Discontinuous Fields Research Articles

Thermal buckling response and fracture analysis for delaminated fiber reinforced composite plates under thermo-mechanical coupling

Fiber reinforced composites are often subjected to severe thermal-mechanical coupling loads. In order to predict the stiffness and strength of the designed composites, thermal buckling response of the delaminated fiber reinforced composite plates and fracture analysis along the delamination front under thermo-mechanical coupling are investigated based on the generalized layerwise plate theory. Delamination between individual layers is considered as discontinuities in the displacement field using Heaviside step functions in the finite element model of delaminated composite plates. Governing equations are derived using virtual work principle and fracture analysis is performed by calculation of the strain energy release rate along the delamination front by means of the virtual crack closure technique. The effect of laying angle, delamination size, and delamination position on the critical thermal buckling temperature of laminated composite plates are investigated. Numerical results reveal that the critical thermal buckling temperature is insensitive to the delamination size less than an ‘irrelevant size’ and then significantly decreases with the increase of delamination sizes. The inside delamination has a greater influence on the critical thermal buckling temperature than the outside delamination. The maximum values of strain energy release rate always occur in the ‘equivalent material direction’ when the delamination is located in the middle of composite plates, while it is determined by laying angle and delamination position together for non-middle plane delamination.

Discontinuous Galerkin Method Using Laguerre Polynomials for Solving a Time-Domain Electric Field Integral Equation

A discontinuous Galerkin time-domain electric field integral equation method based on a marching-on-in-degree (MOD) scheme for simulating transient responses of perfect electric conductor objects is proposed in this letter. With the help of half-Rao–Wilton–Glisson spatial basis functions, we can simulate transient scattering responses of three-dimensional structures with either conformal or nonconformal meshes. The weighted Laguerre polynomials are chosen as temporal basis functions and implemented for the MOD scheme. Under such circumstances, the developed algorithm eliminates late-time instabilities and the limitation of Courant–Friedrichs–Lewy criteria. In addition, we adopt a fast-Fourier-transform-based blocking scheme to accelerate the temporal convolution of the MOD procedure. Some numerical examples are given to validate its stability and accuracy.

Interaction of the Interplanetary Shock and IMF Directional Discontinuity in the Solar Wind

AbstractThe solar wind is not stationary and variations of the magnetic field magnitude and/or direction and plasma parameters are frequent. Interactions of fast forward shocks and interplanetary magnetic field discontinuities with the bow shock were analyzed in details theoretically as well as experimentally. However, an oblique interaction between a fast‐forward interplanetary shock and a directional interplanetary magnetic field discontinuity was studied only within the framework of the ideal magnetohydrodynamics. A fortunate position of six spacecraft on 22 June 2015 facilitates detailed observations of an interplanetary shock modification due to the interaction with the directional discontinuity in the solar wind. We present a multispacecraft analysis of the event supported with magnetohydrodynamic (MHD) modeling showing that this interaction can lead to a bifurcation of the velocity jump across the shock.

Quasistatic elastoplasticity via Peridynamics: existence and localization

Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years. We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive $\Gamma$-convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero.

Investigating the anatomy of magnetosheath jets – MMS observations

Abstract. We use Magnetosphere Multiscale (MMS) mission data to investigate a small number of magnetosheath jets, which are localized and transient increases in dynamic pressure, typically due to a combined increase in plasma velocity and density. For two approximately hour-long intervals in November, 2015 we found six jets, which are of two distinct types. (a) Two of the jets are associated with the magnetic field discontinuities at the boundary between the quasi-parallel and quasi-perpendicular magnetosheath. Straddling the boundary, the leading part of these jets contains an ion population similar to the quasi-parallel magnetosheath, while the trailing part contains ion populations similar to the quasi-perpendicular magnetosheath. Both populations are, however, cooler than the surrounding ion populations. These two jets also have clear increases in plasma density and magnetic field strength, correlated with a velocity increase. (b) Three of the jets are found embedded within the quasi-parallel magnetosheath. They contain ion populations similar to the surrounding quasi-parallel magnetosheath, but with a lower temperature. Out of these three jets, two have a simple structure. For these two jets, the increases in density and magnetic field strength are correlated with the dynamic pressure increases. The other jet has a more complicated structure, and no clear correlations between density, magnetic field strength and dynamic pressure. This jet has likely interacted with the magnetosphere, and contains ions similar to the jets inside the quasi-parallel magnetosheath, but shows signs of adiabatic heating. All jets are associated with emissions of whistler, lower hybrid, and broadband electrostatic waves, as well as approximately 10 s period electromagnetic waves with a compressional component. The latter have a Poynting flux of up to 40 µW m−2 and may be energetically important for the evolution of the jets, depending on the wave excitation mechanism. Only one of the jets is likely to have modified the surrounding magnetic field into a stretched configuration, as has recently been reported in other studies. None of the jets are associated with clear signatures of either magnetic or thermal pressure gradient forces acting on them. The different properties of the two types also point to different generation mechanisms, which are discussed here. Their different properties and origins suggest that the two types of jets need to be separated in future statistical and simulation studies. Keywords. Magnetospheric physics (magnetosheath; plasma waves and instabilities; solar wind–magnetosphere interactions)

