Nonlinear Strength Research Articles

A two-step dynamic FEM-FELA approach for seismic slope stability assessment

AbstractThe determination of the factor of safety (FoS) of slopes during seismic excitation can be complex if the relevant effects of pore water pressure accumulation, nonlinear material response and variable shear strength are duly accounted for. A rational two-step approach to tackle this task based on a hydro-mechanically coupled dynamic simulation and finite element limit analyses is henceforth introduced. To ensure accurate transfer of the hydro-mechanical soil state, a mapping concept is presented, accounting for spatial distributions of stresses, excess pore water pressures, inertial forces and shear strength. The proposed approach is compared to limit equilibrium method (LEM) for the case of a large-scale water-saturated open cast mine slope subjected to seismic loading. In comparison with LEM, the new approach to assess seismic slope stability proves to be simpler in its implementation and straightforward, which could be an important asset for practitioners.

Effect of the over-aging degree on high cycle fatigue properties of an ultra-high strength Al-Zn-Mg-Cu alloy

An ultra-high strength Al-Zn-Mg-Cu alloy with high Zn content was subjected to T6, T79, T76, T74 and T73 ageing treatments in order to investigate the effect of the over-aging degree on the high cycle fatigue (HCF) properties of the alloy. The microstructures and fatigue fracture morphologies were analyzed. The results showed that the fatigue strengths exhibited a non-linear trend of first increasing and then decreasing from the T6 to T73 aged samples. The T79 aged sample obtained the highest fatigue strength, was 247MPa. The Basquin equation was used to describe the changes in HCF properties. The physical meanings and causes of changes in the parameters of the fitted Basquin equation were rationalized by combining quantitative analysis of the microstructures and existing models. The combination of microstructural evolution and the trend of parameters in the fitted Basquin equation was ultimately employed to elucidate the underlying mechanism of the specific non-linear fatigue strength trend.

Theoretical and Numerical Study of Electrohydrodynamic Flow in a Planar, Cylindrical, and Spherical Conduit

This paper analyzes the mathematical model of electrohydrodynamic (EHD) fluid flow in a general conduit (planar, cylindrical and spherical) with an ion drag configuration. The phenomenon is modelled using a nonlinear differential equation. The velocity field is obtained by solving this nonlinear equation using two analytical methods. The effects of the Hartmann electric number and nonlinearity strength are discussed and presented graphically. Additionally, we compare this method with a numerical solution obtained using MATLAB, demonstrating that the proposed approaches are less computational intensive and more efficient for solving the underlined problem.

Seismic stability charts for three-dimensional rock slopes using Hoek–Brown criterion

Seismic excitation serves as a crucial trigger for slope collapse in seismically active regions. This study employs the non-linear shear strength reduction (SSR) technique in conjunction with the pseudo-static method to analyse the seismic stability of three-dimensional (3D) rock slopes following the generalised Hoek–Brown (GHB) criterion. Considering the non-linear characteristics of the GHB envelope, the instantaneous Mohr–Coulomb (MC) parameters for rock masses are identified by locating the tangent at the intersection of the GHB envelope with the shear and normal stress planes. These parameters are subsequently incorporated into the non-linear SSR analysis for seismic stability based on the MC criterion. The non-linear SSR technique is then validated by comparing the calculated factor of safety (FOS) with those from other methods and used to assess the impact of geometric and GHB parameters on the FOS of 3D rock slopes. Finally, a set of seismic stability charts for 3D rock slopes in GHB media has been developed and applied to evaluate the seismic stability of two practical rock slope cases following the GHB failure envelope.

