless, the HB model neglects the effect of the intermediate principal stress on material properties. Limited studies on the variation of apparent cohesion and friction angle under polyaxial stresses in concrete are available in the literature. Therefore, this paper aims to investigate the effect of true triaxial stresses on concrete cohesion and friction angle using a polyaxial strength criterion developed by Mogi. The results of concrete show that the intermediate principal stress has a pronounced effect on cohesion degradation and the mobilization of internal friction angle as the ratio of the intermediate to the minor principal stress changes. The results are expected to provide a framework for a more realistic design of underground concrete structures at depth.

Investigation of rock slope stability using a 3D nonlinear strength-reduction numerical manifold method

Due to rock masses' nonlinear failure property, it is inappropriate to investigate the stability of rock slopes using the traditional SRM (strength reduction method) which is based on the linear MC (Mohr-Coulomb) failure criterion. To conduct 3D analysis (three dimensional) of rock slopes, we propose a 3D-NSRNMM (3D nonlinear strength reduction numerical manifold method) that is based on the nonlinear GHB (Generalized Hoek-Brown) failure criterion. To effectively implement the proposed 3D-NSRNMM, two methods are adopted to convert the GHB parameters into the average and instantaneous equivalent MC parameters. With the proposed 3D-NSRNMM, the influences of different types of equivalent MC parameters, and boundary conditions on rock slopes' stability are investigated. The numerical results assessed from the proposed 3D-NSRNMM indicate that: 1) boundary conditions will significantly influence the safety factor and failure mode of a rock slope obtained from 3D analysis; 2) the safety factor from two-dimensional analysis is more conservative compared with 3D analysis; 3) Furthermore, safety factors based on the instantaneous equivalent MC parameters are very close to those based on the average equivalent MC parameters, but 3D rock slopes' failure modes based on the two different types of equivalent MC parameters are a little different from each other.

Suppression of symmetry breaking of nonlinear modes by defocusing saturable nonlinearity in parity-time symmetric potentials

Symmetry breaking of nonlinear localized modes and suppression of symmetry-breaking bifurcations are reported in the framework of the nonlinear Schrödinger equation with defocusing saturable nonlinearity in parity-time symmetric potentials. We found that, beyond a critical point, one type of the nonlinear modes with asymmetric profiles bifurcates from the branch of the first excited state. We prove that the bifurcation is essentially triggered by instability of the first excited state by linear stability analysis, which implies the symmetry breaking of the nonlinear modes is steerable by changing the stability of the first excited state of the nonlinear mode. A suppressing effect is that the symmetry-breaking bifurcation of the nonlinear modes can be completely suppressed by adjusting the strength of the saturable nonlinearity. This suppressing effect of symmetry-breaking bifurcation is illuminated by analyzing the stability behaviors of the nonlinear modes.

Reliability back analysis of a 3D wedge slope based on the nonlinear Barton-Bandis failure criterion

Due to the development of joints, wedge failure has become the main failure type of rock slopes. Obtaining accurate parameters is an important prerequisite in studying slope stability. However, these are difficult to obtain due to the restrictions of field conditions. Based on a real and simple wedge, the method of stability analysis and parameter acquisition of a wedge with the nonlinear Barton-Bandis failure criterion is discussed, and then this method is extended to the conventional form of a wedge. With minimal available data, a simple field test and the reliability back analysis method are combined to propose a specific method for determining the most likely combination of nonlinear strength parameters when wedge failure occurs. This approach can provide a simple and practical method for determining the nonlinear strength parameters for engineering applications. Thus, the small frequent collapse incidences in jointed rock slopes can be effectively utilized to provide a reference for the prevention and control of large-scale failure.

Shallow Layer Destruction Law of Expansive Soil Slope under Rainfall and the Application of Geogrid Reinforcement

A large number of instability cases and laboratory tests of expansive soil slopes show that its shallow layer destruction happens because of the insufficient shear strength under the usual action of low stress and repeated dry-wet cycles. We can obtain the strength nonlinear distribution law fitted by generalized power function based on a series of shear strength tests of expansive soil considering low stress and can construct the numerical model considering the nonlinear strength distribution by FISH, to realize the shear strength dynamic distribution with the vertical stress. Based on the numerical model, the whole-process contrastive analysis has been conducted on the stress field, the slip surface depth, and the seepage field of plain soil and reinforced expansive soil cut slope under different rainfall conditions. Besides, the mechanics characteristic of the geogrid under various design schemes has been compared and analyzed. A further explanation has been given for the expansive soil cut slope prone to shallow layer failure after rainfall and on the effect of geogrid reinforcement. The numerical results provide a reference for slope stability analysis in rainy expansive soil areas.