Breaking Criterion Research Articles

Peridynamics model of torsion-warping: Application to lattice beam structures

This paper presents a finite deformation beam model based on Simo-Reissner theory in peridynamics (PD) framework to deal with torsion induced warping deformation. Seven degrees of freedom, viz. three translational, three rotational, and one warping amplitude are considered at each material point. The governing equations of the beam are obtained by employing global balance of linear and angular momenta in conjunction with Simo's assumption on the deformation field. The relation between PD resultant force, moment, bi-moment, and bi-shear states with their classical counterparts is established using the constitutive correspondence method. Numerical implementation strategy is furnished for both quasi-static and dynamic cases. The solution for quasi-static load is obtained through the Newton-Raphson method. The proposed model is validated against finite element solutions considering cantilever beam and lattice structures. Quasi-static deformation responses of 3 × 3 × 3 octet and single unit compression-torsion lattice structures are presented further to demonstrate the effectiveness of proposed beam model. A new bond breaking criterion is proposed based on critical stretch, critical relative rotation, and critical relative warping amplitude and failure of the compression-torsion lattice structures under compressive load is simulated. The Newmark-beta method is utilized to solve the governing equations for dynamic loading. Numerical simulations include dynamic analysis of octet and compression-torsion lattice structures.

Finite deformation peridynamics shell theory: Application to mechanical metasurfaces

A finite deformation Simo-Reissner peridynamics (PD) shell theory is developed to investigate wave propagation and crack growth in shell structures. Simo-Reissner deformation approximation is utilized to derive the governing equations of the proposed theory from the three-dimensional PD equation. Deformation states for the PD shell theory are identified from the reduced stress power equation. Classical shell constitutive equations are seamlessly incorporated in PD framework by constitutive correspondence approach where a particular form of the classical reduced stress power expression suitable for constitutive correspondence is used. Rotation tensor is updated using an exponential map. A new bond breaking criterion is proposed for PD shell based on critical stretch and critical relative rotation. The solutions of the PD shell governing equations for quasi-static and dynamic cases are obtained through the Newton-Raphson method and the Newmark-beta method, respectively. Numerical simulations include finite deformation of cylindrical shell under both quasi-static and dynamic loading conditions. The PD shell model is validated against finite element solutions obtained using ANSYS®. Crack propagation through the cylindrical shell is simulated under quasi-static and dynamic loading. Wave propagation through cylindrical shell embedded with periodically arranged holes and cracks is investigated. Significant wave attenuation and large bandgap demonstrates the efficacy of the present proposal.

Local-in-space wave breaking criteria for a generalized rod equation

A generalized rod equation including the celebrated Camassa–Holm shallow water model is considered. The blow-up features of the equation are discussed on the line R. Using the method to construct the Lyapunov functions, local-in-space wave breaking criteria to the equation are established. Our wave breaking results are only involved in the initial values V0(x0) and V0′(x0) at a single local point x0∈R.

Warps and breaks in circumbinary discs

ABSTRACT Disc warping, and possibly disc breaking, has been observed in protoplanetary discs around both single and multiple stars. Large warps can break the disc, producing multiple observational signatures. In this work, we use comparisons of disc time-scales to derive updated formulae for disc breaking, with better predictions as to when and where a disc is expected to break and how many breaks could occur. Disc breaking is more likely for discs with small inner cavities, cooler temperatures, and steeper power-law profiles, such that thin, polar-aligning discs are more likely to break. We test our analytical formulae using three-dimensional grid-based simulations of protoplanetary discs warped by the gravitational torque of an inner binary. We reproduce the expected warp behaviours in different viscosity regimes and observe disc breaking at locations in agreement with our derived equations. As our simulations only show disc breaking when disc viscosity is low, we also consider a viscous criterion for disc breaking, where rapid alignment to the precession vector can prevent a break by reducing the maximum misalignment between neighbouring rings. We apply these results to the GW Orionis circumtriple disc and find that the precession induced from the central stars can break the disc if it is relatively thin. We expect repeated or multiple disc breaking to occur for discs with sufficiently steep power-law profiles. We simulate a polar-aligning disc around an eccentric binary with steep power-law profiles and observe two separate breaking events at locations in rough agreement with our analytical predictions.