Recirculation through western boundary currents varies nonlinearly with the ocean basin's aspect ratio

Recirculation gyres adjacent to western boundary currents (WBCs) in the ocean enhance the poleward transport of these currents. While it is well-established that the WBC in a barotropic ocean strengthens with increase in basin's aspect ratio (the meridional-to-zonal extent ratio), how intensity of the recirculation through the western boundary layer varies with this parameter remains unexplored. I address this using the non-dimensional form of the nonlinear, wind-driven Stommel–Munk model of westward intensification that comprises three parameters—the aspect ratio (δ), the damping coefficient (ϵ), and the β-Rossby number (Rβ). Here, ϵ is set by the ratio of Rayleigh friction coefficient (or eddy viscosity) to the meridional gradient of the Coriolis frequency and the basin's zonal dimension, while Rβ is proportional to wind stress amplitude and quantifies the strength of nonlinearity. In the weak-to-moderate nonlinearity limit (Rβ<∼ϵ), perturbation analysis reveals that recirculation varies concavely with aspect ratio, suggesting existence of an optimal aspect ratio (δopt) for which the recirculation is maximum and for typical values of ϵ (10−3−10−2), δopt follows the power-law relation δopt=4.3ϵ. Numerical simulations further validate the existence of δopt. For large ϵ (>5×10−3), the power-law predicts δopt for the numerical solutions rather accurately, but does not hold for smaller ϵ (2×10−3) due to increased importance of nonlinear terms. Nevertheless, the nonlinear variation in recirculation through the western boundary layer with aspect ratio is observed for all ϵ values and may contribute to the heterogeneous increase in the WBC's transport across different ocean basins in a warming climate.

Assessing the Reliability of Rock Slopes Based on the Nonlinear Strength Criterion

Assessing the Reliability of Rock Slopes Based on the Nonlinear Strength Criterion

Input-to-state hybrid impulsive formation stabilization for multi-agent systems with impulse delays

This paper addresses the input-to-state formation stabilization problem of nonlinear multi-agent systems within a hybrid impulsive framework, considering delay-dependent impulses, strong nonlinearity, and deception attack signals. By leveraging Lyapunov functionals, impulsive comparison theory, average impulsive interval methods, and graph theory, we develop novel criteria for possessing locally input-to-state and integral input-to-state formation stabilization across different impulse sequence classes. These criteria are expressed in terms of continuous/impulsive feedback gains, time delay size, nonlinearity strength, uniform upper bound of impulsive interval, and length of average impulsive interval. Notably, the design of control impulses benefit the destabilizing continuous dynamics in the formation stabilization process. To demonstrate the effectiveness and validity of the analytical results, we provide numerical simulation examples involving various types of external attack signals.

Stress-controlled medium-amplitude oscillatory shear (MAOStress) of PVA–Borax

We report the first-ever complete measurement of MAOStress material functions, which reveal that stress can be more fundamental than strain or strain rate for understanding linearity limits as a function of Deborah number. The material used is a canonical viscoelastic liquid with a single dominant relaxation time: polyvinyl alcohol (PVA) polymer solution cross-linked with tetrahydroborate (Borax) solution. We outline experimental limit lines and their dependence on geometry and test conditions. These MAOStress measurements enable us to observe the frequency dependence of the weakly nonlinear deviation as a function of stress amplitude. The observed features of MAOStress material functions are distinctly simpler than MAOStrain, where the frequency dependence is much more dramatic. The strain-stiffening transient network model was used to derive a model-informed normalization of the nonlinear material functions that accounts for their scaling with linear material properties. Moreover, we compare the frequency dependence of the critical stress, strain, and strain-rate for the linearity limit, which are rigorously computed from the MAOStress and MAOStrain material functions. While critical strain and strain-rate change by orders of magnitude throughout the Deborah number range, critical stress changes by a factor of about 2, showing that stress is a more fundamental measure of nonlinearity strength. This work extends the experimental accessibility of the weakly nonlinear regime to stress-controlled instruments and deformations, which reveal material physics beyond linear viscoelasticity but at conditions that are accessible to theory and detailed simulation.

