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Material Law (material + law)
Selected AbstractsTwo-scale method for shear bands: thermal effects and variable bandwidthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Pedro M. A. Areias Abstract A method for the analysis of shear bands using local partition of unity is developed in the framework of the extended finite element method (XFEM). Enrichments are introduced for both the displacement field and the thermal field. The shear band width is determined by minimizing the plastic work. A coupled finite strain thermo-elastoplastic constitutive law is used. The enrichment is injected into the mesh when the material law becomes unstable. The criterion based on a complete stability analysis for materials in the finite strain regime including heat conduction, strain hardening, strain rate hardening and thermal softening is presented. A mixed continuous quadrilateral element is employed. The method is applied to the Nesterenko experiments, which exhibit multiple propagating shear bands and other problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] A practical large-strain solid finite element for sheet formingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005Jue Wang Abstract An alternative approach for developing practical large-strain finite elements has been introduced and used to create a three-dimensional solid element that exhibits no locking or hourglassing, but which is more easily and reliably derived and implemented than typical reduced-integration schemes with hourglassing control. Typical large-strain elements for forming applications rely on reduced integration to remove locking modes that occur with the coarse meshes that are necessary for practical use. This procedure introduces spurious zero-energy deformation modes that lead to hourglassing, which in turn is controlled by complex implementations that involve lengthy derivations, knowledge of the material model, and/or undetermined parameters. Thus, for a new material or new computer program, implementation of such elements is a daunting task. Wang,Wagoner-3-dimensions (WW3D), a mixed, hexahedral, three-dimensional solid element, was derived from the standard linear brick element by ignoring the strain components corresponding to locking modes while maintaining full integration (8 Gauss points). Thus, WW3D is easily implemented for any material law, with little chance of programming error, starting from programming for a readily available linear brick element. Surprisingly, this approach and resulting element perform similarly or better than standard solid elements in a series of numerical tests appearing in the literature. The element was also tested successfully for an applied sheet-forming analysis problem. Many variations on the scheme are also possible for deriving special-purpose elements. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the design of energy,momentum integration schemes for arbitrary continuum formulations.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Applications to classical, chaotic motion of shells Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source] A numerical model for the cyclic deterioration of railway tracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003Akke S. J. Suiker Abstract An elasto-plastic material model is proposed that can be used to simulate the cyclic deterioration of railway tracks. The model describes the envelope of the irreversible, plastic material response generated during a cyclic loading process, thereby distinguishing the mechanisms of frictional sliding and volumetric compaction. The reversible response is represented by a pressure-dependent, hypo-elastic material law. After the numerical integration of the model is specified, the model is calibrated on laboratory experiments and employed in a finite-element case study of the long-term settlement behaviour of a railway track. The main features of the model are illustrated by comparing the computed response with the response obtained by in situ track measurements. Copyright © 2003 John Wiley & Sons, Ltd. [source] Equilibrium problem for thermoelectroconductive body with the Signorini condition on the boundaryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001D. Hömberg Abstract We investigate a boundary value problem for a thermoelectroconductive body with the Signorini condition on the boundary, related to resistance welding. The mathematical model consists of an energy-balance equation coupled with an elliptic equation for the electric potential and a quasistatic momentum balance with a viscoelastic material law. We prove the existence of a weak solution to the model by using the Schauder fixed point theorem and classical results on pseudomonotone operators. Copyright © 2001 John Wiley & Sons, Ltd. [source] Sound Insulation by Laminated Viscoelastic PlatesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003S. Langer Dr.