Concurrently coupled solid shell-based adaptive multiscale method for fracture

Artículo Open Access en el sitio web del editor. Pago por publicar en abierto.A solid shell-based adaptive atomistic–continuum numerical method is herein proposed to simulate complex crack growth patterns in thin-walled structures. A hybrid solid shell formulation relying on the combined use of the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods has been considered to efficiently model the material in thin structures at the continuum level. The phantom node method (PNM) is employed to model the discontinuities in the bulk. The discontinuous solid shell element is then concurrently coupled with a molecular statics model placed around the crack tip. The coupling between the coarse scale and the fine scale is realized through the use of ghost atoms, whose positions are interpolated from the coarse scale solution and enforced as boundary conditions to the fine scale model. In the proposed numerical scheme, the fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened in order to reduce the computation costs. An energy criterion is used to detect the crack tip location. All the atomistic simulations are carried out using the LAMMPS software. A computational framework has been developed in MATLAB to trigger LAMMPS through system command. This allows a two way interaction between the coarse and fine scales in MATLAB platform, where the boundary conditions to the fine region are extracted from the coarse scale, and the crack tip location from the atomistic model is transferred back to the continuum scale. The developed framework has been applied to study crack growth in the energy minimization problems. Inspired by the influence of fracture on current–voltage characteristics of thin Silicon photovoltaic cells, the cubic diamond lattice structure of Silicon is used to model the material in the fine scale region, whilst the Tersoff potential function is employed to model the atom–atom interactions. The versatility and robustness of the proposed methodology is demonstrated by means of several fracture applications.Unión Europea ERC 306622Ministerio de Economía y Competitividad DPI2012-37187, MAT2015-71036-P y MAT2015-71309-PJunta de Andalucía P11-TEP-7093 y P12-TEP -105

Conceptual Design of High Temperature Superconducting Toroidal Field Coils for Future Fusion Power Plants

Aus der langjährigen Forschung im Bereich der magnetischen Eingrenzung sind Stellaratoren und Tokamaks entstanden, die starken und ungleichmäßigen Magnetfelder zum Einfangen der Plasmapartikel nutzen und es ihnen ermöglichen, sich frei auf bestimmten Wegen zu bewegen. Die Tokamaks haben durch ein einfacheres Spulendesign, verschachtelte magnetische Oberflächen und die Fähigkeit, mit positiver magnetischer Scherung zu arbeiten, an Bedeutung gewonnen. Derzeit plant die Europäische Union (EU), ihre Studien über Tokamak auf Demonstrationskraftwerke (EU-DEMO) auszudehnen, der Strom erzeugen können. Ziel dieser Studie ist es, ein Konzept für die Ringkernfeldspule (TF-Spule) für zukünftige Kraftwerke mit dem Systemcode PROCESS zu entwickeln. Ziel dieser Studie ist es, ein Konzept für die Toroidalfeldspule (TF-Spule) für zukünftige Kraftwerke mit dem Systemcode PROCESS zu entwickeln. Der PROZESS-Code gibt bestimmte Informationen wie die ungefähre Form der TF-Spule, die Fläche des Wickelpakets, das Magnetfeld an der Plasmaachse. Ausgehend vom Eingang wird das Wickelpaket der TF-Spule entworfen. Zum Beispiel, wenn die Pancake-Wicklung gegenüber der Lagen-Wicklung bevorzugt wird. Zum Beispiel, wenn die Pancake-Wicklung gegenüber der Lagen-Wicklung bevorzugt wird. Die erste Lage, die der Plasmawärme zugewandt ist, wird angesammelt, da sie sich im Hochfeldbereich befindet, wodurch der Magnet mit einer geringeren Betriebsmarge arbeitet. Der Leiter der Pancake-Wicklung ist jedoch in Umfangsrichtung und nicht entlang der Achse eines Magneten gewickelt und jedes Modul ist separat gewickelt und elektrisch in Reihe geschaltet. Der wesentliche Vorteil bei diesem Verfahren ist, dass die Temperatur im Hochfeldbereich am niedrigsten ist, da sich der Heliumeinlass im Hochfeldbereich des Wickelpakets und der Auslass im Niederfeldbereich befindet. Das Wicklungspaket mit der elektrischen Schaltung ist in Reihe geschaltet und die hydraulische Schaltung ist parallel geschaltet. Aus dem PROZESS-Code wird überprüft, ob das Magnetfeld an der Plasmaachse gleich dem erforderlichen Magnetfeld ist. Das Spitzenmagnetfeld wird auch zur Bestimmung des Arbeitspunktes des Leiters berechnet. Die 3D Elektromagnetische Simulation wird mit dem Präprozessor TOKEF und dem Code EFFI durchgeführt. Codes zur Magnetfeldberechnung einer allgemeinen dreidimensionalen Stromverteilung, die Formulierungen verwenden, die auf einer fadenförmigen Annäherung und der endlichen Leitergröße basieren. Diese Codes werden durch eine Reihe von verteilten Filamenten unter Verwendung der EFFI-Formel, die aus dem Bio-Savart Gesetz für die Volumenstromverteilung abgeleitet wurde, approximiert. Die Statik der TF-Spule bestimmt die Spannungen im Spulengehäuse und im Wickelpaket. Der Bereich mit den höchsten Spannungen liegt in der Mittelebene des inneren Schenkels, was durch eine ähnliche Analyse mit dem Spulenmagnetsystem JT-60SA TF bestätigt wird. In der EU DEMO führt die TF-Spule hohe Ströme (in MA) und erzeugt hohe Felder. Die TF-Spule ist daher hohen magnetischen Drücken und Kräften ausgesetzt. Um die Spannungen im Wickelpaket und am Gehäuse zu untersuchen, werden in COMSOL und ANSYS verschiedene Methoden zur Analyse der Spannungen am Gehäuse, des Lösens des Wickelpakets und der Spannungen in Isolationsbauteilen betrachtet. Ein wichtiger Fehler, der bei der Konstruktion supraleitender Magnete zu berücksichtigen ist, ist der Übergang von der supraleitenden zur normal leitenden Phase, dem sogenannten Quench. Da im normal leitenden Modus der elektrische Widerstand des Supraleitermaterials hoch ist, erzeugt die Einführung von Kupfer als elektrischer Ableiter für den Stromfluss eine Joule-Erwärmung. Der Magnet muss durch Anschluss eines externen Widerstandes parallel zum Magneten entladen werden, um einen übermäßigen Temperaturanstieg zu vermeiden. Die maximal zulässige adiabatische Hotspot-Temperatur, wie sie vom International Thermonuclear Experimental Reactor (ITER) festgelegt wurde, ist auf 150 K begrenzt, wobei alle Materialien im Leiter berücksichtigt werden, d.h. Supraleiter, Kupfer, Helium, Edelstahlmantel und Isolierung. Um die Quenchausbreitung zu simulieren, wird eine externe Heizung in den Supraleiter eingesetzt und überprüft, wie die Ausbreitung ist und welche maximale Temperatur sie während der Entladungszeit erreicht

