Discontinuous Fields Research Articles

Automated crack propagation measurement on asphalt concrete specimens using an optical flow-based deep neural network

ABSTRACT This article proposes a deep neural network, namely CrackPropNet, to measure crack propagation on asphalt concrete (AC) specimens. It offers an accurate, flexible, efficient, and low-cost solution for crack propagation measurement using images collected during cracking tests. CrackPropNet significantly differs from traditional deep learning networks, as it involves learning to locate displacement field discontinuities by matching features at various locations in the reference and deformed images. An image library representing the diversified cracking behaviour of AC was developed for supervised training. CrackPropNet achieved an optimal dataset scale F-1 of 0.755 and optimal image scale F-1 of 0.781 on the testing dataset at a running speed of 26 frame-per-second. Experiments demonstrated that low to medium-level Gaussian noises had a limited impact on the measurement accuracy of CrackPropNet. Moreover, the model showed promising generalisation on fundamentally different images. As a crack measurement technique, the CrackPropNet can detect complex crack patterns accurately and efficiently in AC cracking tests. It can be applied to characterise the cracking phenomenon, evaluate AC cracking potential, validate test protocols, and verify theoretical models.

Monotone ODEs with discontinuous vector fields in sequence spaces

We consider a system of ODE in a Fréchet space with unconditional Schauder basis. The right side of the ODE is a discontinuous function. Under certain monotonicity conditions we prove an existence theorem for the corresponding initial value problem. We employ an idea of the partial order which seems to be new in this field.

Bearing capacity of concentric anchorage zones in post-tensioned members: A stress field solution

The post-tensioned anchorage zones are generally subdivided into local and general zones, which are treated with semi-empirical approaches and strut-and-tie models separately in many design codes. Even with their functions that look different, the two adjacent zones are intrinsically related in terms of the compression dispersion mechanism. Holding this view, this paper intends to present a mechanical model to integrate their combined actions. Firstly, two confinement effects in anchorage zones are studied: the local confinement under the bearing plate and the passive confinement by bursting reinforcement. Then, a discontinuous stress field model for concentric anchorage zones is proposed, which allows for a triaxial state of compression stresses in the local zone and the contribution of bursting reinforcement in the general zone simultaneously. After that, an explicit bearing capacity formula for anchorage zones is derived, in which the ultimate failure can be attributed to either the yielding of the distributed tension subfield or the crushing of fan subfields. The prediction of bearing capacity is in fairly good agreement with the collected test results.

Modeling and design of concrete hinges under general loading

AbstractDespite their successful applications in practice for over a century, the design of concrete hinges still entails considerable modeling uncertainty. Their dimensioning still relies on semi‐empirical recommendations originally proposed for admissible stress design, based on limited experimental data and generalized with engineering judgment. This presumably results in overly conservative designs in many cases, particularly when applied with modern design codes based on partial safety factors. This paper addresses these issues by revisiting the analytical modeling for one‐way Freyssinet concrete hinges under general loading based on approaches compatible with current design codes. A cross‐sectional analysis with confined concrete properties is proposed for the behavior under axial forces and bending moments, where the strength of the triaxially compressed concrete in the hinge throat is determined with a discontinuous stress field. The hinge resistance to shear forces is investigated with failure mechanisms inspired by failure modes observed in experiments. Based on the shear strength, a simple approach to estimate the torsional resistance of the throat is proposed. Remarks are also made on the analysis of combined actions. The predictions of the proposed models are validated against a wide range of test data, including a series of recently conducted own experiments. Overall, the proposed models agree better with the available experimental data than the existing approaches, potentially allowing for a more efficient design of new and assessment of existing concrete hinges.

On the Computation of the Attenuation Constant by Using the Generalized Telegraphist’s Equations Based Electromagnetic Analysis Method

Numerical results for the attenuation constant obtained by using the generalized telegraphist’s equations (GTEs) based electromagnetic analysis method and comparison with the HFSS (High Frequency Structure Simulator) results are reported. To calculate the attenuation constant with the GTEs method, not only the amplitudes of the voltage modes but also the amplitudes of the current modes must be found. In this paper, it is demonstrated that the relationships reported by other authors for the amplitudes of the current modes are not correct and new ones are proposed. To validate these relationships, the attenuation constants for homogeneous and different partially dielectric-filled rectangular waveguides are computed for the fundamental propagation mode by using the GTEs based analysis method and the results are compared with those obtained with HFSS. It is shown that using the revised relationships for the amplitudes of the current modes, the GTE method can be used to compute accurately the propagation and attenuation constant, but only for propagation modes in which the components of the electric field are not oriented perpendicular to the interface between different dielectrics. This limitation is not due to the proposed current mode relationships, but is due to the GTE method which cannot highlight the electric field discontinuities.

