Discontinuous Fields Research Articles

Isothermal extrusion of thicknesses and flanges on axisymmetrical workpieces

Technological scheme and ratios for calculating of the extrusion modes of thickenings and flanges on pipe workpieces are proposed. The viscous-plasticity state of the deformable material is accepted. The kinematics and power mode of the process are established using the extreme upper-boundary plasticity theorem with the involvement of the discontinuous fi eld of displacement velocities. Estimate of the continuity loss of the workpiece material is given. The diagram of the die tooling and sample of product are presented.

Calculation of technological modes of hot direct extrusion of viscous-plastic material

The relations for calculating of the extrusion technology modes are proposed. The material under conditions of hot deformation is assumed to be viscoplastic, relaxing due to creep. The energy equation of equilibrium applied to the discontinuous fi eld of displacement velocities and the damage kinetics equations to the deforming material are used. Calculation and technological data and product samples are given.

Control Volume Isogeometric Analysis for groundwater flow modeling in heterogeneous porous media

Many important groundwater transport applications require solving the Darcy flow in heterogeneous porous media. Flow simulations, especially in large, highly heterogeneous aquifers, require extensive computational resources, a multiresolution (multiscale) approach to resolve the different heterogeneity scales and an accurate calculation of the velocity field. Common methods, such as finite volumes and elements, assume a discontinuous conductivity field introducing velocity discontinuities along the cell or element interfaces due to using classic discrete operators or Lagrangian basis functions. Over the last decade, the development of isogeometric analysis (IGA) eliminates many of the aforementioned limitations bridging the gap between CAD and numerical analysis. Since classic IGA uses the Galerkin and collocation approach, in this paper, we present a third concept in the form of Control Volume IsoGeometric Analysis (CV-IGA) enabling local and global mass conservation as well as multiresolution description of all heterogeneity scales. Due to the approximation properties of spline basis functions, the velocity field and its derivatives are continuous and are obtained by an optimal convergence rate. The CV-IGA methodology is verified with 2-D numerical and stochastic benchmark flow simulations, including comparisons with classic methods and two other IGA formulations as well as the convergence analysis of the head and velocity fields for different orders of Fup and B-spline basis functions.

An asynchronous and task-based implementation of peridynamics utilizing HPX—the C++ standard library for parallelism and concurrency

On modern supercomputers, asynchronous many task systems are emerging to address the new architecture of computational nodes. Through this shift of increasing cores per node, a new programming model with the focus on handle the fine-grain parallelism of this increasing amount of cores per computational node is needed. Asynchronous Many Task (AMT) run time systems represent an emerging paradigm for addressing fine-grain parallelism since they handle the increasing amount of threads per node and concurrency. HPX, a open source C++ standard library for parallelism and concurrency, is one AMT which is confirm with the C++ standard. Which means that HPX's Application Programming Interface (API) is confirm with its definition by the C++ standard committee. For example for the concept of futurization the hpx:future can be replaced by std::future without breaking the API. Peridynamics is a non-local generalization of continuum mechanics tailored to address discontinuous displacement fields arising in fracture mechanics. As many non-local approaches, peridynamics requires considerable computing resources to solve practical problems. This paper investigates the implementation of a peridynamics EMU nodal discretization in an asynchronous task-based fashion. The scalability of asynchronous task-based implementation is to be in agreement with theoretical estimations. In addition, to the scalabilty the code is convergent for implicit time integration and recovers theoretical solutions. Explicit time integration, convergence results are presented to showcase the agreement of results with theoretical claims in previous works.

Periodic smoothing splines for FFT-based solvers

The aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An automatic smoother based on polynomial splines is developed, which permits to add smoothness to initial material properties. The method, which is applied in various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields and reduces spurious oscillations.

Hybrid Large Eddy Simulation for low-order Discontinuous Galerkin methods using an explicit filter

In this paper we present a simple, easily implemented and effective approach for explicitly-filtered Large Eddy Simulation with a Discontinuous Galerkin (DG) discretisation for velocity. DG formulations are often desirable due to their stability and increased accuracy, however this can come at greater computational expense due to the additional degrees of freedom in the velocity field. Additionally, data output can also be an issue, due to the increased storage requirements. Here we present a hybrid approach, based upon the construction of an approximation of the velocity shear tensor using information from a projected Continuous Galerkin (CG) version of the discontinuous velocity field. The resulting turbulence algorithm is implemented within Fluidity, an open-source computational fluid dynamics solver. The model is then validated with a well known test case, and shown to agree favourably with published results. Comparisons are also made between the CG/DG hybrid LES with DG-only LES, which demonstrate the superior computational performance of the hybrid model.