Crack patterns in heterogenous rocks using a combined phase field-cohesive interface modeling approach: A numerical study

Rock fracture in geo-materials is a complex phenomenon due to its intrinsic characteristics and the potential external loading conditions. As a result, these materials can experience intricate fracture patterns endowing various cracking phenomena such as: Branching, coalescence, shielding, and amplification, among many others. In this article, we present a numerical investigation concerning the applicability of an original bulk-interface fracture simulation technique to trigger such phenomena within the context of the phase field approach for fracture. In particular, the prediction of failure patterns in heterogenous rock masses with brittle response is accomplished through the current methodology by combining the phase field approach for intact rock failure and the cohesive interface-like modeling approach for its application in joint fracture. Predictions from the present technique are first validated against Brazilian test results, which were developed using alternative phase field methods, and with respect to specimens subjected to different loading case and whose corresponding definitions are characterized by the presence of single and multiple flaws. Subsequently, the numerical study is extended to the analysis of heterogeneous rock masses including joints that separate different potential lithologies, leading to tortuous crack paths, which are observed in many practical situations.Ministerio de Economía y Competitividad MAT2015-71036-

Some Mathematical Aspects of Spread and Stability of Time-Delay Gonorrhea

A mathematical model of time-delay gonorrhea among hetero and homosexuals is presented as a system of first order ordinary coupled integro-differential equations with delayed arguments. A theorem on the positivity of the solutions is proved to establish the feasibility of the proposed mode. Further, the only possible diseased equilibrium state has been identified and the stability analysis of such a state for some epidemiological possibilities has been carried out. It has been observed that the impulsive type inflow of infectives into the population maintained the stability of the diseased equilibrium state and is valid even for the exponential type inflows. In contrast to this, instability sets in when one or other of infective inflows is of the gate type

Couette Flow of a Dusty Incompressible Fluid with One of the Horizontal Moving Boundaries Suddenly Stopped

The unsteady flow of an incompressible viscous fluid with a uniform distribution of dust particles between two parallel plates when one of which is impulsively stopped from the state of uniform motion is studied. Analytical expressions for velocities of the fluid and dust particles have been obtained. It is found that the dust particles slip on the wall which is brought to rest impulsively instead of sticking to it; on the other hand, they stick to the stationary plate. The slip-velocity of the dust is noticed to be decreasing as the physical time increases and the relaxation time of the dust particles decrease