Finite deformation micropolar peridynamic theory: Variational consistency of wryness measure

This paper concerns developments in both classical and peridynamic (PD) finite deformation micropolar elasticity theory. The first part presents an alternative proof of a theorem that demonstrates variational consistency of the wryness measure in classical finite deformation micropolar elasticity which is one of the novel contributions of this work. The linearized version of the proposed wryness measure is compared with the wryness measure of small deformation micropolar elasticity. In the second part of this work, a finite deformation micropolar PD theory is presented. After proposing an additional integro-differential equation along with the standard PD equation of motion, the global balance of angular momentum is proved to be satisfied. The balance of virtual work is derived for the micropolar PD theory. Next, constitutive correspondence approach is used to relate PD force and moment states with their classical counterparts. The nonlocal versions of the strain and the proposed wryness measure are used in the constitutive correspondence. The constitutive equations of the classical micropolar theory are presented and how they can be incorporated in PD framework is discussed. We introduce a new bond breaking criterion for PD micropolar materials based on critical stretch and critical relative rotation. Quasi-static numerical simulations on deformations of plate with a hole and fracture of a double notched sheet are presented. Dynamic simulations concern wave propagation through a solid specimen and plate with a hole. Validation of the simulation results with the finite element solutions, boundary element solutions, and experimental observations demonstrate the potential of our approach.

Lagrangian approach to nonlinear waves in non-dispersive and dispersive rotating shallow water magnetohydrodynamics

A Lagrangian approach to both hydrostatic non-dispersive in the short-wave range and non-hydrostatic dispersive rotating shallow-water magnetohydrodynamics is developed, and used to analyse weakly and fully nonlinear waves described by the model. Hyperbolic structure in the non-dispersive case is displayed and Riemann invariants are constructed. Characteristic equations are used to establish criteria of breaking and formation of shocks by magneto-gravity waves, and conditions of the appearance of contact discontinuities in Alfvén waves. As in the case of non-magnetic rotating shallow water, rotation cannot prevent breaking. The Lagrangian equations of the model are reduced to a single partial differential ‘master’ equation, which is used to analyse the propagation of weakly nonlinear waves of both families, with or without weak rotation, and with or without weak short-wave dispersion. Corresponding modulation equations are constructed and their main properties sketched. The same master equation is used to obtain fully nonlinear finite-amplitude wave solutions in particular cases of no short-wave dispersion or no rotation.

Local-in-space wave breaking criteria for a shallow water wave equation

A shallow water wave equation including the famous Degasperis-Procesi model is considered. Firstly, the L 2 conservation law for the equation is derived. Secondly, using the methods of transport equation, we establish the boundedness of solutions for the shallow water wave equation. Finally, utilizing the approaches to construct Lyapunov functions, we find local-in-space wave breaking criteria of its solutions on the line R and circle S under certain restrictions on the coefficients of the equation.

Motion of a submerged body under a free surface and an ice cover in finite water depth conditions

In this study, we consider the motion of a submerged body near the free surface of a liquid and a liquid covered with an ice cover in finite water depth conditions. The influence of water depth on the nature of motion of a submerged body has been experimentally and theoretically analysed. The experiments were performed in an ice tank. The use of a cable towing system allowed the researchers to measure the magnitude of the relative vertical displacement of the submerged body resulting from the action of the lift force. The influence of ice cover on the relationship between the vertical displacement, trim angle, criterion for ice breaking, and speed of movement of the submerged body model was established. For theoretical research, the ice cover was modelled by a viscoelastic floating plate, and the submarine was modelled by a source–sinks system in a fluid flow. The influence of water depth, the presence of an ice cover, changes in the submergence depth, and the speed of movement of the submerged body on the wave resistance, lift force, and trimming moment were analysed. Theoretical results are supported by experimental data.

When Quantum Fluctuations Meet Structural Instabilities: The Isotope- and Pressure-Induced Phase Transition in the Quantum Paraelectric NaOH.

Anhydrous sodium hydroxide, a common and structurally simple compound, shows spectacular isotope effects: NaOD undergoes a first-order transition, which is absent in NaOH. By combining abinitio electronic structure calculations with Feynman path integrals, we show that NaOH is an unusual example of a quantum paraelectric: zero-point quantum fluctuations stretch the weak hydrogen bonds (HBs) into a region where they are unstable and break. By strengthening the HBs via isotope substitution or applied pressure, the system can be driven to a broken-symmetry antiferroelectric phase. In passing, we provide a simple quantitative criterion for HB breaking in layered crystals and show that nuclear quantum effects are crucial in paraelectric to ferroelectric transitions in hydrogen-bonded hydroxides.