-Ing. Plates are basic components in industrial structural design whose acoustical properties are often very important to reduce noise, e.g., in a car or a building. The sound insulation by plates is influenced by various effects, e.g., by the plate's mass but also by their damping capability. Hence, for a realistic analysis, damping should be taken into account which can approximatively be modelled by the use of a viscoelastic material law. Moreover, in automotive industry and structural engineering, laminated plates are very common to improve stiffness and stability, where plates with a viscoelastic core and rigid faces show additionally an excellent acoustical behaviour. Those laminated panes with a viscoelastic core are used in the design of windscreens, and, to improve sound insulation, in the design of building windows. Here, the mechanical behaviour of such a laminated plate is described by using a homogenisation procedure. The damping property of the plate is influenced by the stiffness of the viscoelastic core, it's dissipation factor, and by the thickness of the dissipating layer. These properties of a three-layer-plate are mapped on homogenised material parameters of a simple plate via the Ansatz of Ross, Kerwin and Ungar (RKU-Ansatz). Finally, the sound insulation effectiveness of plates is analysed numerically. [source] Lebensdauerermittlung bei mehrachsigen wechselnden Beanspruchungen im niedrigen und hohen TemperaturbereichMATERIALWISSENSCHAFT UND WERKSTOFFTECHNIK, Issue 9 2003E. Roos multiaxial fatigue; creep fatigue; stress theories; material laws Abstract Zur Berechnung der Dauerfestigkeit von Bauteilen aus duktilen Werkstoffen bei komplexer Schwingbeanspruchung stehen unterschiedliche Verfahren zur Verfügung. Hierbei wird im Wesentlichen zwischen den Festigkeitshypothesen der Integralen Anstrengung und denen der Kritischen Schnittebene unterschieden. Als typische Repräsentanten werden die Schubspannungsintensitätshypothese (SIH) sowie die Methode der kritischen Schnittebene (MKS) ausgewählt und für körperfeste und nicht körperfeste Hauptspannungsrichtungen gegenübergestellt. Für synchrone Beanspruchungen wird darüber hinaus das Berechnungsverfahren mit dem Anstrengungsverhältnis nach Bach verglichen. Die Berechnungsmethodik wird deutlich komplexer, wenn zeitabhängige Werkstoffeigenschaften bei entsprechend hohen Temperaturen mit in die Betrachtung einbezogen werden müssen. Für diesen Fall wird die Anwendung von viskoplastischen Stoffgesetzen erforderlich, die eine Beschreibung von Kriechen und Ermüdung in Kombination ermöglichen. Am Beispiel eines modifizierten Werkstoffmodells nach Chaboche / Nouailhas wird die Berechnung mehrachsiger Kriechermüdungsversuche vorgestellt. Life time assessment on multiaxial cyclic loadings at low and high temperatures For the calculation of fatigue strength of components made out of ductile materials under complex cyclic load different assessments are present. As typical representatives of stress theories the shear stress intensity hypothesis (SIH) as well as the method of critical plane approach (MKS) are considered and compared for rigid and non rigid principle stress directions. Furthermore for synchronous loads the calculation methods are compared with Bach's method. The calculation method becomes more complex, if time dependent material properties at corresponding high temperatures have to be taken into account. In this case the application of viscoplastic material models is necessary, which allows the consideration of combination of creep and fatigue. As an example a modified material model by Chaboche / Nouailhas is used in order to present the calculation of multiaxial creep fatigue tests. [source] A structural observation for linear material laws in classical mathematical physicsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2009Rainer Picard Abstract A class of linear material laws is considered, which covers a number of diverse initial boundary-value problems of classical mathematical physics. The claim that this class is indeed to a large extent sufficiently general is exemplified for a number of specific models from classical physics. Copyright © 2009 John Wiley & Sons, Ltd. [source] Thermo,mechanical behaviour of steel including phase transitions and transformation,induced plasticityPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Michael Wolff In the framework of Rational Mechanics, we formulate a continuum-mechanical model for the thermo-mechanical behaviour of steel. Our plasticity model is based on the assumption of intermediate configurations. We include phase transitions, plasticity as well as transformation-induced plasticity (TRIP) and allow for general material laws. Some consequences will be derived from the Clausius-Duhem inequality. The resulting model is a system of strongly coupled PDE's for displacement, temperature and phase distributions. A quenching test is numerically simulated. This work has been partially supported by the DFG via the SFB 570 "Distortion Engineering", University of Bremen. [source] Untersuchungen zum Werkstoffverhalten des Feinkornbaustahls S 460 unter erhöhten TemperaturenBAUTECHNIK, Issue 10 2007Jörg Lange Prof. Dr.