Discontinuous Fields Research Articles

Explicit solutions for multi-layered wide plates and beams with perfect and imperfect bonding and delaminations under thermo-mechanical loading

Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical loading. The expressions are general and apply to plates composed of an arbitrary number of layers, of arbitrary thickness and elastic/thermal properties, and where the interfaces between the layers may be imperfect and allow relative sliding. The closed-form solutions are obtained using a multiscale homogenized model which depends on only three displacement variables and overcomes limitations of current models based on discrete-layer approaches. The accuracy of the expressions in predicting the highly complex and discontinuous fields, which characterize the response of thick and highly anisotropic plates with interlayer damage and delaminations, is verified using exact 2D thermo-elasticity solutions. The asymptotic limits of the model/solution correspond to the problems of an intact and a multiply delaminated plate. They are derived using a perturbation technique, which also explains the multiscale dependence of the model on the parameters.

On producing sea ice deformation data sets from SAR-derived sea ice motion

Abstract. We propose a method to reduce the error generated when computing sea ice deformation fields from synthetic aperture radar (SAR)-derived sea ice motion. The method is based on two steps. The first step consists of using a triangulation of the positions taken from the sea ice trajectories to define a mesh on which a first estimate of sea ice deformation is computed. The second step consists of applying a specific smoother to the deformation field to reduce the artificial noise that arises along discontinuities in the sea ice motion field. This method is here applied to RADARSAT Geophysical Processor System (RGPS) sea ice trajectories having a temporal and spatial resolution of about 3 days and 10 km, respectively. From the comparison between unfiltered and filtered fields, we estimate that the artificial noise causes an overestimation of about 60% of opening and closing. The artificial noise also has a strong impact on the statistical distribution of the deformation and on the scaling exponents estimated with multifractal analysis. We also show that a similar noise is present in the deformation fields provided in the widely used four-point deformation RGPS data set. These findings may have serious implications for previous studies as the constant overestimation of the opening and closing could lead to a large overestimation of freezing in leads, salt rejection and sea ice ridging.

Active vibration control of smart composite laminates with partial debonding of actuator

The effect of actuator debonding on the performance of active vibration control is analytically investigated through an optimal control strategy. An improved layerwise theory with Heaviside step functions, which addresses discontinuous displacement fields, is used for modeling the actuator debonding. General finite element procedures are developed to derive the governing equation taking into consideration the electro-mechanical coupling effect. A reduced-order model based on the state-space model is adopted for the design of the active controller. Generally, debonding in actuators reduces their load carrying capability, dynamic properties and vibration control characteristics. The effect of debonding on the vibration control is investigated by the proposed analytical modeling. Numerical results using a 16-layer cross-ply laminate with healthy actuator and partially debonded actuator are given for the investigation of the vibration suppression efficiency and control effort. It is observed that the control authority of the composite laminates with partially debonded piezoelectric actuator is dramatically reduced by increasing the size of the actuator debonding. Since debonding failure may occur during the service life of smart composite laminates, the results showed that actuator debonding must be considered as an uncertainty parameter in the design of active controllers.

On the feasibility of crack propagation tracking and full field strain imaging via a strain compatibility functional and the Direct Strain Imaging method

The simultaneous tracking of the trajectory of a moving crack along with the measurement of the corresponding full field strain fields associated with this motion due to quasi-static or dynamic impact loading, is a problem of high interest from both the perspectives of the engineering practice and engineering science alike. However, full field optical methodologies have not yet been able to address the issues arising in experiments with moving boundaries such as dynamically evolving cracks. Such a problem requires solving simultaneously the problem of identifying the dynamically evolving geometry of the cracks as well as the problem of introducing these cracks into the full-field representation of a relevant full field method. In the present work we are introducing a methodology that can solve this problem. Specifically, we describe an optical method that can be used to detect dynamically evolving discontinuities on the surface of a body even if they are invisible to the eye, by using a strain compatibility functional that makes no continuity assumptions about the underlying medium. The relevant data from this process are then introduced in a full field representation that leads to an acceptable estimation of the discontinuous strain field. The proposed method is based on the recently introduced Direct Strain Imaging method that can be used to visualize and quantify the full fields of the strain tensor components. Synthetic numerical experiments were performed to generate synthetic crack propagation data along with the associated strain fields in order to assess the feasibility of the proposed method. The approach employed for this purpose was that of applying the extended finite element method to solve the problem of a propagating crack in an elastic medium with inclusions and holes under quasi-static tension. Finally, we present the results of detecting the synthetically produced crack trajectory as well as the relevant strain fields.