Qualitative Analysis of Crossing Limit Cycles in a Class of Discontinuous Liénard Systems with Symmetry

In this paper, we investigate some qualitative properties of crossing limit cycles for a discontinuous symmetric Lienard system with two zones separated by a straight line. In each zone, it is a smooth Lienard system. Firstly, by Poincare mapping method and geometrical analysis, we provide two criteria concerning the existence, uniqueness and stability of a crossing limit cycle. Secondly, we consider the position problem of the unique crossing limit cycle. Several lemmas are given to obtain an explicit upper bound of amplitude of the limit cycle. Finally, an application to van der Pol model with discontinuous vector field is given, and Matlab simulations are presented to illustrate the obtained theoretical results.

Subwavelength light confinement and enhancement enabled by dissipative dielectric nanostructures.

Dissipative loss in optical materials is considered one of the major challenges in nano-optics. Here we show that, counter-intuitively, a large imaginary part of material permittivity contributes positively to subwavelength light enhancement and confinement. The Purcell factor and the fluorescence enhancement of dissipative dielectric bowtie nanoantennas, such as Si in ultraviolet (UV), are demonstrated to be orders of magnitude higher than their lossless dielectric counterparts, which is particularly favorable in deep UV applications where metals are plasmonically inactive. The loss-facilitated field enhancement is the result of a large material property contrast and an electric field discontinuity. These dissipative dielectric nanostructures can be easily achieved with a great variety of dielectrics at their Lorentz oscillation frequencies, thus having the potential to build a completely new material platform boosting light-matter interaction over broader frequency ranges, with advantages such as bio-compatibility, CMOS compatibility, and harsh environment endurance.

Regional precipitation estimations in Central America using the Weather Research and Forecast model

Abstract: Using the regional climate model WRF, and the NCEP-NCAR Reanalysis Project data as boundary and initial conditions, regional precipitation for Central America was estimated by means of the dynamical downscaling technique for two selected periods: January 2000 and September 2007. Four-nested domains, d01, d02, d03 and d04 with a grid-resolution of 90 km, 30 km, 10 km, and 3.3 km respectively, were configured over this region. The runs were reinitialized every 5 days with 6 h of spin-up time for adjustment of the model. A total of eight experiments (four per month) were tested in order to study: a) two important Cumulus Parameterization Schemes (CPS): Kain-Fritsch (KF) and Grell-Devenyi (GD); and b) the physical interaction between nested domains (one- and two-way nesting), during each simulated month. The modeled precipitation was in agreement with observations for January 2000, and also captured the mean climate features of rainfall concerning magnitude, and spatial distribution, such as the particular precipitation contrast between the Pacific and the Caribbean coast. Outputs of the coarse domains (d01, d02, and d03) for September 2007 revealed differences between experiments within the domains when a visual comparison of the spatial distribution was made. However, for the inner grid (d04), all the experiments, showed a similar spatial distribution and magnitude estimation, mainly in those runs using one-way nesting configuration. The results for the month of September differed substantially with the observations, which could be related to associated deficiencies in the boundary condition that do not reproduce well the transition periods from warm to cold ENSO episodes for the selected periods of study. In all the experiments, the KF scheme calculated more precipitation than the GD scheme and it was associated to the ability of the GD scheme to reproduce spotty but intense rainfall, and apparently, this scheme was reluctant to activate, showing frequent events of low intensity rain. However, when rainfall did develop, it was very intense. Also, the time series did not replicate specific precipitation events. Thus, the 5-days integration period used in this study was not enough to reproduce short-period precipitation events. Finally, physical interaction issues between the nested domains were reflected in discontinuities in the precipitation field, which have been associated with mass field adjustment in the CPS. Rev. Biol. Trop. 66(Suppl. 1): S231-S254. Epub 2018 April 01.