Dislocation structures formation induced by thermal stress in additive manufacturing: Multiscale crystal plasticity modeling of dislocation transport

The motion of dislocations governs the plastic deformation of crystalline materials, which in turn determines the mechanical properties. The complex thermal history, large temperature gradients and high cooling rates during the process of additive manufacturing (AM) can induce high dislocation density and unique dislocation structures in the material. The origin of these dislocation structures and their stability during mechanical loading are debated. A novel temperature dependent continuum dislocation dynamics (CDD) model is developed, in which four state variables are used for each slip system representing the total dislocation density, edge and screw geometrically necessary dislocation densities and dislocation curvature. The CDD model is fully coupled with a crystal plasticity solver, which captures the plastic deformation induced by the dislocation motion. A hybrid continuous and discontinuous Galerkin formulation is developed to accurately reproduce the dynamics of highly discontinuous dislocation density fields that are typical of dislocation structures. A multiscale modeling approach is used, in which the thermally induced deformation in specific grains of a polycrystal is extracted from larger scale crystal plasticity simulations of the laser powder-bed fusion process, and is then used for single crystal scale dislocation dynamics simulations. Simulation results reveal the dynamics of dislocation structure formation in grains at different positions during laser scanning and cooling stages. The effect of the cyclic thermal stress during multi-layer AM fabrication is also investigated. The simulations provide a new perspective on the specific conditions that should be satisfied during AM process for the formation of stable dislocation structures.

Variable Thickness Strain Pre-Extrapolation for the Inverse Finite Element Method.

The inverse Finite Element Method (iFEM) has recently gained much popularity within the Structural Health Monitoring (SHM) field since, given sparse strain measurements, it reconstructs the displacement field of any beam or shell structure independently of the external loading conditions and of the material properties. However, in principle, the iFEM requires a triaxial strain measurement for each inverse finite element, which is seldom feasible in practical applications due to both costs and cabling-related limitations. To alleviate this problem several techniques to pre-extrapolate the measured strains have been developed, so that interpolated or extrapolated strain values are inputted to elements without physical sensors: the benefit is that the required number of sensors can be reduced. Nevertheless, whenever the monitored components comprise regions of different thicknesses, each region of constant thickness must be extrapolated separately, due to thickness-induced discontinuities in the strain field. This is the case in many practical applications, especially those concerning fiber-reinforced composite laminates. This paper proposes to extrapolate the measured strain field in a thickness-normalized space, where the thickness-induced trends are removed; this novel method can significantly decrease the number of required sensors, effectively reducing the costs of iFEM-based SHM systems. The method is validated in a simple but informative numerical case study, highlighting the potentialities and benefits of the proposed approach for more complex application scenarios.

High frequency modelling of electric motor vibration in the presence of adhesive bonded components

Electric motors often include adhesive joints to bond magnets to shells. In this paper, the variability of the frequency response function is assessed with regards to high frequency, finite element modelling and validation. The adhesive bond is used to fix the permanent magnets to the motor shell for the typical PMDC motor as it provides a smoother, more continuous surface than fixings without discontinuity of the magnetic field. To obtain the dynamic response of the motor housing at specified settings of the adhesive layer, which include variations in thickness and stiffness, a finite element model is established in ABAQUS. Given the relative stiffness of the adhesive is lower, this has a significant effect on the overall stiffness of the casing, for a fixed mass and thus the response frequencies and loss factor. When using frequency response functions to couple motors to components, this variability can be significant and thus this work is useful for the e-motor noise optimization at its design stage.

