Discontinuous Behavior Research Articles

A new finite element formulation unifying fluid-structure and fluid-fluid interaction problems

When the accurate simulation of two materials that interact through their common and deformable interface is of interest, the efficient treatment of the interface determines the success or failure of a numerical method. In this work, we propose a new, robust and easy-to-code finite element formulation for such interaction problems. The remedy of the interface constraints, namely the continuity of velocities and stresses, is accomplished using a single-node approach and the same continuous basis functions for the velocities in both materials. Given that only Newtonian fluids will be examined, we do not have to introduce basis functions for the stress components. The XFEM method, which enriches locally the continuous basis function of a variable that presents a discontinuity, is employed to tackle the discontinuous behavior of the pressure across the interface. The incorporation of Petrov-Galerkin stabilization schemes enhances further our formulation and allows the usage of equal order interpolants for velocities and pressure. We solve the coupled system of equations in a monolithic manner to alleviate the convergence problems of the segregated approach. The novel aspect of our method is that its ingredients do not differentiate based on the constituent materials of the problem, and it can be used interchangeably for either a fluid-structure or a fluid-fluid interaction problem. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: i) the flow through a partially collapsible channel, ii) the induced motion of a flexible elastic plate, iii) the filament stretching of a Newtonian thread surrounded by another immiscible viscous fluid. In all cases, we are in agreement with the results of the literature. Furthermore, we conduct a challenging, 3D simulation for a setup that resembles the motion of a three-leaflet stented aortic heart valve.

Hidden-like Attractors in a Class of Discontinuous Dynamical Systems

In continuous dynamical systems, a hidden attractor occurs when its basin of attraction does not connect with small neighborhoods of equilibria. This research aims to investigate the presence of hidden-like attractors in a class of discontinuous systems that lack equilibria. The nature of non-smoothness in Filippov systems is critical for producing a wide variety of interesting dynamical behaviors and abrupt transient responses to dynamic processes. To show the effects of non-smoothness on dynamic behaviors, we provide a simple discontinuous system made of linear subsystems with no equilibria. The explicit closed-form solutions for each subsystem have been derived, and the generalized Poincaré maps have been established. Our results show that the periodic orbit can be completely established within a sliding region. We then carry out a mathematical investigation of hidden-like attractors that exhibit sliding-mode characteristics, particularly those associated with grazing-sliding behaviors. The proposed system evolves by adding a nonlinear function to one of the vector fields while still preserving the condition that equilibrium points do not exist in the whole system. The results of the linear system are useful for investigating the hidden-like attractors of flow behavior across a sliding surface in a nonlinear system using numerical simulation. The discontinuous behaviors are depicted as motion in a phase space governed by various hidden attractors, such as period doubling, period-m segments, and chaotic behavior, with varying interactions with the sliding mode.

A finite element based approach for nonlocal stress analysis for multi-phase materials and composites

AbstractThis study proposes a numerical method for calculating the stress fields in nano-scale multi-phase/composite materials, where the classical continuum theory is inadequate due to the small-scale effects, including intermolecular spaces. The method focuses on weakly nonlocal and inhomogeneous materials and involves post-processing the local stresses obtained using a conventional finite element approach, applying the classical continuum theory to calculate the nonlocal stresses. The capabilities of this method are demonstrated through some numerical examples, namely, a two-dimensional case with a circular inclusion and some commonly used scenarios to model nanocomposites. Representative volume elements of various nanocomposites, including epoxy-based materials reinforced with fumed silica, silica (Nanopox F700), and rubber (Albipox 1000) are subjected to uniaxial tensile deformation combined with periodic boundary conditions. The local and nonlocal stress fields are computed through numerical simulations and after post-processing are compared with each other. The results acquired through the nonlocal theory exhibit a softening effect, resulting in reduced stress concentration and less of a discontinuous behaviour. This research contributes to the literature by proposing an efficient and standardised numerical method for analysing the small-scale stress distribution in small-scale multi-phase materials, providing a method for more accurate design in the nano-scale regime. This proposed method is also easy to implement in standard finite element software that employs classical continuum theory.