A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions

In computational simulations of hydraulic fracturing problems, consideration of interactions between the propagating fracture zone and the fluid flow through the porous material requires an appropriate up-scaling procedure from the spatial scale of the local crack, which usually is much smaller compared to the scale of typical finite elements in poromechanics problems. This scale transition refers to both the displacement field (discontinuity across cracks) as well as to the fluid flow (accelerated flow within cracks and the interaction with the flow in the bulk material). To resolve the small and the large scale portion of the solution, the Generalized Finite Element Method (GFEM) exploiting the partition of unity property of shape functions is used. Accordingly, the displacements u and the liquid pressure pl are locally enriched to better resolve their distribution in the vicinity of cracks by means of an additive decomposition into a large and a small scale part. As far as the representation of cracks is concerned, the Extended Finite Element Method (XFEM) is used by enriching the displacement field by means of a jump function as well as crack tip functions. In the framework of the GFEM physically motivated enrichment functions for the local enrichment of the C1 discontinuity of the liquid pressure field across cracks are proposed in the paper. The space and time variant analytical solutions obtained from the 1D transient response of saturated porous materials subjected to the liquid pressure within the crack are applied as enrichment functions to locally improve the approximation of the liquid pressure field at discontinuities. Applying these space and time variant functions, which are the exact solutions of the pressure field in the vicinity of cracks, as local enrichment functions lead to a significant improvement in the local approximation of the pressure field at discontinuities. The new GFEM model is formulated in a poromechanics framework for fully saturated porous materials. Representative analyses demonstrate the improvement of the solution quality compared to existing FEM and XFEM models.

A transport approach for analysis of shock waves in cellular materials

This paper is concerned with a new approach for analytical modelling of shock-like behaviour encountered with high velocity crushing of cellular materials. The presented methodology is founded on integral transport equations which describe the response of a control volume moving inside another moving control volume and thus provides a technique for the direct handling of material discontinuities such as shock waves. The transport approach (being based on integration as opposed to differentiation) is shown to readily accommodate discontinuities in physical fields. Control volume movement is described by means of judiciously defined velocity fields that account for shock movement and domain distortion. A feature of the approach is the realisation of governing differential equations whose derivatives reflect the movement of the transporting control volume, which also serve as a means to establish the exactness of proposed solutions.The transport approach is applied to investigate issues raised in the literature concerning discrepancies in results obtained from momentum and energy approaches. The ability of the transport approach to enforce global balances of energy and momentum reveal the correct approach to shock modelling in cellular materials. The efficacy of the method is demonstrated through its application to three case studies. The first two cases involve impact applied to the well-known Taylor-cellular bar and a rigid mass on a cellular bar; the results of which are shown to be exact agreement with the solutions provided in the literature. The third case study presents a new analytical solution for impact involving compacted material described with a Bingham plasticity model.

ON WEAK DISCONTINUITIES AND JUMP EQUATIONS ON WAVE SURFACES IN MICROPOLAR THERMOELASTIC CONTINUA

The present study is devoted to problem of propagating surfaces of weak and strong discontinuities of translational displacements, microrotations and temperature in micropolar (MP) thermoelastic (TE) continua. Problems of propagation of weak discontinuities in type-I MPTE continua are discussed. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. Weak discontinuities are discriminated according to spatial orientations of the discontinuities polarization vectors (DPVs). It is shown that the surfaces of weak discontinuities can propagate exist without weak discontinuities of the temperature field. Second part of the paper is concerned the discussions of the propagating surfaces of strong discontinuities of field variables in type-II MPTE continua. Constitutive relations for hyperbolic thermoelastic type-II micropolar continuum is derived by the field theory. The special form of the first variation of the action integral is used in order to obtained 4-covariant jump conditions on wave surfaces. Three-dimensional form of the jump conditions on the surface of a strong discontinuity of thermoelastic field are derived from 4-covariant form.