Cracks in anisotropic media: pseudodifferential equations, wave fronts, and Irwin’s energy release rate extension

3D problems for plane cracks of arbitrary shape in anisotropic media are considered. The stress intensity factors are determined by the intensity factors of the crack displacement discontinuity field. Strong ellipticity of the constructed pseudodifferential operator is proved. The solution of the pseudodifferential operator of the crack theory is obtained by the specially constructed potentials with densities concentrated at the crack front. Irwin’s relation for the energy release rate is obtained for a plane crack of arbitrary shape in a medium with arbitrary elastic anisotropy.

Optimisation of the harvesting time of rice in moist and non-moist dispersed fields

Optimisation of the harvesting time of rice is significant for wheat growth and reducing the operational cost of harvesting rice in wheat-rice rotation regions. In China, rice grows in discontinuous and dispersed fields, and it is harvested with combine-harvesters provided by an agricultural machinery cooperative. The dispersed fields are divided into two types, moist and non-moist. The moist fields can be harvested only by a crawler-harvester, and the non-moist farmlands can be harvested by a crawler-harvester or a wheeled harvester. The objective of the agricultural machinery cooperative is to minimise the harvesting time of the rice. Minimising the differences in the operational time between different types of combine-harvesters is constrained. In this study, we proposed an operational model that considers using two different types of combine-harvester to harvest rice in dispersed fields with different soil moisture levels. Three versions of this operational model were derived for different types of farmland. Actual data from a village in Bengbu city were used to parameterise the model. The results indicate that optimisation significantly decreased the harvesting time of rice. The characteristics of the operational time of combine-harvesters are discussed separately to promote the efficient use of combine-harvesters.

Zeno breaking, the Contact effect and sensitive behaviour in piecewise-linear systems

Non-smooth approximations of steep sigmoidal switching networks, such as those used as qualitative models of gene regulation, lead to analytic and computational challenges that arise as a result of the discontinuities in the vector fields. In order to highlight the need for care in dealing with such systems, several particular phenomena are presented here through illustrative examples, including ‘Zeno breaking’, or computing beyond the finite time convergence of an infinite sequence of threshold transitions; the ‘Contact’ effect, in which in the discontinuous limit, trajectories can pass through a ‘saddle point’ without stopping, though these solutions are not unique and other solutions stop for arbitrary time intervals; and sensitive behaviour that arises from exotic dynamics within switching regions.

X-FEM Modeling of Multizone Hydraulic Fracturing Treatments Within Saturated Porous Media

In this paper, a fully coupled hydro-mechanical model is presented for the study of multizone hydraulic fracturing. The momentum balance equation of the bulk together with the mass balance and momentum balance equation of the fluid phase are employed in order to derive the hydro-mechanical coupled system of governing equations of the porous media known as the $$({\mathbf{u}} - p)$$ formulation. The hydro-fracture inflow is modeled based on the Darcy law, where the fracture permeability is determined by using the cubic law. Provisions are made for the plausible closure as well as the frictional resistance of the fracture edges in the solid phase by means of Kuhn–Tucker inequalities embedded in an X-FEM penalty method. In addition, for the fluid phase, the zero leak-off constrain is imposed through the application of the large time increment-based contact algorithm in the case of crack closure. The cohesive crack model is employed to account for the nonlinear fracturing process at the hydro-fracture tips. Multiple crack growth patterns are determined by means of energy based cohesive stress functions. Based on the X-FEM, the strong discontinuities in the displacement field due to fracture opening as well as the weak discontinuities within the pressure field due to leak-off flow are incorporated by using the Heaviside and modified level-set enrichment functions, respectively. A consistent computational algorithm is proposed for the determination of the fracturing fluid flow distribution across the existing perforations. Finally, several numerical examples are presented to demonstrate the robustness of the proposed X-FEM framework in the study of multizone hydraulic fracturing treatments through saturated porous media. The results appear to accord with the field observations reporting numerous failed attempts of multistage multizone fracturing treatments, which provide a great insight into the complexities encountered in practice.