An Active Electromagnetic 3-D Surface Cloak

An active interior cloak is composed of a conformal array of radiating sources surrounding a target object. With proper configuration, this array radiates a field discontinuity which cancels out any scattering which occurs when the object is illuminated by an impinging electromagnetic wave. Unlike many other cloaking methods, an interior cloak can be completely constructed using conventional components while its active nature allows it to circumvent passivity-based constraints. This enables an interior cloak to hide an object of virtually any size, shape, and material composition as well as accommodate multiple frequencies and polarizations. Despite its potential, this approach has only been demonstrated on 2-D and quasi-2-D targets to date. As such, this article presents the first 3-D implementation of an interior cloak. Here, the design of a cloak array capable of hiding a conductive, circular cylinder in free space is first presented. Cloaking performance is then validated via full-wave simulations and an experimental demonstration in which the device successfully suppresses scattering when the target is illuminated by a ridged horn antenna at 1.2 GHz.

An adaptive coupling modeling between peridynamics and classical continuum mechanics for dynamic crack propagation and crack branching

Current techniques for the objective simulation of dynamic crack propagation are highly complex and remain computationally expensive, making the simulation of dynamic crack propagation challenging. Based on the peridynamic theory, it allows discontinuities in the displacement field and promises the fracture simulation. However, a peridynamic model often involves intractable computational costs. As an alternative, an adaptive coupling modeling between the peridynamics and classical continuum mechanics is developed for the dynamic crack propagation and crack branching in this work, using the Morphing coupling method presented in previous work (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The Morphing method is promising for the adaptive introduction of the peridynamic model (i.e., a nonlocal model) during the dynamic crack propagation, while the rest of the structure outside the peridynamic region is described using the local model based on the continuum mechanics. Thus, a hybrid local/nonlocal model system is established through adaptive coupling modeling. Moreover, the discontinuous Galerkin finite elements (DGFEs) are adopted in the pure peridynamic and hybrid regions, while the finite elements are adopted in the rest of the structure. A benchmark dynamic fracture problem containing branching patterns is used to verify the adaptive coupling of dynamic models. The results show that the simulation based on the adaptive coupling of dynamic models captures the main features during the dynamic crack propagation and branching. Furthermore, the convergence studies on time increments and mesh density under uniform grid refinement (m-convergence) and under changing the peridynamic horizon (δ-convergence) are also proposed.

A single–region Finite Volume framework for modeling discontinuous magnetic field distributions

In this paper we present a novel method to model discontinuous distributions of magnetic fields. The method is based on a finite volume discretization of a divergence form of the magnetostatic equations. The theoretical framework is written in terms of the vector potential, therefore, the computational implementation is capable of predicting the magnetic field distribution in permeable, permanently magnetized, and current-carrying media. The use of a single-region meshing scheme simplifies the simulation set-up due to the fact that it avoids the use of interface boundary conditions. This renders it computationally more effective than the multi-region counterpart. In order to test the performance of the present approach we execute several numerical experiments and compare the results against a multi-region discontinuous method and a single-region boundary layerless method. The experiments demonstrate that provided the boundary layer complies with certain topological rules, the method gives accurate results of the magnitude and direction of the magnetic field, both near and far from the interfaces. We show that, for orthogonal meshes, the results obtained with a single-region approach using boundary layers are comparable to the results obtained with a multi-region framework that imposes the magnetic field gradient discontinuity as a boundary condition.

A 3D-Schrödinger operator under magnetic steps with semiclassical applications

We define a Schrödinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the spectrum of the operator. We give sufficient conditions on the strength and the direction of the magnetic field such that the aforementioned infimum is an eigenvalue of a reduced model operator on the half-plane. We use the Schrödinger operator on the half-space to study a new semiclassical problem in bounded domains of the space, considering a magnetic Neumann Laplacian with a piecewise-constant magnetic field. We then make precise the localization of the semiclassical ground state near specific points at the discontinuity jump of the magnetic field.

Periodic orbits in piecewise Riccati vector fields

In this paper a class of planar vector fields is characterized and their periodic orbits are studied. The class under study is formed by vector fields that can be written as Riccati ordinary differential equations. The characterization is stated in terms of some homogeneity conditions on the vector fields. The study of periodic orbits is done through Poincaré maps defined around monodromic points. In particular, some properties of the so-called Möbius transformations are considered. In the study, both smooth and discontinuous vector fields defined by sectors are studied.Theorem 2.2 characterizes the Riccati vector fields and Theorem 3.4 proves that the Poincaré maps of such vector fields are Möbius transformations. In Theorem 4.1 a sharp upper bound of two periodic orbits is stated. The polynomial case is considered in Theorems 4.3 and 4.4 for which existence, upper bounds, and hyperbolicity of periodic orbits are stated.