MorphFlow: Estimating Motion in In-Situ Tests of Concrete

Abstract Background In situ Computed Tomography is a valuable tool to investigate failure mechanics of materials in 3D. For brittle materials with sudden fracture like concrete however, state-of-the-art methods such as Digital Volume Correlation fail to produce displacement fields that display the discontinuous behavior of load induced cracking correctly. Objective The main objective is to develop an algorithm that calculates displacement fields for large-scale in situ experiments on concrete. Methods The algorithm presented is based on a 3D Optical Flow method solved by a primal-dual procedure and equipped with a coarse-to-fine scheme based on morphological wavelets. The algorithm is publicly available. Our evaluation focuses on the beneficial use of morphological wavelets over classical ones, and on the ability to produce reliable results with limited data. Applying the primal-dual scheme to in situ tests and using morphological wavelets are novel contributions. Results The results show that our algorithm cannot only cope with large volume images, but also produces discontinuous displacement fields that yield high strain in fractured regions. It does not only perform better than state-of-the-art methods, but also achieves sufficient results on reduced data. The morphological wavelets play a key role in this finding - they even allow to deduce cracks of widths less than a voxel. Conclusion Displacement calculation for in situ tests of brittle materials requires voxel-accurate displacement fields that allow for discontinuities. The presented algorithm fulfills these requirements and therefore is a powerful tool for future understanding of failure mechanics in concrete.

Stochastic optimization of a mass-in-mass cell with piecewise hybrid nonlinear–linear restoring force

This article investigates the optimization under uncertainty of a mass-in-mass meta-cell for its potential use within a metamaterial. The specificity of the proposed mass-in-mass system stems from the hybrid nonlinear–linear stiffness at the inner level. It is well known that these systems are highly sensitivity to small perturbations in loading conditions or design parameters. In fact, the sensitivity is such that the system can exhibit discontinuous behaviors. Therefore the proposed optimization approach not only accounts for sources of uncertainties but also can handle discontinuous responses. The objective of the stochastic optimization is to find the stiffness properties of the mass-in-mass system which minimize the expected value of a specific efficiency metric. In order to better understand the system’s dynamic behavior and the origins of the discontinuities, slow invariant manifolds and frequency response curves are provided. The efficiency of the optimized system with hybrid stiffness is compared with that of a similar optimized system featuring pure cubic nonlinearity.

Multiphase Viscoelastic Non‐Newtonian Fluid Simulation

AbstractWe propose an SPH‐based method for simulating viscoelastic non‐Newtonian fluids within a multiphase framework. For this, we use mixture models to handle component transport and conformation tensor methods to handle the fluid's viscoelastic stresses. In addition, we consider a bonding effects network to handle the impact of microscopic chemical bonds on phase transport. Our method supports the simulation of both steady‐state viscoelastic fluids and discontinuous shear behavior. Compared to previous work on single‐phase viscous non‐Newtonian fluids, our method can capture more complex behavior, including material mixing processes that generate non‐Newtonian fluids. We adopt a uniform set of variables to describe shear thinning, shear thickening, and ordinary Newtonian fluids while automatically calculating local rheology in inhomogeneous solutions. In addition, our method can simulate large viscosity ranges under explicit integration schemes, which typically requires implicit viscosity solvers under earlier single‐phase frameworks.

Impact of Barrow’s entropy on topological classification of higher-dimensional black holes

In this paper, we explore the impact of Barrow’s entropy on the topological classification of d-dimensional black holes (BHs). Specifically, we examine the Gauss–Bonnet (GB) and singly rotating Kerr black holes (KBHs) as well as their AdS counterparts. We notice that Barrow’s entropy significantly influences the topological numbers of these BHs. To understand these effects, we use the thermodynamic domain — the space defined by thermodynamic variables like temperature and pressure — to study topologically inspired defects in the BHs. These defects are points in the thermodynamic domain where singular or discontinuous behavior occurs. By computing the winding numbers of these defects, which are integers that count how many times a loop around the defect encircles the origin, we can understand the local and global topology of the BHs. Our analysis suggest that the topological number [Formula: see text] derived from Barrow’s statistics differs from the one obtained using Gibbs–Boltzmann statistics. Furthermore, we observe that BHs can undergo topological phase transitions that characterize them in different thermodynamic topological classes. Overall, these findings demonstrate the importance of Barrow’s entropy in understanding the topological classification of BHs, and highlight the potential for further research in this area.