Improving oncoplastic breast tumor bed localization for radiotherapy planning using image registration algorithms

Knowledge about tumor bed localization and its shape analysis is a crucial factor for preventing irradiation of healthy tissues during supportive radiotherapy and as a result, cancer recurrence. The localization process is especially hard for tumors placed nearby soft tissues, which undergo complex, nonrigid deformations. Among them, breast cancer can be considered as the most representative example. A natural approach to improving tumor bed localization is the use of image registration algorithms. However, this involves two unusual aspects which are not common in typical medical image registration: the real deformation field is discontinuous, and there is no direct correspondence between the cancer and its bed in the source and the target 3D images respectively. The tumor no longer exists during radiotherapy planning. Therefore, a traditional evaluation approach based on known, smooth deformations and target registration error are not directly applicable. In this work, we propose alternative artificial deformations which model the tumor bed creation process. We perform a comprehensive evaluation of the most commonly used deformable registration algorithms: B-Splines free form deformations (B-Splines FFD), different variants of the Demons and TV-L1 optical flow. The evaluation procedure includes quantitative assessment of the dedicated artificial deformations, target registration error calculation, 3D contour propagation and medical experts visual judgment. The results demonstrate that the currently, practically applied image registration (rigid registration and B-Splines FFD) are not able to correctly reconstruct discontinuous deformation fields. We show that the symmetric Demons provide the most accurate soft tissues alignment in terms of the ability to reconstruct the deformation field, target registration error and relative tumor volume change, while B-Splines FFD and TV-L1 optical flow are not an appropriate choice for the breast tumor bed localization problem, even though the visual alignment seems to be better than for the Demons algorithm. However, no algorithm could recover the deformation field with sufficient accuracy in terms of vector length and rotation angle differences.

Numerical simulation of liquid droplet breakup in supersonic flows

A five-equation model based on finite-difference frame was utilized to simulate liquid droplet breakup in supersonic flows. To enhance the interface-capturing quality, an anti-diffusion method was introduced as a correction of volume-fraction after each step of calculation to sharpen the interface. The robustness was guaranteed by the hybrid variable reconstruction in which the second-order and high-order method were respectively employed in discontinuous and continuous flow fields. According to the recent classification of droplet breakup regimes, the simulations lay in the shear induced entrainment regime. Comparing to the momentum of the high-speed air flows, surface tension and viscid force were negligible in both two-dimensional and three-dimensional simulations. The inflow conditions were set as Mach 1.2, 1.5 and 1.8 to reach different dynamic pressure with the liquid to gas density ratio being 1000 initially. According to the results of simulations, the breakup process was divided into three stages which were analyzed in details with the consideration of interactions between gas and liquid. The shear between the high-speed gas flow and the liquid droplet was found to be the sources of surface instabilities on windward, while the instabilities on the leeward side were originated by vortices. Movement of the liquid mass center was studied, and the unsteady acceleration was observed. In addition, the characteristic breakup time was around 1.0 based on the criterion of either droplet thickness or liquid volume fraction.

Effect of Heterogeneous Sediment Distributions on Hyporheic Flow in Physical and Numerical Models.

Variations in permeability have been found to significantly affect the flow of water though hyporheic systems, especially in regions with discontinuous transitions between distinct streambed lithologies. In this study, we probabilistically arranged two sediments (sand and sandy gravel) in a grid framework and imposed a single hyporheic flow cell across the grid to investigate how discontinuous permeability fields influence volumetric flow and residence time distributions. We used both a physical system and computer simulations to model flow through this sediment grid. A solution of blue dye and salt was pumped into the system and used to detect flow. We recorded the dye location using time-lapse photography and measured the electrolytic conductivity levels as the water exited the system as a proxy for salt concentration. We also used a computer simulation to calculate dye-fronts, residence times, and exiting salt concentrations for the modeled system. Comparison between simulations and physical measurements yielded strong agreement. In further simulations with 300 different grids, we found a strong correlation between volumetric flow rate and the placement of high permeability grid cells in regions of high hydraulic head gradients. One implication is that small anomalies in streambed permeability have a disproportionately large influence on hyporheic flows when located near steep head gradients such as steps. We also used moving averages with varying window sizes to investigate the effect of the abruptness of transitions between sediment types. We found that smoother permeability fields increased the volumetric flow rate and decreased the median residence times.

A Fast Discontinuous Galerkin Method for a Bond-Based Linear Peridynamic Model Discretized on a Locally Refined Composite Mesh

