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  • 1
    Electronic Resource
    Electronic Resource
    Direct computation of instability points with inequality constraints using the FEM (2003)
    Bradford : Emerald
    Engineering computations 20 (2003), S. 611-628 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: The subject of this paper is the computation of instability points in mechanical problems with the finite element method. The objective is to extend the application of critical point detection methods to problems with inequality constraints originating from damage and contact. A simple bilinear model is considered for the damage problems. A bilateral, frictionless contact formulation is used for the contact problems. Among the critical point detection methods the focus is laid on the critical displacement method and the extended system. At first a possible combination of both methods is evaluated by applying them to damage problems. A prediction method based on the extended system is developed to facilitate the comparison of both methods. Secondly, the extended system is used as a computation method for critical points in two-dimensional contact problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400310488781
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  • 2
    Electronic Resource
    Electronic Resource
    An algebraic multigrid solver for finite element computations in solid mechanics (1997)
    Bradford : Emerald
    Engineering computations 14 (1997), S. 202-215 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: Presents an implementation of the algebraic multigrid method. It can work in two ways: as pure multigrid method and as a pre-conditioner for the conjugate gradient method. Shows applications of the iterative solvers for problems in linear and non-linear elasticity. Shows the range of possible applications with different examples with regular and non-regular meshes and three-dimensional problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644409710166181
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  • 3
    Electronic Resource
    Electronic Resource
    Comparative crash simulations incorporating the results of sheet forming analyses (2001)
    Bradford : Emerald
    Engineering computations 18 (2001), S. 744-758 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: To obtain more reliable crash simulations the history of the structure related to the forming process is considered. For this goal the variables defining the current state have to be transferred from one mesh to the other in order to maintain a consistent discretization of the whole structure consisting of several pre-formed parts. This is accomplished here by remeshing the structure after the forming process and by transferring the current mechanical properties. In performing such a transfer a numerical error cannot be avoided; the results of this approach are therefore compared with computations in which this transfer is not applied to assess the performance of the presented procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/EUM0000000005786
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  • 4
    Electronic Resource
    Electronic Resource
    A superlinear convergent augmented Lagrangian procedure for contact problems (1999)
    Bradford : Emerald
    Engineering computations 16 (1999), S. 88-119 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: The numerical solution of contact problems via the penalty method yields approximate satisfaction of contact constraints. The solution can be improved using augmentation schemes. However their efficiency is strongly dependent on the value of the penalty parameter and usually results in a poor rate of convergence to the exact solution. In this paper we propose a new method to perform the augmentations. It is based on estimated values of the augmented Lagrangians. At each augmentation the converged state is used to extract some data. Such information updates a database used for the Lagrangian estimation. The prediction is primarily based on the evolution of the constraint violation with respect to the evolution of the contact forces. The proposed method is characterised by a noticeable efficiency in detecting nearly exact contact forces, and by superlinear convergence for the subsequent minimisation of the residual of constraints. Remarkably, the method is relatively insensitive to the penalty parameter. This allows a solution which fulfils the constraints very rapidly, even when using penalty values close to zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644409910251292
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  • 5
    Electronic Resource
    Electronic Resource
    Modeling and simulation of the decohesion of particulate aggregates in a binding matrix (2001)
    Bradford : Emerald
    Engineering computations 18 (2001), S. 79-95 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: A model for the decohesion of aggregates of suspended particulate material in a binding matrix is developed. In the model cohesive zones which envelop each particle individually are introduced at the particulate/binder interface. During progressive loading, the deterioration of the cohesive zones is initiated if constraints placed on the microstress fields are violated. In order for the material behavior to be energetically admissible, the deterioration of the material at a point is in the form of a reduction of the elasticity tensor's eigenvalues at that point. The material within the cohesive zones deteriorates until the constraints are met. In order to isolate and study the effects of interfacial deterioration, outside of the cohesive zones, the material is unaltered. Mathematical properties of the model, as well as physical restrictions, are discussed. Numerical simulations are performed employing the finite element method to illustrate the approach in three-dimensional applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400110365824
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  • 6
    Electronic Resource
    Electronic Resource
    Phenomenological modeling and numerical simulation of the environmental degradation of multiphase engineering materials (2000)