A mechanical model to interpret distributed fiber optic strain measurement at displacement discontinuities

Distributed fiber optic (strain) sensing, which provides the unique advantage of sensing damage (e.g. cracking) at locations that are not known a priori, has been increasingly used in civil engineering. Quantitative crack measurement requires the translation of a discontinuous displacement field at the crack to a continuous strain deformation in the fiber. The main purpose of this article is to develop a mechanical model to explain the fiber deformation in the presence of a displacement discontinuity. The proposed mechanical model is validated with experimental results from cable calibration tests and concrete cracking tests. The model is extended to simulate the effects of multiple closely spaced cracks on fiber optic strain measurement, and this model is used to create an algorithm to automatically distinguish multiple cracks in distributed fiber optic (strain) sensing strain distributions. Using the model and two shape parameters, kurtosis and standard variation, the effects of cable properties (i.e. shear stiffness between cable and fiber, cable radius, elastic modulus, and interface cohesion) on the shape of fiber optic strain distributions across cracks are also quantified. The results provide an indication of beneficial cable properties for various measurement objectives.

Dynamic Identification of HTS Maglev Module for Suspended Vehicle by Using a Single-Degree-of-Freedom Generalized Bouc–Wen Hysteresis Model

The energy dissipation phenomenon of a high-temperature superconducting (HTS) magnetic levitation (Maglev) transport system is investigated by using a single degree of freedom generalized Bouc–Wen hysteresis model. The Maglev system under test consists of a bogie with HTS skaters, which interacts with permanent magnets distributed on the guideways; thanks to a passive and self-balanced magnetic interaction, the vehicle is suspended and guided in all phases of the motion, including zero speed. The response of the HTS skate is tested under pseudo-static cyclic load in the vertical and lateral directions. The parameters of the generalized Bouc–Wen (GBW) model are calibrated on the experimental hysteresis loops using an ordinary least squares–based algorithm. The vertical dynamics of the levitating HTS skate is affected by the magnetic field discontinuities of the guideway. The dissipated hysteretic energy is simulated to assess the dependence on the velocity and pattern of the magnetic field. The displacement response is obtained by solving the nonlinear differential equation representative of the moving HTS skater, modelled as a single degree of freedom system, whose interactions with the magnetic guideway are described by the identified GBW hysteresis law.

An extended finite element method formulation for modeling multi-phase boundary interactions in steady state heat conduction problems

The present paper proposes an XFEM formulation for heat transfer analysis of multi-phase materials with explicit treatment of boundary interactions. The existence of interfacial resistance at the boundaries of the material phases produces discontinuities in the temperature field and a standard finite element treatment would require complex domain discretizations and additional surface elements to capture the jumps of the temperature values. To overcome this problem, the proposed method captures these jumps by enriching the temperature field around the phase boundaries with appropriate discontinuous functions. Specifically, a new XFEM enrichment scheme is developed to address the issue of multiple-phase junctions, that is, areas where multiple boundaries with different properties intersect. This approach offers the advantage of bypassing the need for complex meshes required by the standard FE method and thus it significantly simplifies the analysis procedure. The elaborated methodology is first validated with existing results from the literature on heat conduction in polycrystalline materials. Then, a detailed model for heat conduction analysis of polymers reinforced with carbon-nanotubes is introduced, which takes into account the role of the interfacial resistance between different material phases. Even though the proposed method is demonstrated in heat conduction problems, it can be straightforwardly extended to other similar problem types, such us electrical conduction or equivalent mechanical properties.

Monitoring structural behaviour of concrete beams reinforced with steel and GFRP bars using acoustic emission and digital image correlation techniques

The paper investigates the flexure behaviour and cracking pattern of reinforced concrete beams utilizing steel and GFRP reinforcement using a judicious combination of non-destructive testing techniques of Acoustic Emission (AE) and Digital Image Correlation (DIC). AE parameters including amplitude, number of AE hits, average frequency (AF) and rise angle (RA) successfully correlate with cracking initiation and its progression in steel reinforced concrete (RC) and GFRP RC beams. The plot between AF-RA value effectively classifies the different failure modes in the two types of beams. Simultaneous drop in AF and a significant jump in AE duration at the same instant give a fair indication of critical failure points. AE-XY plots and longitudinal strain profiles obtained from DIC give a real-time representation of progressive AE activity and strains respectively. While AE is proposed to characterize the onset and propagation of the cracking pattern and mode of failure in the beams, DIC assists to visualize the displacement and strain fields while highlighting discontinuities in the displacement field. The work is aimed at developing a health monitoring strategy for RC beams with steel or GFRP bars which is in-situ, non-invasive and provides pre-emptive warning in real-time so that catastrophic failures can be completely avoided.