2DH modelling and mapping of surfbeat-driven flooding in the shadow of a jettied tidal inlet

Near estuaries and harbours, submerged shoals and defence structures impact the exposure to overtopping. These features may be accounted for in two-dimensional horizontal (2DH) numerical models, either based on phase-resolving or phase-average solvers for wave propagation. In between, surfbeat solvers, such as in XBeach, combine an affordable computational cost with the ability to generate and propagate the longer infragravity (IG). However, surfzone wave characteristics and the overtopping exposure modelled with XBeach are sensitive to settings such as the shape of the forcing wave spectra and the numerical scheme for wave propagation. The present paper explores this sensitivity and assesses the performance of different inundation models built with the 2DH surfbeat solver of XBeach. These models were forced with downscaled water levels and directional wave spectra and the results fuelled a discussion bounded by data collected downdrift of the entrance to the harbour of Figueira da Foz (Portugal). The original second-order upwind scheme, which propagates short-waves with a lower numerical diffusion improved the model performance in terms of long-wave height, and an unconventional breaking criterion better represented the cross-shore distribution of short-wave height near the shore. A calibrated model was validated through the hindcast of an overtopping event observed under moderate swell forcing, and was used to map the overtopping exposure during a hypothetical combination of an energetic swell with a water level having a return period of ∼70 years. Compared to the default wave spectra shape and model settings, using an appropriate representation of the short-wave directional spectrum at the open boundary was necessary to reproduce the observed overtopping extent. Refining the cross-shore resolution of the model helped to better represent the observed inundation extents, as also did the reduction of the friction coefficient. Additional phase-resolving simulations in 1DH overestimated IG wave energy and produced higher and more frequent overtopping discharges. However, differences with the calibrated 2DH surfbeat model increased with the proximity of the inlet and with short-wave height and angle of incidence. Overall, required calibration steps were provided. They aim at making 2DH XBeach surfbeat a credible tool for 1) predicting short and IG wave characteristics until the shoreline, as well as for 2) providing first estimates of exposure to overtopping in areas with shallow and alongshore-irregular morphologies.

Estimation of breaking wave region based on coupled wave and storm surge simulations of historical typhoons: A case study of Hangzhou Bay

Breaking waves pose a serious threat to offshore structures. Estimating the breaking wave region is hence important for structural design and construction. This paper developed a numerical approach for estimating the breaking wave region based on the coupled wave and storm surge simulations of typhoons. The SWAN + ADCIRC coupling model was employed to hindcast the wave height, wave period, and storm surge under historical typhoons. The values of two breaking prediction variables at different mean return periods (MRPs) were calculated by probability models. The breaking wave region can then be estimated by either a univariate or bivariate probability model of the breaking prediction variables. The developed approach was illustrated using Hangzhou Bay as a case study. Hindcast simulations of 40 typhoons in the past 25 years were conducted. The effects of breaking criteria, probability model, and breaking threshold on the breaking wave region were investigated and discussed as a function of MRP. The main findings include that 1) the waves on the north shore of Hangzhou Bay break more easily; 2) the distribution and area of the estimated breaking wave region depend on the selection of breaking criteria and thresholds; and 3) neglecting the correlation between variables results in an underestimation of breaking wave hazards. This study provides engineers with an efficient tool to estimate the breaking wave hazards for projects located in tropical cyclone-prone sea areas.

The unified nonlocal peridynamics-based phase-field damage theory

The peridynamic correspondence model is a promising and attractive candidate for the modeling of localized failure in solids, in that it can incorporate many local classical damage constitutive models through introducing a nonlocal averaged deformation gradient. However, the zero-energy mode and the limited bond breaking criterion greatly restrict the potential applications of this correspondence model. To address these two problems, a unified nonlocal peridynamics-based phase-field damage theory is proposed within the framework of thermodynamics. Firstly, the unified correspondence principle for the displacement field is developed on the basis of the energy compensation method in such a way that a new peridynamic deformation gradient, shape matrix and force state are derived and redefined. And then, the proposed principle is applied to derive the nonlocal phase-field damage constitutive model that the general nonlocal phase-field flux, phase-field flow state and phase-field internal force are defined. Moreover, we propose a mixed variational derivative method to obtain the coupled equilibrium governing equation and present the general linearization approach of the proposed peridynamics-based phase-field model (PD-PFM), where the double states for the coupled displacement and phase fields are derived in detail. It will be found that PD-PFM can not only resolve the zero-energy mode existed in the conventional peridynamic correspondence model, but also provide a rational criterion for the breakage of the peridynamic bond. Some representative numerical examples including mixed mode fracture of single-material media and interface fracture of ceramic coating systems are presented for the validation of PD-PFM. The satisfactory results show both quantitative and qualitative agreement with the available experiment.