Coordinate‐invariant phase field modeling of ferro‐electrics, part I: Model formulation and single‐crystal simulations

AbstractAn electro‐mechanically coupled phase field model for ferroelectric domain evolution is introduced. Based on Gurtin's concept of a microforce balance, a generalized Ginzburg‐Landau evolution equation is derived from the second law of thermodynamics. The thermodynamic potential is formulated for transversely isotropic material behavior by adopting a coordinateinvariant formulation. The model is reduced to 2D and implemented into a finite element framework. The numerical simulations concern the microstructure evolution in mechanically clamped BaTiO3 single‐crystals. In the second part of this contribution Keip et al. [1], the poling behavior of ferroelectric composites and polycrystals is investigated with regard to size effects and the influence of a discontinuous order parameter field across grain boundaries. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Crack detection in concrete gravity dams using a genetic algorithm

The main aim of this paper is to introduce an efficient procedure for crack detection in concrete gravity dams. A genetic algorithm and finite-element modelling are employed to perform the optimisation tasks. A two-dimensional cracked element is formulated for non-linear analysis. In this investigation, the kinematics of the discontinuous displacement field in a body with an internal discontinuity is utilised. Based on the suggested interpolation functions for the discrete segments, and also the element displacement field, the element stiffness matrix is calculated. Moreover, a genetic algorithm approach for crack identification is proposed, which can identify the location and magnitude of cracks in concrete gravity dams. By minimising the difference between the analytical responses given by the authors' element and the measured ones, the genetic algorithm identifies the crack. Finally, several numerical examples are analysed for the accuracy test and a few of them are presented here.

Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method

Scalar CSAMT is only suitable for measurements in one and two dimensions perpendicular to geological structures. For complex 3D geoelectric structure, tensor CSAMT is more suitable. In this paper, we discuss 3D tensor CSAMT forward modeling using the vector finite-element method. To verify the feasibility of the algorithm, we calculate the electric field, magnetic field, and tensor impedance of the 3D CSAMT far-zone field in layered media and compare them with theoretical solutions. In addition, a three-dimensional anomaly in half-space is also simulated, and the response characteristics of the impedance tensor and the apparent resistivity and impedance phase are analyzed. The results suggest that the vector finite-element method produces high-precision electromagnetic field and impedance tensor data, satisfies the electric field discontinuity, and does not require divergence correction using the vector finite-element method.

Progress in high-resolution numerical simulation of explosion mechanics

nitride semiconductor material, microwave power device, power electronic device High-resolution numerical simulation of explosion problems is of significant theoretical value owing to the numerous potential applications in both national defense and civilian projects, such as ammunition design, damage assessment, target protection, and industrial gas explosion prevention. In this paper, we review the research history of explosion mechanics and present the highest-order numerical simulation in decades. Building upon the authors research work in recent years, we specifically discuss the development of high-order positivity-preserving schemes, high-order boundary treatment, an adaptive mesh method, and multi-material interface treatment. We extended the WENO and RKDG methods and constructed conservative positivity-preserving high-order schemes. The problems of negative density and pressure were solved through the simulation of complex detonation propagation. The detonation wave front structure and flow characteristics were captured clearly. In this paper, a high-order inverse Lax-Wendroff method on a Cartesian mesh is presented to treat the complex boundary. The main principle is that the first-order normal derivative can be obtained by the inverse Lax-Wendroff method, while all the higher-order normal derivatives can simply be obtained by fifth-order WENO-type extrapolation. The efficient implementation in the detonation process further indicates that the inverse Lax-Wendroff method is stable and robust when applied to a complex-geometry boundary. An a posteriori error estimate, which is often used as a refinement criterion, is applied to solve the Euler equations. To achieve mesh refinement, WENO and Hermite interpolations are used to prolong the solutions from coarse to fine grid in space and time, respectively. For mesh merging, the direct point value replacement method is employed to update the solutions of coarse grids. For this study, a local level-set tracking method was developed to treat the multi- material interface, and the velocity field in the computational domain was modified in order to effectively avoid errors caused by velocity field discontinuity when the interface position was solved. The method presented in this paper combines the GFM (Ghost Fluid Method) with the RGFM (Real Ghost Fluid Method) to deal with the material interface, thereby avoiding non-physical solutions when the GFM is used to deal with a strong discontinuity, and the CPU running time is increased when RGFM is employed to deal with a weak discontinuity in solving the Riemann problem repeatedly. Finally, the future of high-order numerical simulation of explosion mechanics is discussed.