Degradation mechanism of cement–sodium silicate hardened grout bodies under ion erosion

Cement-sodium silicate (C-S) grout is extensively employed as a grouting material in shield tunnel synchronous grouting projects. However, in water-rich areas, its hardened grout bodies are vulnerable to erosion damage caused by various ions. In order to elucidate the degradation mechanism of C-S hardened grout bodies' strength under salt ion erosion. This study analyzed the influence of SO42- ions, Cl- ions, and SO42- and Cl- mixed ions at different concentrations on the compressive strength of C-S hardened grout bodies through laboratory experiments. Moreover, microscopic techniques (XRD, SEM-EDS) were employed to illustrate the phase characteristics and microstructure of ion-eroded C-S hardened grout bodies, and the distribution of surface calcium elements. Molecular dynamics (MD) simulation investigated the adsorption, diffusion degree, and energy change of erosive ions in C-S-H gel. The results show that the higher the concentration of erosion ions, the faster the erosion rate. A nonlinear spatiotemporal strength degradation prediction model was developed, assessing the deterioration degree of hardened grout bodies due to ions: SO42- > SO42-and Cl- mixture > Cl- > water. Additionally, microscopic observations reveal a tight correlation between the degradation level of C-S hardened grout bodies and the loss of Ca2+ ions inside. The more significant the loss of Ca2+ ions from hydration products, the more evident the strength degradation of C-S hardened grout bodies. MD simulations demonstrate that SO42- ions and Cl- ions occupy adsorption sites like SiOCa+ and SiOH, altering interatomic Coulomb forces and intermolecular van der Waals forces, changing system energy, thereby influencing the structure of C-S-H gel, leading to strength degradation in C-S hardened grout bodies.

Multiscale modeling of diffuse damage and localized cracking in quasi-brittle materials under compression with a quadratic friction law

The diffuse damage and localized cracking of quasi-brittle materials (i.e., rocks and concretes) under compression can be delineated by a matrix-microcrack system, wherein a solid matrix phase is weakened by a large number of randomly oriented and distributed microcracks, and the macroscopic cracking is formed by a progressive evolution of microcracks. Several homogenization-based multiscale models have been proposed to describe this matrix-microcrack system, but most of them are based on a linear friction law on the microcrack surface, rendering a linear strength criterion. In this paper, we propose a new quadratic friction law within the local multiscale friction-damage (LMFD) model to capture the plastic distortion due to frictional sliding along the rough microcrack surface. Following that, a macroscopic Ottosen-type nonlinear strength criterion is rationally derived with up-scaling friction-damage coupling analysis. An enhanced semi-implicit return mapping (ESRM) algorithm with a substepping scheme is then developed to integrate the complex nonlinear constitutive model. The performance of LMFD model is evaluated compared to a wide range of experimental data on plain concretes, and the robustness of ESRM algorithm is assessed through a series of numerical tests. Subsequently, to effectively describe the localized cracking process, a regularization scheme is proposed by combining the phase-field model with the established LMFD model, and the discretization independent crack localization is numerically verified.

Dynamic reliability and seismic fragility analysis for high concrete-faced rockfill dam slopes subjected to stochastic earthquake and parameter excitation via PDEM

The randomness of material parameters and earthquake excitation greatly impacts the seismic stability of high concrete-faced rockfill dam (CFRD) slopes. However, no research has comprehensively analyzed the impacts of stochastic earthquake excitations, random parameters and their coupled effects on seismic stability of CFRD slopes and selected a multi-indicator evaluation criterion to carry out performance-based safety assessment. This paper develops a novel and comprehensive framework for evaluating the seismic stability of CFRD slopes based on the generalized probability density evolution method (GPDEM) with high efficiency and accuracy. The effects of three kinds of randomness on seismic stability of CFRD slopes were comprehensively compared and analyzed on the basis of multi-indices (safety factor (FS), cumulative slip displacement and cumulative time with FS < 1.0). Firstly, the nonlinear shear strength parameters of 40 high CFRDs were statistically collected to obtain the statistical characteristics of rockfill material strength parameters of actual CFRD projects. Secondly, three kinds of random samples were generated using generalized F-discrepancy (GF-discrepancy) method and Spectral expression-Random function (SERF) method. Then, the GPDEM was introduced to combine with three indices to perform the stochastic analysis and reliability evaluation. Finally, the fragility analysis of the CFRD slope was conducted. The results reveal that FS is more sensitive to the ground motions randomness, while cumulative slip displacement and cumulative time with FS < 1.0 are more sensitive to the material parameters randomness. The seismic safety evaluation of CFRD slopes based on multiple indices with full consideration of coupled randomness effects is necessary.