We develop a family of fast discontinuous Galerkin (DG) finite element methods for a bond-based linear peridynamic (PD) model in one space dimension. More precisely, we develop a preconditioned fast piecewise-constant DG scheme on a geometrically graded locally refined composite mesh which is suited for the scenario in which the jump discontinuity of the displacement field occurs at the one of the nodes in the original uniform partition. We also develop a preconditioned fast piecewise-linear DG scheme on a uniform mesh that has a second-order convergence rate when the jump discontinuity occurs at one of the computational nodes or has a convergence rate of one-half order otherwise. Motivated by these results, we develop a preconditioned fast hybrid DG scheme that is discretized on a locally uniformly refined composite mesh to numerically simulate the PD model where the jump discontinuity of the displacement field occurs inside a computational cell. We use a piecewise-constant DG scheme on a uniform mesh and a piecewise-linear DG scheme on a locally uniformly refined mesh of mesh size $$O(h^2)$$ , which has an overall convergence rate of O(h). Because of their nonlocal nature, numerical methods for PD models generate dense stiffness matrices which have $$O(N^2)$$ memory requirement and $$O(N^3)$$ computational complexity, where N is the number of computational nodes. In this paper, we explore the structure of the stiffness matrices to develop three preconditioned fast Krylov subspace iterative solvers for the DG method. Consequently, the methods have significantly reduced computational complexity and memory requirement. Numerical results show the utility of the numerical methods.

Горячее выдавливание внутренних ступеней на корпусах

A technological scheme and computation for the process of stage extrusion in housings of high-strength aluminum alloys are offered. Blank material is assumed to be viscoplastic during hot working, that is, deformation strengthening is followed by softening in view of viscous deformations growth (short-term creep). An extreme theorem of plasticity is used, in accordance with which the deformation kinematics defines the upper boundary assessment of pressure. The flow kinematics is defined with the aid of a discontinuous field of traverse speeds. At the same time a power in the deformation areas and on the surfaces of a speed gap is computed. The pressure of the operation is defined through a power equation of equilibrium in powers and depends upon strengthening and a rate of deformation. The assessment of damageability of blank material is given according to equations of the energetic and kinetic theories of strength at viscoplasticity. The calculated data and a product sample are shown.

Cohesive delamination and frictional contact on joining surface via XFEM

In the present paper, the complex mechanical behaviour of the surfaces joining two different bodies is analysed by a cohesive-frictional interface constitutive model. The kinematical behaviour is characterized by the presence of discontinuous displacement fields, that take place at the internal connecting surfaces, both in the fully cohesive phase and in the delamination one. Generally, in order to catch discontinuous displacement fields, internal connecting surfaces (adhesive layers) are modelled by means of interface elements, which connect, node by node, the meshes of the joined bodies, requiring the mesh to be conforming to the geometry of the single bodies and to the relevant connecting surface. In the present paper, the Extended Finite Element Method (XFEM) is employed to model, both from the geometrical and from the kinematical point of view, the whole domain, including the connected bodies and the joining surface. The joining surface is not discretized by specific finite elements, but it is defined as an internal discontinuity surface, whose spatial position inside the mesh is analytically defined. The proposed approach is developed for two-dimensional composite domains, formed by two or more material portions joined together by means of a zero thickness adhesive layer. The numerical results obtained with the proposed approach are compared with the results of the classical interface finite element approach. Some examples of delamination and frictional contact are proposed with linear, circular and curvilinear adhesive layer.

Generation of surface plasmon-polaritons by edge effects

By using numerical and analytical methods, we describe the generation of fine-scale lateral electromagnetic waves, called surface plasmon-polaritons (SPPs), on atomically thick, metamaterial conducting sheets in two spatial dimensions (2D). Our computations capture the two-scale character of the total field and reveal how each edge of the sheet acts as a source of an SPP that may dominate the diffracted field. We use the finite element method to numerically implement a variational formulation for a weak discontinuity of the tangential magnetic field across a hypersurface. An adaptive, local mesh refinement strategy based on a posteriori error estimators is applied to resolve the pronounced two-scale character of wave propagation and radiation over the metamaterial sheet. We demonstrate by numerical examples how a singular geometry, e.g., sheets with sharp edges, and sharp spatial changes in the associated surface conductivity may significantly influence surface plasmons in nanophotonics.

An Improved Fractional-Order Optical Flow Model for Motion Estimation

The Horn and Schunck (HS) optical flow model cannot preserve discontinuity of motion estimation and has low accuracy especially for the image sequence, which includes complex texture. To address this problem, an improved fractional-order optical flow model is proposed. In particular, the fractional-order Taylor series expansion is applied in the brightness constraint equation of the HS model. The fractional-order flow field derivative is also used in the smoothing constraint equation. The Euler-Lagrange equation is utilized for the minimization of the energy function of the fractional-order optical flow model. Two-dimensional fractional differential masks are proposed and applied to the calculation of the model simplification. Considering the spatiotemporal memory property of fractional-order, the algorithm preserves the edge discontinuity of the optical flow field while improving the accuracy of the estimation of the dense optical flow field. Experiments on Middlebury datasets demonstrate the predominance of our proposed algorithm.