A novel fiberglass-reinforced polyurethane elastomer as the core sandwich material of the ship–plate system

Abstract A novel low-cost polyurethane (PU) elastomeric material reinforced with mat-form fiberglass for alternative ship material was developed. The hand lay-up technique was used to prepare samples with glass fiber contents of 0, 7, 9, 11, and 15% by weight. Several tests, including density, tensile, and hardness tests, have been conducted to investigate the effect of fiber content on the material properties of the developed materials. The test results found that only composites with 0% (PU) and 7% (PFg-7) fiberglass had met all Lloyd’s Register criteria. PFg-7 has a density of 1,098 kg/m3, a hardness of 66.15 shore-D, a tensile strength of 21.32 MPa, and an elongation at break of 47.06%, a higher hardness, elastic modulus, and yield strength than PU. PFg-15 achieved the highest density, hardness, tensile strength, elastic modulus, and yield strength, which were 1,228 kg/m3, 68.85 shore-D, 32.13, 2,176, and 30.89 MPa, respectively. The elastic modulus and yield strength of PFg-15 were 5.6 times and 3 times higher than those of PU but PFg-15 did not meet the elongation at break criteria. PFg-9, PFg-11, and PFg-15 showed brittle properties, as indicated by relatively high hardness, elastic modulus, and yield strength compared to the results from various references.

Characteristics of negative and undular surges in an impounded channel

ABSTRACT Physical experiments were conducted in an impounded channel to study the propagation of negative surges advancing in still water and evolution of undular surges against an instantaneously varied flow. The results demonstrated that the initial wave height of a negative surge could be accurately predicted using the simple wave solution of the Saint–Venant equations. Moreover, the wave height evolution during surge propagation could be satisfactorily described using the solution by Ippen and Kulin. The main characteristics of an undular surge were strongly correlated to the surge Froude number and turbulent boundary layer development at the toe of the surge. However, the occurrence of wave breaking at the first wave crest was independent of the inflow conditions and was close to the breaking criterion for solitary waves. Furthermore, the present results indicated the largest turbulent Reynolds stress components beneath the wave crests of an undular surge.

Unified stability criteria of electrostatically actuated initially curved micro-beams in the presence of curved electrodes

Following increasing interest in electrostatic actuation of curved beams via curved electrodes, a rigorous limit point and bifurcation analyses are carried out to view how the beam reacts when it is driven by a bell-shaped electrode. The culmination of the study lies in a set of criteria, specifying the conditions for bistability and symmetry breaking as a function of beam and electrode geometries. The study is based on a single and a two degree-of-freedom (DOF) reduced order (RO) models, derived via Galerkin’s decomposition, allowing an analytical extraction of a bistability condition, revealing the emergence of three limit points and a semi-analytical derivation of symmetry breaking criteria, for the emergence of bifurcation points. The former is based on the existence of a vanishing discriminant of a cubic equation, which forms a boundary in the geometrical space of both beam and electrode geometries. The extraction of the latter is carried out by demanding existence of two different bifurcation points on the one hand, and the crossing of either point to its respective stable region, on the other hand. The overall criteria show that while actuation voltages will indeed increase or decrease as a function of electrode curvature, along with its operational range, it plays a key role in determining both symmetric and asymmetric responses of the beam. Such results can serve researchers and engineers alike in designing curved beam-electrode systems for usage in future studies, promoting their usage in micro-electro-mechanical (MEMS) based applications.

Violation of German rest break regulation criteria and health complaints while working in the office and from home

The aim of this survey study (n = 534) was to clarify if work from home (WFH) affects employees’ compliance with six German mandatory rest break regulations and how this relates to health complaints. 92% reported at least one violation of these rest break principles. WFH (frequency) did not affect the (non-)compliance with these regulations but was associated with increased risk for muscular tension. Frequent break skipping increased risk of headache. Noncompliance with three or more of these rest break criteria related to risk of depressive mood and headache, and noncompliance related to risk of exhaustion in a dose-response relationships. WFH does not relate to violation of German rest break regulation criteria but is associated to musculoskeletal complaints. Organizations should improve employees’ compliance with national break standards since this can reduce health risks.