Discontinuous coarsening behavior and kinetics of L12 precipitate in high-entropy alloys

Coarsening is a metallurgical process that is related to solute transmission and system energy decrease. However, for the coarsening behavior of the L12 precipitate in high-entropy alloys, the influence of moving boundary is still an open question. Here, we found the moving boundary accelerates the discontinuous coarsening of L12 phase. The multiple defects-accelerated diffusion and continual particle-capturing ability of the moving boundary provide a high-efficiency solute transport for the fast-coarsening kinetics of L12 phase. In addition, a boundary-encountered assisted precipitate formation mechanism is also validated in the recrystallized area.

Measuring thermal contact resistance across solid and liquid interface mediums by thermal imaging technique: Applications on bearing steel

This study introduces a versatile method for measuring thermal contact resistance in bearing steel with solid–solid and liquid–solid interfaces using lock-in thermography (LIT) technique. The method relies on analyzing the lock-in thermal response across the layers of the bearing structure induced by periodic surface-laser heating. Thermal contact resistance is determined from the discontinuous behavior analysis of the thermal response at the solid–solid or liquid–solid contact interface, based on the resolved heat equation for the multilayered structure. The usability of the method is demonstrated through measurements conducted on a conventional bearing steel configuration, using air and lubricating oil as the interface mediums. Furthermore, the versatility of the method allows for investigating the impact of mechanical load on thermal contact resistance. This proposed approach represents an advanced tool for analyzing thermal contact resistance with applications beyond bearing steel to various multilayered materials. It has the potential to assist in enhancing thermal analysis, improving reliability, extending the lifetime, and reducing maintenance costs of different thermal engineering applications including bearings.

Crack layer modeling of butt-fusion joints induced slow crack growth in high-density polyethylene pipes

The design and reliability of high-density polyethylene (HDPE) pipes can be dictated by the damage tolerance of their butt-fusion joints. A slow crack growth (SCG) model based on the crack layer theory for HDPE pipes internal and external circumferential and butt-fusion joints cracks is developed to investigate the discontinuous SCG behavior and lifetime tf variations. Using the developed model, the discontinuous SCG patterns, jump lengths and lifetime tf can be accurately simulated. In addition, the effects of pipes standard dimension ratio, internal pressure, and temperature on the SCG behavior and tf are investigated. Compared to pipe cracks, it was found that butt-fusion induced SCG can reduce the pipe tf > 60 %. Unlike longitudinal cracks, tf of external circumferential cracks, were found shorter than the internal ones, mandating an earlier evaluation. The new SCG model shows good accuracy with the experimental results. The same substitute geometry approach used can be followed for othercomplex designs, which aids in establishing a fundamental methodology for more realistic lifetime predictions.

Nonlinear energy harvesting system with multiple stability

The nonlinear energy harvesting systems of the forced vibration with an electron-mechanical coupling are widely used to capture ambient vibration energy and convert mechanical energy into electrical energy. However, the nonlinear response mechanism of the friction induced vibration (FIV) energy harvesting system with multiple stability and stick-slip motion is still unclear. In the current paper, a novel nonlinear energy harvesting model with multiple stability of single-, double- and triple-well potential is proposed based on V-shaped structure spring and the belt conveying system. The dynamic equations for the energy harvesting system with multiple stability and self-excited friction are established by using Euler-Lagrangian equations. Secondly, the static characteristics of the nonlinear restoring force, the friction force, and the potential energy surfaces are obtained to show the nonlinear stiffness, multiple equilibrium points, discontinuous behaviors and multiple well responses. Then, the equilibrium surface of bifurcation sets for the autonomous system is given to show the third-order quasi zero stiffness (QZS3), fifth-order quasi zero stiffness (QZS5), double well (DW) and triple well (TW). The co-dimension bifurcation sets of the self-excited vibration system are analyzed and the corresponding phase portraits for the coexistent of multiple limit cycles are obtained. Furthermore, the analytical formula of amplitude frequency response of the approximated system are obtained by the complex harmonic method. The response amplitudes of charge, current, voltage and power of the forced electron-mechanical coupled vibration system for QZS3, QZS5, DW and TW are analyzed by using the numerically solution. Finally, a prototype of FIV energy harvesting system is manufactured and the experimental system is setup. The experimental works of static restoring forces, damping forcse and the electrical outputs are well agreeable with the numerical results, which testified the proposed FIV energy harvesting model.