Mixed finite element formulation based on the discontinuous stress approximation

The paper is devoted to the development of the mixed form of finite element method for the calculation of constructions and structures. We consider the approach based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. Using the given approach, solutions of some problems were obtained and analyzed, in particular, the calculation of the cantilever beam-wall. The results obtained were compared with the decisions on the FEM in displacements and stresses, as well as with the exact solutions. It is shown that solutions based on the approximation of discontinuous stress fields in mixed form FEM converge to exact values from below and are more flexible in comparison with the solutions obtained by FEM in displacements. In addition, the accuracy of determining stresses is higher here.

A Displacement Discontinuity Method of High-Order Accuracy in Fracture Mechanics

In this paper the displacement discontinuity method of high-order accuracy and its application to the problems of fracture mechanics are considered. In common practice of applications of boundary element methods, the methods with the piecewise-constant function of boundary displacement are often used. Their advantage against other algorithms is the simplicity of calculation scheme with a rather good accuracy of the solution at the points of region distant from the boundary. In the fracture mechanics (with lines of surfaces of discontinuity of the displacement field), it is required to describe the stress behavior in the proximity of the crack edges with the highest accuracy possible, which leads to necessity of increasing the degree of accuracy of the used numerical methods. It is shown that the methods with high-order continuity of displacements at the boundary proposed in this work substantially improve the accuracy of computation of displacement and stress fields in the neighborhood of crack edges within the region.

A new look at the causes of “polarization” horns in electromagnetic well logging

So-called polarization horns appear in electromagnetic well logs when the sondes move through the interface between formations of different conductivities. Since the early 1990s, peaks in the logs have been attributed to the influence of surface charges due to the presence of electric field components perpendicular to the interfaces. A new analysis finds that surface charges should not be pinpointed as the immediate cause for the appearance of interface peaks in electromagnetic logs from any tool operating in any frequency range. This is accomplished by calculating the derivatives of the magnetic field components with respect to the sonde’s vertical position as it crosses the interface between two homogeneous isotropic media. The mathematical expressions reveal the components with smooth transitions and the ones with discontinuities in their rates of change across the interface. The analysis is applied to the four components needed to simulate the responses of coaxial and coplanar coil configurations in dipping logs. The results show that only the horizontal field from a horizontal dipole source suffers an influence from the current density field perpendicular to the interface between the two media, which gives rise to surface charges, but even for this component, the nonsmooth transitions are not associated with the perpendicular current. An anisotropic example gives further support to the conclusion that the polarization horns are associated with the discontinuous current density field parallel to the interface rather than with the continuous current across the interface.

A dual interpolation boundary face method for 3D elasticity

The dual interpolation boundary face method (DiBFM) proposed recently has been successfully applied to solve various problems in two dimensions. Compared with the conventional boundary element method (BEM), it has been proved that the DiBFM has the advantages of higher accuracy, convergence rate and computational efficiency. In addition, the DiBFM is suitable to unify the conforming and nonconforming elements in the BEM implementation, as well as to approximate both continuous and discontinuous fields. Moreover, there are no geometric errors by the DiBFM in the computational process. In this paper, the DiBFM is extended successfully to solve the elasticity problems in three-dimensions (3D) with formulations derived in details. A number of numerical examples are presented in order to validate the accuracy and convergence rate of the proposed method.

Upper bound finite element limit analysis method with discontinuous quadratic displacement fields and remeshing in non-homogeneous clays

As is known, limit analysis is a common way to study stability and failure mechanism of geotechnical engineering. This paper presents an upper bound finite element limit analysis (UB-FELA) formulation for non-homogeneous clays using discontinuous quadratic displacement fields and second-order cone programming (SOCP). The details are provided about the application of SOCP to the UB-FELA formulation for non-homogeneous clays. To reduce the calculation error, the analytic expressions are proposed concerning the rate of external work done by body forces and power dissipation caused by the plastic deformation following discontinuous quadratic displacement fields. With SOCP solver MOSEK, large-scale optimization problems of UB-FELA can be achieved in minutes via a desktop computer. The method is then applied to analyzing the stability of an undrained square tunnel and an undrained plane strain heading. The numerical results are compared with those reported in related studies. This method helps to obtain highly precise upper bound solution and clear failure mechanism of the computational domain.