    Springer
    Archive of applied mechanics 70 (2000), S. 47-64 
    Details
    ISSN: 1432-0681
    Keywords: Key words Multiphase materials ; micromechanics ; environmental degradation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary In this paper a coupled thermodynamical/chemical/mechanical model is developed to simulate the time dependent degradation of heterogeneous solid materials subjected to corrosive environments. The model, which is based on a description of the microscale, employs the first law of thermodynamics, a mass balance of a diffusing corrosive species, and a balance of momentum. The presence of the corrosive species is phenomenologically modeled as irreversibly reducing the material stiffness, dependent on the amount and time present. Numerical experiments are given to illustrate some characteristics of the model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004199900032
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  • 7
    Electronic Resource
    Electronic Resource
    Theory and numerics of thin elastic shells with finite rotations (1989)
    Springer
    Archive of applied mechanics 59 (1989), S. 54-67 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird eine Biegetheorie elastischer Schalen mit endlichen Drehungen dargestellt und die numerische Behandlung mit der Methode der finiten Elemente beschrieben. Dazu müssen die Verzerrungen und die schwache Form des Gleichgewichts angegeben werden. Es wird eine Reissner-Mindlin-Kinematik zugrunde gelegt. Die Verwendung des Greenschen Verzerrungstensors führt im Schalenraum bei endlichen Drehungen auf sehr komplizierte Ausdrücke. Daher wird von der polaren Zerlegung des materiallen Deformationsgradienten ausgegangen. In diesem Fall sind die Kräfte und Momente Spannungsresultierende des Biot-Spannungstensors, der invariant gegenüber Starrkörperbewegungen und somit für ein Stoffgesetz geeignet ist. Als Drehkinematen werden Eulerwinkel verwandt. Um allgemeine Schalengeometrien beschreiben zu können, wird eine isoparametrische Elementformulierung gewählt. Endliche Drehungen können in den berechneten Platten- und Schalenproblemen in einem Lastschritt aufgebracht werden. Die Lastschrittweite wird nur durch das Lösungsverfahren und das Auftreten von Stabilitätspunkten beschränkt.
    Notes: Summary A bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a Reissner-Mindlin theory. The starting point for the derivation of the strain measures is the polar decomposition of the material deformation gradient. The work-conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and therefore appropriate for the formulation of constitutive equations. The rotations are described by using Eulerian angles. The finite element discretization of arbitrary shells is performed using isoparametric elements. The advantage of the proposed shell formulation and its numerical model is shown by application to different non-linear plate and shell problems. Finite rotations can be calculated within one load increment. Thus the step size of the load increment is only imited by the local convergence behaviour of Newton's method or the appearance of stability phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536631
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  • 8
    Electronic Resource
    Electronic Resource
    An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 465-477 
    Details
    ISSN: 1432-0681
    Keywords: Key words FEM ; shell ; finite plasticity ; associated flow rule ; isotropic hardening
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00835659
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  • 9
    Electronic Resource
    Electronic Resource
    An axisymmetrical quasi-Kirchhoff-type shell element for large plastic deformations (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 465-477 
    Details
    ISSN: 1432-0681
    Keywords: FEM ; shell ; finite plasticity ; associated flow rule ; isotropic hardening
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary An axisymmetrical shell element for large plastic strains is developed. The theory is based on the multiplicative decomposition of the material deformation gradient into an elastic and a plastic part. For quasi-Kirchhoff-type axisymmetric shells this leads to a product of the elastic and plastic stretches. By introduction of logarithmic strains the decomposition becomes additive. Plastic incompressibility is fulfilled in an exact manner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00835659
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  • 10
    Electronic Resource
    Electronic Resource
    On the treatment of nonlinear unilateral contact problems (1993)
    Springer
    Archive of applied mechanics 63 (1993), S. 116-129 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird das Kontaktverhalten eines deformierbaren Körpers beschrieben, der endliche Deformationen erfährt, wenn er auf ein starres Hindernis gedrückt wird. Dabei findet die Penalty-Formulierung Anwendung. Zur Kontakterkennung werden isoparametrische Kontaktelemente verwendet. Ausgehend von deren Gausspunkten wird der Abstand des Körpers zum Hindernis bestimmt, das alsC 2-stetige Funktion beschrieben wird. Variation und anschließende konsistente Linearisierung liefern die Tangentenmatrix für die Kontaktelemente in allgemeiner Form, die dann in ein standardmäßiges Finit-Element-Programm eingebaut werden kann.
    Notes: Summary This paper is concerned with finite deformations of elastic bodies in the presence of unilateral constraints. The penalty formulation is applied to introduce the contact constraints. We develop special isoparametric contact elements. Starting from their Gaussian points the distance between the body and the obstacle is determined, where the obstacle is given as aC 2 continuous function. Variation and subsequent consistent linearization yield the tangent matrix of the contact elements in its general form, which can be incorporated into standard finite element schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00788917
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