Anchoring-mediated stick-slip winding of cholesteric liquid crystals.

The stick-slip phenomenon widely exists in contact mechanics, from the macroscale to the nanoscale. During cholesteric-nematic unwinding by external fields, there is controversy regarding the role of planar surface anchoring, which may induce discontinuous stick-slip behaviors despite the well-known continuous transitions observed in past experiments. Here we observe three regimes, namely, constrained, stick-slip, and sliding-slip, under mechanical winding with different anchoring conditions, and measure the corresponding forces by the surface force balance. These behaviors result from a balance of cholesteric elastic torque and surface torque, reminiscent of the slip morphology on frictional substrates [T. G. Sano et al., Phys. Rev. Lett. 118, 178001 (2017)10.1103/PhysRevLett.118.178001], and provide evidence of dynamics in static rotational friction.

A phase field-immersed boundary-lattice Boltzmann coupling method for fluid-structure interaction analysis

Fluid-structure interaction (FSI) is critical in numerous engineering and scientific applications. This paper presents a numerical model for FSI simulations that integrates the lattice Boltzmann method (LBM) for fluid dynamics, the phase field method (PFM) for structural deformation and fracture, and the immersed boundary method (IBM) for fluid-solid coupling. The fluid employs an explicit time integration scheme with a smaller time step than the solid, which uses an implicit time integration scheme, satisfying the CFL condition. During the synchronization of fluid-solid interaction information, a multi-substep strategy is applied. The IBM is implemented using the iterative velocity method for boundary treatment. This approach facilitates the information transfer between domains with different time steps, enhancing the coupling accuracy through iterative computation. The effectiveness of the improved immersed boundary-lattice Boltzmann (IB-LBM) has been verified by the classical cylindrical flow case, which effectively prevents the particle penetration phenomenon and improves the calculation accuracy. The phase field-immersed boundary-lattice Boltzmann method (PF-IB-LBM) is subsequently deployed to simulate the deformation of an aluminum plate under hydrostatic pressure and the aftermath of a dam-break impact on an elastic plate. Verification of the coupling method substantiates its feasibility and efficacy. In addition, the proposed PF-IB-LBM is implemented to simulate the entire process of structural deformation and failure in response to fluid dynamics, which further confirms its capability to predict discontinuous mechanical behaviors such as damage and crack propagation under intricate fluid flows. The results emphasize the flexibility and efficiency of the proposed approach, providing a robust framework for solving more complex scenarios in engineering FSI problems.

Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression

The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.

Micromechanical response of dual-hardening martensitic bearing steel before and after rolling contact fatigue

Material decay in bearing steels under rolling contact fatigue (RCF) leads to fatigue initiation and failure. This study examines the local structure-property relationship in decayed material through in-situ compression testing of micropillars prepared from a dual-hardening martensitic bearing steel (Hybrid 60) before and after RCF testing. The results demonstrate a pronounced enhancement in local yield strength for decayed regions (2200–2340 MPa) as compared to non-decayed regions (1755–1780 MPa). The higher initial stress for dislocations glide in the decayed regions and their discontinuous yield behavior are attributed to the presence of ferrite microbands. Crystal plasticity simulations corroborated these findings, showingincreased critical resolved shear stress (CRSS) and reduced strain hardening in decayed samples.

Analysis of discontinuous dynamical behaviors for a 3-DOF friction collision system with dynamic vibration absorber

Analysis of discontinuous dynamical behaviors for a 3-DOF friction collision system with dynamic vibration absorber

Shear thickening of cementitious suspensions: effect of high-volume fraction and hydration

The lubrication layer (LL) formed at the concrete–pipe interface plays a crucial role in facilitating concrete pumping. Shear thickening in this layer significantly affects concrete pumping. However, very few studies are available for understanding the onset and intensity of shear thickening of the LL. In this study, the effect of solid volume fraction (SVF), superplasticiser dosage, supplementary cementitious materials and hydration on the shear thickening (continuous and discontinuous) behaviour of cementitious suspensions were investigated. Results show that an increase in SVF reduces the shear thickening intensity for systems using ordinary Portland cement (OPC), whereas the intensity is amplified for systems with fly ash (FA) or ground granulated blast furnace slag (GGBS). An increase in superplasticiser dosage results in an early onset of shear thickening and increases the shear thickening intensity, regardless of the binder used. Systems including GGBS exhibit the highest shear thickening intensity, followed by OPC- and FA-based systems. Based on these results, it is evident that the superplasticiser dosage for OPC-based systems needs to be optimised based on the structural buildup, while, for FA- or GGBS-based systems, the superplasticiser dosage needs to be optimised based on shear thickening behaviour with respect to hydration.