Nonlinear chiral forms in the Sen formulation

The Sen formulation for chiral (2p)-form in 4p+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4p+2$$\\end{document} dimensions describes a system with two separate sectors, one is physical while the other is unphysical. Each contains a chiral form and a metric. In this paper, we focus on the cases where the self-duality condition for the unphysical sector is linear while for the physical sector can be nonlinear. We show the decoupling at the Hamiltonian and Lagrangian levels. The decoupling at the Hamiltonian level follows the idea in the literature. Then by an appropriate field redefinition of the corresponding first-order Lagrangian, the separation at the Lagrangian level follows. We derive the diffeomorphism of the theory in the case where the chiral form in the physical sector has nonlinear self-dual field strength and couples to external (2p+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2p+1)$$\\end{document}-form field. Explicit forms of Sen theories are also discussed. The Lagrangian for the quadratic theory is separated into two Henneaux–Teitelboim Lagrangians. We also discuss the method of generating explicit nonlinear theories with p=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=1$$\\end{document}. Finally, we also show that the M5-brane action in the Sen formulation is separated into a Henneaux–Teitelboim action in unphysical sector and a gauge-fixed PST in physical sector.

Piecewise Linear Strength Models for Analyzing Multiple Failure Mechanisms in Rocks Materials.

Rock materials failures are accompanied by the co-existence of various failure mechanisms, including rock fracturing, shearing, and compaction yield. These mechanisms manifest macroscopically as multiple failure modes and nonlinear strength characteristics related to stress levels. Considering the limitations of current rock mechanics strength theories, which are primarily derived from single failure mechanisms, this study evaluates the applicability of alternative strength theories. Based on the extensional-strain criterion and the PMC (Paul-Mohr-Coulomb) model, a piecewise linear strength model was proposed that is suitable for analyzing multiple failure mechanisms in rocks, revealing the intrinsic mechanisms of multi-mechanism rock material failure. A multiple failure mechanism strength model in the form of inequalities was proposed, using the generalized shear stress, mean stress, and stress Lode angle as parameters. Strength tests conducted on sandstone and granite rock material samples under different stress conditions revealed distinct piecewise linear strength characteristics for both rock types, validating the rationality and applicability of the multiple failure mechanism model. The findings construct a multi-mechanism failure model for rocks, providing enhanced predictive capabilities and aiding in the prevention of rock structural failures.

Stress-dependent instantaneous cohesion and friction angle for the Mohr–Coulomb criterion

The strength criterion of rock is essential for stability control and safety design of geotechnical engineering constructions. Due to its widespread adoption, the Mohr–Coulomb (M-C) criterion is prominent among strength criteria. However, the M-C criterion is constrained by three significant limitations: it fails to capture the nonlinear strength response, overlooks the critical state, and disregards σ2. This study introduces a novel Stress-dependent Instantaneous Friction angle and Cohesion (SIFC) model for the M-C criterion to represent the convex strength envelope of intact rock, covering the spectrum from non-critical to critical states. In pursuit of this objective, an innovative approach for calculating these instantaneous shear parameters at each corresponding σ3 is initially introduced. By examining the confining pressure dependency of the instantaneous friction angle and cohesion, the SIFC model is derived and introduced to the M-C criterion. The SIFC-enhanced M-C criterion, utilizing parameters obtained from triaxial tests under lower σ3, delineates the complete non-linear strength envelope in (σ1, σ3) space, covering brittle to ductile behavior. This criterion is then extended to polyaxial stress conditions. Validation through triaxial test data confirms that the SIFC-enhanced M-C criterion accurately reflects the strength characteristics of the tested rocks.