An Improved XFEM With Multiple High-Order Enrichment Functions and Low-Order Meshing Elements for Field Analysis of Electromagnetic Devices With Multiple Nearby Geometrical Interfaces

This paper proposes an improved extended finite element method for modeling electromagnetic devices with multiple nearby geometrical interfaces. In regions near these interfaces, the magnetic vector potential approximation is enriched by incorporating multiple derivative discontinuous fields based on the partition of unity method such that the interfaces can be represented independent of the mesh. The support of a node or an element can be cut by several interfaces. This method results in the high accuracy in the approximation field and derivative field. Numerical examples applied to the iron core in 1-D eddy current field involving level set-based parts, error analysis, and electromagnetic field computations are provided to demonstrate the utility of the proposed approach.

Numerical Analysis of the Transpose Diffusive Term for Viscoplastic-Type Non-Newtonian Fluid Flows Using a Collocated Variable Arrangement

The aim of this work is to delve into the numerical analysis of viscoplastic-type non-Newtonian fluid flows. Specifically, improvements in the spatial discretization schemes and the temporal integration methods have been proposed to overcome the numerical problems introduced by the transpose diffusive term and associated with the velocity field discontinuity, the artificial viscous diffusion, and the transpose viscous coupling. The resulting knowledge may be useful, among many other reasons, to improve the corresponding numerical simulations and gain insight into the underlying physics of this class of non-Newtonian fluid flows.

Modeling shallow avalanche onset over complex basal topography

This paper deals with modeling of the onset of a shallow avalanche (soils, snow or other geomaterials) over various bottom topologies (mountains, valleys, ...). In order to do that, we use the shallow visco-plastic model with topography, developed in Ionescu (J. Non-Newtonian Fluid Mech. 193:116---128 2013), and we introduce a simple criterion to distinguish if an avalanche occurs or not. This criterion, relating the yield limit (material resistance) to the distribution of the external forces, is deduced from an optimization problem, called limit load analysis. The plastic dissipation functional which is involved in the limit load problem is non smooth and non coercive in the classical Sobolev spaces. To prove the existence of an onset velocity field (collapse flow) the appropriate functional space consists of bounded tangential deformation functions. We propose therefore a numerical strategy to solve the limit load problem and to get the onset flow field. A mesh free method, called the discontinuous velocity domain splitting (DVDS), is adapted here. The limit load problem is thus reduced to the minimization of a shape dependent functional. The discontinuous collapse flow velocity field is associated to a sub-domain and a rigid flow. With a level set of a Fourier function we give a description of the sub-domains and then we use genetic algorithms to solve the resulted non convex and non smooth global optimization problem. Finally, we illustrate the proposed numerical approach by solving several safety factor problems.

Poroelastic two-phase material modeling: theoretical formulation and embedded finite element method implementation

This paper presents the formulation of FEMs for the numerical modeling of a poroelastic two-phase (aggregates/mixture phase) solid. The displacement and pressure fields are decomposed, following the Enhanced Assumed Strain (EAS) method, into a regular part and an enhanced part. This leads to discontinuous strain and pressure gradient fields allowing to capture the jump in mechanical and hydrical properties passing through the interface between the aggregates and the mixture phase. All these enhanced fields are treated in the context of the embedded FEM through a local enhancement of the finite element interpolations as these jumps appear. The local character of these interpolations leads after a static condensation of the enhanced fields to a problem exhibiting the same structure as common poroelastic finite element models but incorporating now the mechanical and hydrical properties of a two-phase solid. Copyright © 2015 John Wiley & Sons, Ltd.