Large eddy simulation of focused breaking waves with different wave steepness

The profile of fluid field and wave geometry, kinematic and dynamic characteristics of focused breaking waves in finite water depth with different wave steepness are studied with a constant wave steepness wave focusing method in this paper. The flow field is solved by the two-phase flow model in REEF3D based on the incompressible Navier–Stokes equation and the Large Eddy Simulation (LES) model to simulate the complex breaking process. The numerical model is validated by comparing wave elevation of both focused non-breaking and breaking case with the experimental results and satisfactory agreements are achieved. A series of simulation cases with different global steepness are carried out to analyze the focused waves of different breaking types. The difference between the preset focused condition and the real ones and the area of air cavity rolled by the wave jets are both indicates that the process of wave focusing and breaking show a strong nonlinear profile. The maximum values of the horizontal velocity occur after the impingement moment and can reach 2.5 Cp for extreme steep waves. Three typical wave breaking criteria in finite water depth are calculated and discussed successively. For the geometric criterion analysis, the global wave steepness and local steepness have a good performance both for predicting wave breaking and presenting the breaking intensity. The kinematic breaking criterion ratio shows that the previous threshold 1 at the breaking incipient scenario is not sufficient to predict the wave breaking. Besides, it is found that the time interval when the kinematic breaking criterion ratio big than 1 may related to the wave breaking type. The energy changing rate for both the focusing and dissipation processes increase linearly with the global wave steepness and show a good ability as a dynamic breaking criterion and also prove the asymmetric profile of breaking waves.

Neutrino seesaw models at one-loop matching: discrimination by effective operators

Using the functional method, one-loop matching of the type-I, -II and -III see-saw models are investigated and the results are presented in both the Green’s and the Warsaw bases. Although these models generate the same dimension-5 Weinberg operator, they could induce quite different types of dimension-6 effective operators that can be utilized for model discrimination. We also find the threshold effects from one-loop matching could be significant, which turn out to allow triggering electroweak symmetry breaking radiatively in type-II seesaw while forbid that in type-I/-III models. An analytical criterion for such radiative symmetry breaking is also derived in type-II seesaw. Finally, we investigate the indirect signatures from different types of dimension-6 operators at high-energy colliders, low-energy precision experiments and forward physics facilities for model discrimination.

Mechanical Analysis and Structural Optimization of Air Hammer Drill Teeth Based on ANSYS /LS_DYNA

Air drilling is a prevailing technology of oil and gas energy industry in today’s world, it can solve problems when drilling in complex layer that can not be done by conventional drilling way. At the same time, some failures of dill bit teeth in air hammer drilling like teeth falling, breaking and severe abrasion seriously affect the drilling efficiency. Thus this paper intended to investigate rock breaking criteria and damage constitutive model, establish a finite element simulation model of single tooth rock breaking and use the impact of dynamic finite element software ANSYS/LS-DYNA to analysis characteristics of rock crushing under confining pressure, which includes fragmentation process, drilling tooth impact and the crush volume of rock broken. The study found that the tapered tooth has the highest efficiency in rock breaking under the same conditions and with edge teeth at 25°angle that increases the rock crushing volume significantly. In addition, the configuration of tooth surface was examined, which showed that the pattern of “spherical teeth in the middle and tapered teeth in the peripheral” has highest rock breaking efficiency.

Mechanical Analysis and Structural Optimization of Air Hammer Drill Teeth Based on ANSYS /LS_DYNA

Air drilling is a prevailing technology of oil and gas energy industry in today’s world, it can solve problems when drilling in complex layer that can not be done by conventional drilling way. At the same time, some failures of dill bit teeth in air hammer drilling like teeth falling, breaking and severe abrasion seriously affect the drilling efficiency. Thus this paper intended to investigate rock breaking criteria and damage constitutive model, establish a finite element simulation model of single tooth rock breaking and use the impact of dynamic finite element software ANSYS/LS-DYNA to analysis characteristics of rock crushing under confining pressure, which includes fragmentation process, drilling tooth impact and the crush volume of rock broken. The study found that the tapered tooth has the highest efficiency in rock breaking under the same conditions and with edge teeth at 25°angle that increases the rock crushing volume significantly. In addition, the configuration of tooth surface was examined, which showed that the pattern of “spherical teeth in the middle and tapered teeth in the peripheral” has highest rock breaking efficiency.