Adaptive Multiskalen-Methoden zur Modellierung von Materialversagen

One major research focus in the Material Science and Engineering Community in the past decade has been to obtain a more fundamental understanding on the phenomenon 'material failure'. Such an understanding is critical for engineers and scientists developing new materials with higher strength and toughness, developing robust designs against failure, or for those concerned with an accurate estimate of a component's design life. Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. In engineering applications, the global response of the system is often governed by the behaviour at the smaller length scales. Hence, the sub-scale behaviour must be computed accurately for good predictions of the full scale behaviour. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. Since the atomistic dimensions are of the order of Angstroms ( A), approximately 85 billion atoms are required to model a 1 micro- m^3 volume of Copper. Therefore, pure atomistic models are prohibitively expensive with everyday engineering computations involving macroscopic cracks and shear bands, which are much larger than the atomistic length and time scales. To reduce the computational effort, multiscale methods are required, which are able to couple a continuum description of the structure with an atomistic description. In such paradigms, cracks and dislocations are explicitly modeled at the atomistic scale, whilst a self-consistent continuum model elsewhere. Many multiscale methods for fracture are developed for "fictitious" materials based on "simple" potentials such as the Lennard-Jones potential. Moreover, multiscale methods for evolving cracks are rare. Efficient methods to coarse grain the fine scale defects are missing. However, the existing multiscale methods for fracture do not adaptively adjust the fine scale domain as the crack propagates. Most methods, therefore only "enlarge" the fine scale domain and therefore drastically increase computational cost. Adaptive adjustment requires the fine scale domain to be refined and coarsened. One of the major difficulties in multiscale methods for fracture is to up-scale fracture related material information from the fine scale to the coarse scale, in particular for complex crack problems. Most of the existing approaches therefore were applied to examples with comparatively few macroscopic cracks. Key contributions The bridging scale method is enhanced using the phantom node method so that cracks can be modeled at the coarse scale. To ensure self-consistency in the bulk, a virtual atom cluster is devised providing the response of the intact material at the coarse scale. A molecular statics model is employed in the fine scale where crack propagation is modeled by naturally breaking the bonds. The fine scale and coarse scale models are coupled by enforcing the displacement boundary conditions on the ghost atoms. An energy criterion is used to detect the crack tip location. Adaptive refinement and coarsening schemes are developed and implemented during the crack propagation. The results were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale method is one of the first adaptive multiscale method for fracture. A robust and simple three dimensional coarse graining technique to convert a given atomistic region into an equivalent coarse region, in the context of multiscale fracture has been developed. The developed method is the first of its kind. The developed coarse graining technique can be applied to identify and upscale the defects like: cracks, dislocations and shear bands. The current method has been applied to estimate the equivalent coarse scale models of several complex fracture patterns arrived from the pure atomistic simulations. The upscaled fracture pattern agree well with the actual fracture pattern. The error in the potential energy of the pure atomistic and the coarse grained model was observed to be acceptable. A first novel meshless adaptive multiscale method for fracture has been developed. The phantom node method is replaced by a meshless differential reproducing kernel particle method. The differential reproducing kernel particle method is comparatively more expensive but allows for a more "natural" coupling between the two scales due to the meshless interpolation functions. The higher order continuity is also beneficial. The centro symmetry parameter is used to detect the crack tip location. The developed multiscale method is employed to study the complex crack propagation. Results based on the meshless adaptive multiscale method were observed to be in excellent agreement with the pure atomistic simulations. The developed multiscale methods are applied to study the fracture in practical materials like Graphene and Graphene on Silicon surface. The bond stretching and the bond reorientation were observed to be the net mechanisms of the crack growth in Graphene. The influence of time step on the crack propagation was studied using two different time steps. Pure atomistic simulations of fracture in Graphene on Silicon surface are presented. Details of the three dimensional multiscale method to study the fracture in Graphene on Silicon surface are discussed

De-Duplication of Person's Identity Using Multi-Modal Biometrics

The objective of this work is to explore approaches to create unique identities by the de-duplication process using multi-modal biometrics. Various government sectors in the world provide different services and welfare schemes for the beneffit of the people in the society using an identity number. A unique identity (UID) number assigned for every person would obviate the need for a person to produce multiple documentary proofs of his/her identity for availing any government/private services. In the process of creating unique identity of a person, there is a possibility of duplicate identities as the same person might want to get multiple identities in order to get extra beneffits from the Government. These duplicate identities can be eliminated by the de-duplication process using multi-modal biometrics, namely, iris, ngerprint, face and signature. De-duplication is the process of removing instances of multiple enrollments of the same person using the person's biometric data. As the number of people enrolledinto the biometric system runs into billions, the time complexity increases in the de duplication process. In this thesis, three different case studies are presented to address the performance issues of de-duplication process in order to create unique identity of a person

EFFICIENT ROUND ROBIN CPU SCHEDULING ALGORITHM FOR OPERATING SYSTEMS

The main objective of this paper is to develop a new approach for round robin C P U scheduling algorithm which improves the performance of CPU in real time operating system. The proposed Priority based Round-Robin CPU Scheduling algorithm is based on the integration of round-robin and priority scheduling algorithm. It retains the advantage of round robin in reducing starvation and also integrates the advantage of priority scheduling. The proposed algorithm also implements the concept of aging by assigning new priorities to the processes. Existing round robin CPU scheduling algorithm cannot be implemented in real time operating system due to their high context switch rates, large waiting time, large response time, large turnaround time and less throughput. The proposed algorithm improves all the drawbacks of round robin CP U scheduling algorithm. The paper also presents the comparative analysis of proposed algorithm with existing round robin scheduling algorithm on the basis of varying time quantum, average waiting time, average turnaround time and number of context switches