Crack Propagation Velocity Determination by High-speed Camera Image Sequence Processing.

The determination of crack propagation velocities can provide valuable information for a better understanding of damage processes of concrete. The spatio-temporal analysis of crack patterns developing at a speed of several hundred meters per second is a rather challenging task. In the paper, a photogrammetric procedure for the determination of crack propagation velocities in concrete specimens using high-speed camera image sequences is presented. A cascaded image sequence processing which starts with the computation of displacement vector fields for a dense pattern of points on the specimen’s surface between consecutive time steps of the image sequence chain has been developed. These surface points are triangulated into a mesh, and as representations of cracks, discontinuities in the displacement vector fields are found by a deformation analysis applied to all triangles of the mesh. Connected components of the deformed triangles are computed using region-growing techniques. Then, the crack tips are determined using the principal component analysis. The tips are tracked in the image sequence and the velocities between the time stamps of the images are derived. A major advantage of this method as compared to the established techniques is in the fact that it allows spatio-temporally resolved, full-field measurements rather than point-wise measurements. Furthermore, information on the crack width can be obtained simultaneously. To validate the experimentation, the authors processed image sequences of tests on four compact-tension specimens performed on a split-Hopkinson tension bar. The images were taken by a high-speed camera at a frame rate of 160,000 images per second. By applying the developed image sequence processing procedure to these datasets, crack propagation velocities of about 800 m/s were determined with a precision in the order of 50 m/s.

Representation of discontinuous seismic velocity fields by sigmoidal functions for ray tracing and traveltime modelling

SUMMARYWave-modelling methods based on asymptotic ray theory have a lower computational cost than full wave-equation methods but require a smooth velocity field, though discontinuities may be handled by imposing interface conditions between adjacent blocks. We propose to approximate discontinuous velocity fields with model parametrizations based on smooth, rapidly varying functions known as sigmoidal functions. We have implemented the proposed technique on Cartesian grids using the wavelet theory formalism. Numerical experiments with 2-D and 3-D initial-value and two-point ray tracing in heterogeneous media show that the ray paths and traveltimes produced with the sigmoidal representation are consistent with the results produced by conventional ray tracing in block structures, broadening the scope of classical algorithms based on smooth velocity fields.

The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

In this article, peridynamic (PD) theory is applied to analyze two-dimensional heat conduction of thermoelectric plate with discontinuities. It is a well-known fact that heat flux is undefined at the crack tip and causes the temperature field across the crack surface discontinuous. Hence, numerical procedures like finite element method (FEM) became unsuccessful to capture details of moving discontinuities like growing cracks. Therefore, this article proposes a PD theory that is appropriate in resolving moving discontinuities in thermal and electric fields. The PD equations were constructed by writing the continuum-based electrical potentials and temperature fields in the form of their respective non-local integrals that are remarkably powerful in solving continuum problems whether the authors have moving discontinuities or not. To elucidate the trustworthiness of the PD theory, the results in the case of stationary cracks are compared with the one from FEM and witnessed that they were in good agreement.

Extended finite volume method with enriched HPCK shape functions for dynamic crack propagation modeling

In the present work, an extended finite volume method (EFVM) is incorporated with the enriched hp-cloud approximate function which has Kronecker delta property (EHPCK) for modeling crack propagation in 2D media. In this approximation function, appropriate crack path enrichment and crack tip enrichment functions are considered for modeling the discontinuous displacement field of cracked bodies. Unlike the conventional FVM approach, in the proposed EFVM, excessive control volumes (CVs) are embedded inside the main CVs which are called here as enrichment control volumes (ECVs). The EFVM method doesn't restrict the crack propagation path to obey any predefined path or edges of control volumes. To increase the prediction accuracies, the subtriangular technique is applied for the integration on the cracked control volumes. Capability of introduced EFVM is investigated by solving different problems such as dynamic stress intensity factor calculations and dynamic crack propagation.

Effective interactions mediated between two permeable disks in an active fluid

We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.