Electrochemical Approaches for Enhanced Phosphorus Recovery from Synthetic Animal Wastewater: A Comparative Analysis of Response Surface Methodology and Artificial Neural Networks

Electrochemical recovery from animal wastewater is a novel and comprehensive strategy needed in the effort to develop sustainable technology and nutrient delivery solutions, with an emphasis on nitrogen (N) and phosphorus (P) components. This research study addresses critical global environmental sustainability challenges associated with waste by contributing to the evolving conversation on nutrient recovery by using synthetic animal wastewater (SAW) as a substrate. This approach presents a viable solution for wastewater treatment and aligns with the sustainable management of water and energy resources.This research utilized a Box-Behnken experimental design framework formulated with the aid of Minitab Statistical Software. The constructed design laid out a series of experimental runs (comprising 12 distinct conditions, each replicated twice, along with five central points) to explore the influence of three different variables (Mg:Ca molar ratio, N:P molar ratio, and temperature), each at three distinct levels, on phosphorus removal efficiency. The relationship between these three variables and the removal efficiency was then investigated using two distinct modeling methods: Artificial Neural Networks (ANN) and Response Surface Methodology (RSM). ANN, part of machine learning, involves developing a model that learns from experimental data using a network of neurons for training and validation. This allows the ANN to address complex, nonlinear relationships between variables effectively. Conversely, based on statistical analysis, RSM focused on understanding the interactions between the multiple factors, using designed experiments to build a model. Employing both methods leveraged ANN's prowess in handling nonlinearity and RSM's strength in experimental design and optimization, offering a comprehensive approach to enhance P removal efficiency from SAW. The combination of these approaches provided a deep insight into the dynamics of the process, aiding in the effective optimization of the removal response.However, at optimal conditions, the ANN model predicted a higher P removal efficiency (66%) than RSM (45%). The precision of the ANN predictions was reflected in the minimal error margins with Root Mean Squared Error (RMSE) of 2.4, suggesting the robustness of this model in predicting the optimal conditions for P removal compared to the RSM, with an RMSE of 4.7. These findings underscore the potential of employing ANN and RSM to enhance the phosphorus removal process in wastewater treatment applications and show how ANN gives better predictions than RSM. Additional details will be presented at the meeting, including experimental data, regression models, and neural networks.

A Data-Driven DNN Model to Predict the Ultimate Strength of a Ship’s Bottom Structure

Plates and curved plates are essential components in ship construction. In the design stage, the methods used to evaluate the ultimate strength required to confirm the structural safety of plates include prediction through analytical methods, finite-element analysis (FEA), and empirical formulas. However, with nonlinear buckling, the results of the empirical formula and the FEA differ for small flank angles (1~9). As a result, the prediction of the nonlinear ultimate strength of flank angle (1~9) plates still requires significant computation time and cost. To compensate for this, this study performed an ultimate strength prediction method utilizing a deep neural network together with the 4050 curved plate analysis. In addition, this paper presents the analysis results of the nonlinear finite-element method and the geometric shape and ratio of curved plates as training data. Based on the results of this study, designers can more efficiently design appropriate curved plate members by considering the ultimate strength.

Design and characterization of novel broadband chalcone-based THz optical crystals

By combining extended π-conjugated structures and halogen substituents, two novel chalcone-based optical THz crystals were designed: CBC (C22H17ClO2, Pc) and TFBC (C23H17F3O2, P21). These crystals were synthesized and successfully grown using the solution evaporation method. The effects of different types and quantities of halogen substituents on hydrogen bonding interactions, molecular alignment, and nonlinear strength were analyzed. The second harmonic generation (SHG) efficiency, thermal stability, transmission spectra, dielectric constant, and THz generation of the crystals were characterized. Theoretical calculations were conducted to determine the hyperpolarizability, band gap, density of states, and nonlinear optical coefficients of the crystals. The results showed that the synthesized crystals exhibited higher transparency (≥85%) and SHG efficiencies of 9.5 times and 6.2 times that of standard potassium dihydrogen phosphate (KDP), respectively, compared to previously reported chalcone NLO crystals. For the first time, the THz generation efficiency of the two crystals was confirmed through the optical rectification method, with TFBC demonstrating a wider THz spectrum range compared to CBC.