Visualization of Discontinuous Vector Field Topology.

This paper extends the concept and the visualization of vector field topology to vector fields with discontinuities. We address the non-uniqueness of flow in such fields by introduction of a time-reversible concept of equivalence. This concept generalizes streamlines to streamsets and thus vector field topology to discontinuous vector fields in terms of invariant streamsets. We identify respective novel critical structures as well as their manifolds, investigate their interplay with traditional vector field topology, and detail the application and interpretation of our approach using specifically designed synthetic cases and a simulated case from physics.

Two-way wave–vortex interactions in a Lagrangian-mean shallow water model

We derive and investigate numerically a reduced model for wave–vortex interactions involving non-dispersive waves, which we study in a two-dimensional shallow water system with an eye towards applications in atmosphere–ocean fluid dynamics. The model consists of a coupled set of nonlinear partial differential equations for the Lagrangian-mean velocity and the wave-related pseudomomentum vector field defined in generalized Lagrangian-mean theory. It allows for two-way interactions between the waves and the balanced flow that is controlled by the distribution of Lagrangian-mean potential vorticity, and for strong solutions it features a desirable exact energy conservation law for the sum of wave energy and mean flow energy. Our model goes beyond standard ray tracing as we can derive weak solutions that contain discontinuities in the pseudomomentum field, using the theory of weakly hyperbolic systems. This allows caustics to form without predicting infinite wave amplitudes, as would be the case in the standard ray-tracing theory. Suitable wave forcing and dissipation terms are added to the model and a numerical scheme for the model is implemented as a coupled set of pseudo-spectral and finite-volume integrators. Idealized examples of interactions between wavepackets and simple vortex structures are presented to illustrate the model dynamics. The unforced and non-dissipative simulations suggest a heuristic rule of ‘greedy’ waves, i.e. in the long run the wave field always extracts energy from the mean flow.

A Review on phase-field modeling of fracture

In cases with complicated crack topologies, the computational modeling of failure processes in materials owing to fracture based on sharp crack discontinuities fails. Diffusive crack modeling based on the insertion of a crack phase-field can overcome this. The phase-field model (PFM) portrays the fracture geometry in a diffusive manner, with no abrupt discontinuities. Unlike discrete fracture descriptions, phase-field descriptions do not need numerical monitoring of discontinuities in the displacement field. This considerably decreases the complexity of implementation. These qualities enable PFM to describe fracture propagation more successfully than numerical approaches based on the discrete crack model, especially for complicated crack patterns. These models have also demonstrated the ability to forecast fracture initiation and propagation in two and three dimensions without the need for any ad hoc criteria. The phase-field model, among numerous options, is promising in the computer modeling of fracture in solids due to its ability to cope with complicated crack patterns such as branching, merging, and even fragmentation. A brief history of the application of the phase-field model in predicting solid fracture has been attempted. An effort has been made to keep the conversation focused on recent research findings on the subject. Finally, some key findings and recommendations for future research areas in this field are discussed.

Identification of seismically active areas of the Voronezh anteclise by geomorphological and tectonophysical methods

Using the method of cluster analysis of morphometric parameters of the relief, the areas within which most of the epicenters of modern earthquakes of the Voronezh anteclise are located are identified. With the help of computer modeling, the areas of possible formation of new small-length discontinuities in the modern stress field are outlined. On the basis of complex geological and geomorphological data we created a tectonophysical model that explains the nature of seismicity by the development of geodynamically active zones in a shear environment with the orientation of the axis of maximum compression in the north-west direction.