A NURBS‐based interface‐enriched generalized finite element method for problems with complex discontinuous gradient fields

SummaryA non‐uniform rational B‐splines (NURBS)‐based interface‐enriched generalized finite element method is introduced to solve problems with complex discontinuous gradient fields observed in the structural and thermal analysis of the heterogeneous materials. The presented method utilizes generalized degrees of freedom and enrichment functions based on NURBS to capture the solution with non‐conforming meshes. A consistent method for the generation and application of the NURBS‐based enrichment functions is introduced. These enrichment functions offer various advantages including simplicity of the integration, possibility of different modes of local solution refinement, and ease of implementation. In addition, we show that these functions well capture weak discontinuities associated with highly curved material interfaces. The convergence, accuracy, and stability of the method in the solution of two‐dimensional elasto‐static problems are compared with the standard finite element scheme, showing improved accuracy. Finally, the performance of the method for solving problems with complex internal geometry is highlighted through a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.

Classification of Hidden Dynamics in Discontinuous Dynamical Systems

Ordinary differential equations with discontinuous right-hand side, where the discontinuity of the vector field arises on smooth surfaces of the phase space, are the topic of this work. The main emphasis is the study of solutions close to the intersection of two discontinuity surfaces. There, the so-called hidden dynamics describe the smooth transition from ingoing to outgoing solution directions, which occurs instantaneously in the jump discontinuity of the vector field. This paper presents a complete classification of such transitions (assuming the vector fields surrounding the intersection are transversal to it). Since the hidden dynamics are realized by standard space regularizations, much insight is obtained for them. One can predict, in the case of multiple solutions of the discontinuous problem, which solution (classical or sliding mode) will be approximated after entering the intersection of two discontinuity surfaces. A novel modification of space regularizations is presented that permits us to avoid (unphysical) high oscillations and makes a numerical treatment more efficient.

High breakdown voltage AlGaN/GaN HEMT with high‐K/low‐K compound passivation

A novel high breakdown voltage (BV) AlGaN/GaN high-electron mobility transistor (HEMT) with a high-K/low-K compound passivation layer is proposed. The compound passivation layer is formed by blocks of low-K dielectric (Si3N4) embedded in a high-K passivation layer (La2O3). Owing to their different dielectric constants, there is a discontinuity of the horizontal electrical field at the high-K/low-K interface, which can introduce a new electric field peak in the nearby channel in the semiconductor and can also modulate the distribution of the electric field along the channel. Hence, enhancement of BV can be achieved. Compared to the typical field-plate structure, high-K/low-K passivation introduces no parasitic capacitance. On the basis of the physical mechanism, several design principles for the high-K/low-K passivation layer are presented. Numerical simulation demonstrates a BV of 1400 V for the proposed device with four blocks of low-K dielectric embedded in a high-K passivation, compared to the BVs of 917 and 288 V for the device with high-K passivation and the device with low-K passivation, respectively.

An Improved AM–FM-Based Approach for Reconstructing Fingerprints from Minutiae

Reconstructing fingerprint images from a given set of minutiae is an important issue in analyzing the masquerade attack of automated fingerprint recognition systems (AFRSs) and in generating large scale databases of synthetic fingerprint images for the performance evaluation of AFRSs. Existing fingerprint reconstruction methods either cannot generate visually plausible or realistic fingerprint images, or suffer from the occurrence of false minutiae in the reconstructed fingerprint images. In this paper, we analyze the underlying reason of false minutiae generated by state-of-the-art amplitude modulation–frequency modulation (AM–FM)-based methods. Furthermore, we propose an improved approach by devising a better way to cope with the branch cuts (or discontinuities) in the fingerprint ridge orientation fields, and by introducing an effective scheme to remove false minutiae from the reconstructed fingerprint images. Compared with previous AM–FM based methods, the proposed method gets rid of block effects and successfully reduces the number of false minutiae. Theoretic proofs are provided with respect to the effectiveness of the proposed method for fingerprints with multiple singular points. The proposed method has also been evaluated on public fingerprint databases. The results demonstrate that it is superior to the existing methods in reconstructing realistic fingerprint images with fewer false minutiae.

OS1010-224 有限要素メッシュを利用した画像相関法によるき裂近傍の変位・ひずみ分布測定

The use of mesh based global digital image correlation is proposed for measuring displacement fields around a crack tip. Displacement components at all nodes of a finite element model are simultaneously obtainable from images before and after deformation by global digital image correlation. Therefore, discontinuous displacement fields can be obtained using a finite element mesh with a crack. The effectiveness is demonstrated by measuring the displacement fields around a desiccation crack. Results show that the near-tip displacement distributions are obtained using global digital image correlation with singular elements at the crack tip.