Stress-dependent Mohr–Coulomb shear strength parameters for intact rock

Rock strength is imperative for the design and stability analysis of engineering structures. The Mohr–Coulomb (M-C) criterion holds significant prominence in geotechnical engineering. However, the M-C criterion fails to accurately capture the nonlinear strength response and neglects the critical state of rocks, potentially leading to inaccuracies in the design phase of deep engineering projects. This study introduces an innovative stress-dependent friction angle and cohesion (SFC) for the M-C criterion to capture the nonlinear strength responses of intact rocks, spanning from non-critical to critical states (brittle to ductile regions). A novel method for determining these stress-dependent parameters at each corresponding σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{3}$$\\end{document} is initially introduced. Subsequently, an examination of the confinement dependency of the friction angle and cohesion is conducted, leading to the derivation of the SFC model. The SFC-enhanced M-C criterion, utilizing parameters obtained from triaxial tests under lower σ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma_{3}$$\\end{document}, demonstrates the capability to delineate the complete non-linear strength envelope from brittle to ductile regions. Validation through triaxial test data confirms that the predictions of the SFC-enhanced M-C criterion accurately correspond to the strength characteristics of the tested rocks.

Waddington landscape for prototype learning in generalized Hopfield networks

Networks in machine learning offer examples of complex high-dimensional dynamical systems inspired by and reminiscent of biological systems. Here, we study the learning dynamics of generalized Hopfield networks, which permit visualization of internal memories. These networks have been shown to proceed through a “feature-to-prototype” transition, as the strength of network nonlinearity is increased, wherein the learned, or terminal, states of internal memories transition from mixed to pure states. Focusing on the prototype learning dynamics of the internal memories, we observe stereotypical dynamics of memories wherein similar subgroups of memories sequentially split at well-defined saddles. The splitting order is interpretable and reproducible from one simulation to the other. The dynamics prior to splits are robust to variations in many features of the system. To develop a more rigorous understanding of these global dynamics, we study smaller subsystems that exhibit similar properties to the full system. Within these smaller systems, we combine analytical calculations with numerical simulations to study the dynamics of the feature-to-prototype transition, and the emergence of saddle points in the learning landscape. We exhibit regimes where saddles appear and disappear through saddle-node bifurcations, qualitatively changing the distribution of learned memories as the strength of the nonlinearity is varied—allowing us to systematically investigate the mechanisms that underlie the emergence of the learning dynamics. Several features of the learning dynamics are reminiscent of the Waddington's caricature of cellular differentiation, and we attempt to make this analogy more precise. Memories can thus differentiate in a predictive and controlled way, revealing bridges between experimental biology, dynamical systems theory, and machine learning. Published by the American Physical Society 2024

Dynamic analysis of cracked pipe elbows: Numerical and experimental studies

This study aims to investigate the dynamic behaviors of fluid-delivering cracked pipe elbows (FDCPEs), thereby providing theoretical and methodological guidance for vibration-based crack detection in pipe elbows. Specifically, an efficient spectral element-finite element (SE-FE) based modeling method for the FDCPEs is proposed firstly, which considers fluid-structure coupling and breathing effect. For the SE-FE method, the spectral element (SE) and finite element (FE) are constructed to simulate the healthy straight segments and cracked elbows of the pipe, respectively, and a penalty function method is adopted to simulate interface coupling and breathing effects. Furthermore, the computational accuracy and efficiency of the SE-FE method are verified through numerical and experimental studies. Finally, the effects of the elbow and crack parameters on the dynamic behaviors of FDCPE are analyzed. The results indicate that changes in the bending radius and angle may trigger frequency veering behaviors, leading to in-plane and out-plane vibration mode switching. Moreover, the even-mode harmonics of the stress responses can effectively detect cracks in the elbow. Most importantly, the strength of nonlinearity at different measuring locations can be used to predict the crack location and size.