Exploring discontinuous intentions of social media users: a cognition-affect-conation perspective.

Drawing on the cognition-affect-conation (C-A-C) framework, this study investigates how perceived information and social and system feature overload induce depression and anxiety, which leads to affect discontinuous intentions of the social media users. The data collected from 570 social networking site users in China are analyzed through structural equation modeling (SEM). The findings show that perceived information overload, perceived social overload, and perceived system feature overload directly affect depression and anxiety among social networking site users, which directly leads to discontinuous intentions. This study fulfills the identified need for an in-depth investigation of discontinuous behavior in social networking sites. The findings provide social networking site providers with guidelines on how to actively manage social networking site user's behavior to reduce the effects of negative emotions on social networking sites.

Averaging theory for heat transfer in circular hydraulic jumps with a separation bubble

Analytical investigations of heat transfer during the vertical impingement of an unsubmerged axisymmetric liquid jet on a horizontal plate have been limited to the regions ahead of the jump. This limitation is due to the complex flow physics in the jump region arising from sudden changes in the flow field. This is addressed in here by extending the averaging theory (AT) introduced by Bohr et al. (Phys. Rev. Lett., vol. 79, issue 6, 1997, pp. 1038–1041) which was further developed by Watanabe et al. (J. Fluid Mech., vol. 480, 2003, pp. 233–265), to describe the heat transfer problem in circular hydraulic jumps including separation. The applicability of the resulting theory to determine the temperature field in the jump region is evaluated using the data available in the literature and also by means of fully resolved numerical solutions. Good agreement is observed for moderate Prandtl numbers. However, for sufficiently high Prandtl numbers, deviations become notable. The reasons for the deviations according to their relevance are (i) monotonically decreasing temperature profile inherent to the AT, whereas the fully resolved numerical solutions exhibit a local maximum in the temperature profile away from the plate; and (ii) inapplicability of the concept of dividing the flow field into a region affected and a region unaffected by heat transfer according to the thermal boundary layer thickness. This concept leads to the overestimation of the temperature close to the wall and to the existence of a threshold Prandtl number, for which the thermal boundary layer thickness does not meet the free surface anymore. Around this threshold Prandtl number, the temperature field shows a discontinuous behaviour.

Normalized characterization of the causes of discontinuous yield and crystal orientation deflection mechanism of β-Ti alloy during high-temperature deformation

To investigate the changes in grain orientation resulting from dislocation slip systems and propose a novel approach to characterizing discontinuous yield behavior during hot deformation, Ti–6V–5Al–5Mo–5Cr–3Nb–2Zr-0.2Si alloy was melted using vacuum arc furnace and subjected to hot compressed at 740, 790, 840 and 890 °C, along with strain rates (ε˙) of 0.001, 0.01, 0.1 and 0.5 s−1. The results indicate that discontinuous yield is observed at temperatures (T) of 740 or 790 °C and ε˙ of 0.1 and 0.5 s−1. Discontinuous yielding occurs at all strain rates when T is 840 and 890 °C. The presence of discontinuous yield is only observed when the power dissipation value exceeds the critical value, which in this study is 0.2657. Notably, this is the first instance in which the power dissipation value has been utilized to characterize the presence of discontinuous yield. The microstructure of the discontinuous yield reveals the activation of dislocation slip in the β grain. The dislocation slip is initially activated in the <001> oriented β grains during hot compression, followed by activation in the adjacent <101> oriented β grains. When the power dissipation exceeds the critical value, the dislocations more readily spread to the <101> oriented β grains due to higher activation energy, which is an important reason for discontinuous yield. The <101> oriented β grains gradually deflect to <2−3−1> oriented and finally rotate to <001> oriented during the subsequent compression process, as a means of reducing deformation resistance.