-Ing. Die Bestimmung der Tragfähigkeit von Bauteilen aus S 460 im Brandfall auf der Grundlage vereinfachter oder allgemeiner Berechnungsverfahren entsprechend EN 1993-1-2 [1] erfordert die Kenntnis der mechanischen Eigenschaften des hochfesten Feinkornbaustahls unter erhöhten Temperaturen. Hierzu wurden Untersuchungen an Probestäben aus einem normalisierend gewalzten S 460 N und einem thermomechanisch gewalzten S 460 M durchgeführt. Beide Stahlsorten unterscheiden sich sowohl in ihrer chemischen Zusammensetzung als auch in der Temperaturführung beim Walzen. Auf der Grundlage instationärer Warmkriechversuche wurden Werkstoffgesetze für den Temperaturbereich von 20 bis 900 °C hergeleitet. Die Untersuchungen zeigen eine im Vergleich zu S 460 N erhöhte Festigkeit des S 460 M bei hohen Temperaturen. Diese ist zurückzuführen auf die durch das thermomechanische Walzen verursachte Verfestigung und die Verringerung der Kriechgeschwindigkeit durch Niob- und Titanausscheidungen. Beim Vergleich der Ergebnisse mit den in EN 1993-1-2 [1] für S 460 angegebenen Werkstoffgesetzen erkennt man, dass diese sowohl die Festigkeit als auch die Steifigkeit des untersuchten S 460 N überschätzen. Examination of the mechanical properties of the microalloyed grain refined steel S 460 at elevated temperatures. To establish a basis for calculating the load-bearing capacity of steel members made of S 460 in fire, corresponding to EN 1993-1-2 [1], the mechanical properties of the microalloyed grain refined steel S 460 under high temperatures have been examined. Two different kinds of steel have been considered: a normalised rolled S 460 N and a thermomechanically rolled S 460 M, that differ in their chemical composition and the temperature control during the hot-rolling process. On the basis of transient state tensile tests, material laws have been derived for the temperature range from 20 to 900 °C. The test results show an increased strength of S 460 M at elevated temperatures in comparison to S 460 N. This is a result of the strain hardening caused by the thermomechanical deformation and the precipitates formed by niobium and titanium that constrain creep deformations. The data derived from the tests show that the stress-strain relationships given in EN 1993-1-2 [1] for S 460 overestimate both the strength and the stiffness of the examined S 460 N. [source] Anwendung der neuen Stahlbetonnormen für die Bemessung von TunnelinnenschalenBETON- UND STAHLBETONBAU, Issue 2 2004Bruno Mattle Dipl.-Ing. Abstract Die in den letzten Jahren in der Bundesrepublik Deutschland und in Österreich errichteten Verkehrstunnel wurden i. a. zweischalig, d. h. mit einer Spritzbetonaußenschale und einer Innenschale aus unbewehrtem Beton oder Stahlbeton hergestellt. Die Bemessung der Innenschalen erfolgte unter Anwendung der Normen DIN 1045 [1] und ÖN B 4200 [2]. Während die neuen Normen wie EC 2 [3], DIN 1045-1 [4] und ÖN B 4700 [5] im Hochbau schon seit längerem Anwendung finden, ist deren Anwendung für die Bemessung von Tunnelschalen im wesentlichen noch Neuland. Dies betrifft insbesondere die Anwendung des Teilsicherheitskonzeptes und die Möglichkeit, die Schnittgrößen unter Anwendung nichtlinearer Stoffgesetze zu ermitteln. Im vorliegenden Beitrag wird die Problematik dargestellt und anhand von Beispielen der Einfluß unterschiedlicher Annahmen aufgezeigt. Design of Final Tunnel Linings according to the new Codes for Reinforced Concrete The traffic tunnels which have been constructed during the last few years in Germany and Austria in general have an initial shotcrete lining and a final, cast in place reinforced or unreinforced concrete lining. The structural design of the final linings has been based on specific standards from the clients and on the national codes DIN 1045 [1] and ÖN B 4200 [2]. While the new codes EC 2 [3], DIN 1045-1 [4] and ÖN B 4200 [5] have been widely used for the structural design of buildings for a while, their application for the design of tunnel linings is more or less a new field. In particular this is valid for using nonlinear material laws and the partial safety factor concept. In the presented paper this topic is discussed and the consequences of different assumptions are shown on specific examples. [source] Meßtechnische Erfassung von Lage und Verformung eines Stahltragwerks unter TemperatureinflußBAUTECHNIK, Issue 2 2004Hans Schulz Dipl.-Ing. An einem Abschnitt des stählernen Traggerüsts der Wuppertaler Schwebebahn wurden über einen längeren Zeitraum dreidimensionale geodätische Messungen durchgeführt, um die Verformungen von Stahlbauwerken unter Temperaturlast zu untersuchen. Aus einem genauen geodätischen Netz heraus wurden die Koordinaten von am Objekt vermarkten Punkten bei gleichzeitiger Erfassung der Stahltemperatur bestimmt. Ziele der Untersuchungen waren, die mit einem Standardmeßverfahren in der Praxis erreichbaren Meßunsicherheiten für Kontroll-, Überwachungs- und Absteckungsvermessungen an komplexen Stahlkonstruktionen zu ermitteln und gleichzeitig zu überprüfen, ob sich die Konstruktion unter Temperaturlast dem Materialgesetz entsprechend verhält. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) Recording of position and deformation of a steel structure with geodetic measurements under varying climatic conditions. Repeated geodetic 3d-measurements on a part of the steel construction of the Wuppertal Suspension Railway were carried out to analyse the influence of the momentarily prevailing steel temperature on the geometry of the construction. Based on a precise geodetic network the coordinates of points marked out on the construction were determined simultaneously recording the steel temperature. The objectives of the measurement were on the one hand to derive the measuring uncertainties, that can be achieved in practice for control and setting-out measurements on complex steel constructions applying a standard method, and on the other hand to check if the behaviour of the construction under temperature load is according to the material's law. [source] | ||||||||||