A continuum framework for phase field with bulk-surface dynamics

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer et al. (Phys Rev Lett 79:893, 1997), Goldstein et al. (Phys D Nonlinear Phenom 240:754–766, 2011), and Knopf et al. (ESAIM Math Model Numer Anal 55:229–282, 2021). As a byproduct, we generalize these theories. These types of dynamic boundary conditions are described by the coupling between the bulk and surface partial differential equations for phase fields. Our point of departure within this continuum framework is the principle of virtual powers postulated on an arbitrary part mathcal {P} where the boundary partial mathcal {P} may lose smoothness. That is, the normal field may be discontinuous along an edge partial ^2mathcal {P}. However, the edges characterizing the discontinuity of the normal field are considered smooth. Our results may be summarized as follows. We provide a generalized version of the principle of virtual powers for the bulk-surface coupling along with a generalized version of the partwise free-energy imbalance. Next, we derive the explicit form of the surface and edge microtractions along with the field equations for the bulk and surface phase fields. The final set of field equations somewhat resembles the Cahn–Hilliard equation for both the bulk and surface. Moreover, we provide a suitable set of constitutive relations and thermodynamically consistent boundary conditions. In Knopf et al. (2021), a mixed (Robin) type of boundary condition for the chemical potentials is proposed for the model in Fischer et al. (1997), Goldstein et al. (2011). In addition to this boundary condition, we also include this type of mixed boundary condition for the microstructure, that is the phase fields. Lastly, we derive the Lyapunov-decay relations for these mixed type of boundary conditions for both the microstructure and chemical potential.

On the Rarity and Peculiarity of the Early Toarcian (Lower Jurassic) Leukadiellinae Ammonites—Systematic Review and Insights on the Interplay of Environmental Stress, Evolution and Biodiversity

The subfamily Leukadiellinae Macchioni and Venturi, 2000 includes the two rare genera Leukadiella Renz, 1913 and Renziceras Arkell, 1953. Genus Leukadiella is characterised by ornamental and structural features unusual to the family Hildoceratidae Hyatt, 1867; for this reason, it has been occasionally grouped with other “odd” representatives of this family, as, for instance, Frechiella Prinz, 1904 and Paroniceras Bonarelli, 1893. While Renziceras comprises only one species, the eleven species currently recognised within Leukadiella show a noticeably discontinuous variability field; together with rarity of findings, the interpretation of this variability represents a renowned obstacle to their classification and phylogenetic reconstruction. Following an analysis of the morphological characters commonly used for defining Leukadiella species, a revised taxonomic scheme is herein proposed. Two clusters of characters are defined, based on which two morphologically distinct groups of species are distinguished, referred to as Helenae Group and Ionica Group. The genus name Leukadiella is maintained for species of the Helenae Group, which are restricted via synonymy to Leukadiella helenae Renz, 1913 and Leukadiella jeanneti Renz, 1927. The new genus name Neoleukadiella gen. nov. is proposed for species of the Ionica Group, which, by analogous limitation, are Neoleukadiella ionica Renz and Renz, 1946 and Neoleukadiella gallitellii Pinna, 1965. The reduction in the number of species from eleven to four is consistent with their rarity and limited paleogeographic distribution. The closely related Renziceras is considered the direct progenitor of Leukadiella; in turn, the Apennine genus Cingolites Sassaroli and Venturi, 2010 is proposed as transitional between Hildaites Buckman, 1921 and Renziceras. Conversely, the progenitor of Neoleukadiella remains uncertain, although a possible relationship between Leukadiella and Neoleukadiella species is tentatively traced. Finally, some challenging assumptions are made by emphasizing the role of environmental stress in controlling developmental dynamics that may drive striking phenotypic modification, of the kind observed in the Leukadiellinae species.

Topological Evolution of an Unwinding Blowout Jet

We investigate the topological evolution of coronal jet containing a sigmoid-like flux rope using a nonlinear force-free field model obtained with the flux-rope insertion method and magnetofrictional relaxation. We examine the topological evolution predicted by the unstable model with respect to observations from Solar Dynamic Observatory’s Atmospheric Imaging Array. We also calculate the squeezing factor, an approximation for sharp discontinuities in the magnetic field, and the coiling rate, an approximation for the amount of twist in the field. We identify at least two topological features where magnetic reconnection is likely taking place: an internal anemone-like region, near the filament, and an external region between the closed dome of the coronal jet and the ambient field. We also find evidence of reconnection below the filament, but it is not clear if the two inner regions are the same. We find that the internal region inflates the jet dome into the external region, which in turn initiates the fast eruption, allowing the inner region to unwind and the filament to escape. Finally, we examine the thermal evolution of the jet and trace the regions of enhanced emission-measure-weighted temperature (T EM) to the location of the expected reconnection regions. We find that magnetic field lines associated with the internal reconnection region are tied to increased T EM and emission in extreme-UV observations, indicative of heating. We identify this eruption as an untwisting jet, where unwinding magnetic field lines impart energy along the magnetic field forming the observed features of the coronal jet.