ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik

Cover image for Vol. 93 Issue 2‐3

Special Issue: Continuum Mechanics

February 2013

Volume 93, Issue 2-3

Pages 83–194

Issue edited by: Stefan Diebels

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
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      Cover Picture: ZAMM 2–3 / 2013

      Version of Record online: 1 FEB 2013 | DOI: 10.1002/zamm.201390003

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      See T. Schüler et al., ZAMM 93 (2013) 2–3, p. 133, Fig. 5: Effective shear strain state for the different boundary conditions on the microlevel at state of equilibrium (t [RIGHTWARDS ARROW] ∞). Left: Linear displacement (Dirichlet) boundary conditions, middle: Periodic boundary conditions (PBC), right: Constant traction (Neumann) boundary conditions for identical effective shear deformation states.

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. You have free access to this content
      Issue Information: ZAMM 2–3 / 2013

      Version of Record online: 1 FEB 2013 | DOI: 10.1002/zamm.201390004

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. You have free access to this content
      Contents: ZAMM 2–3 / 2013 (pages 83–86)

      Version of Record online: 1 FEB 2013 | DOI: 10.1002/zamm.201309302

  4. Editorial

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. You have free access to this content
      Editorial: ZAMM 2–3 / 2013 (page 87)

      Stefan Diebels

      Version of Record online: 1 FEB 2013 | DOI: 10.1002/zamm.201309344

  5. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. You have free access to this content
      Parameter re-identification in nanoindentation problems of viscoelastic polymer layers: small deformation (pages 88–101)

      Z. Chen and S. Diebels

      Version of Record online: 27 JUN 2012 | DOI: 10.1002/zamm.201100170

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      In the present paper, the inverse method based on the finite element simulation and numerical optimisation is used to characterise the viscoelastic properties of polymers from nanoindentation. First of all, the boundary value problem of nanoindentation considering real geometry, is simulated with the FE code ABAQUS®. A linear viscoelastic model for small strains is currently applied to describe the rate-dependent material behaviour. The rate-dependent properties of the polymer layer under nanoindentation is investigated with various loading histories: cyclic testing, single step relaxation, monotonic testing and sinusoidal oscillatory testing. A parameter re-identification strategy offers a deep insight into the relationship between the accuracy of identification and the loading history. A method to choose a suitable loading history to identify the parameters more accurately is recommended.

  6. Original Paper

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. Modelling the hydrothermomechanical properties of polymers close to glass transition (pages 102–112)

      M. Engelhard and A. Lion

      Version of Record online: 19 APR 2012 | DOI: 10.1002/zamm.201100185

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      In this work a model to describe the behaviour of polymers close to glass transition is presented. The focus lies on the moisture depended properties of polymers. Based on the Coleman & Noll type of evaluation of the Clausius-Duhem inequality a thermomechanically consistent material model is derived, which is based on a series expansion of the Gibbs free energy around thermodynamic equilibrium. Now, besides constraints emanating from the second law of thermodynamics, it is possible to obtain three relations between the stress, the temperature, the internal variables and the water content on the one side and the strain, the entropy and the chemical potential of the water content on the other. Adjusting the free parameters in these relations allows for an accurate reproduction of measuring data from dynamic tension tests with PA 6.

  7. Book Review

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
  8. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Editor's Choice
    7. Original Paper
    8. Book Review
    9. Original Papers
    1. A numerical homogenisation method for sandwich plates based on a plate theory with thickness change (pages 113–125)

      C. Helfen and S. Diebels

      Version of Record online: 24 SEP 2012 | DOI: 10.1002/zamm.201100173

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      In the scope of this work, a composite plate is considered which is composed of a complex assembly of metal layers and carbon fibers reinforced polymers (CFRP) layers. The modelling of the mechanical behaviour of the composite plate is based on a numerical homogenisation: On the one hand, the macroscale is considered as a Finite Element computation of a plate following a plate theory including a thickness change. On the other hand, the mesoscale is obtained with a three-dimensional modell explicitly taking into account the stacking order and the material behaviour of the different layers.

    2. Multi-scale modelling of elastic/viscoelastic compounds (pages 126–137)

      T. Schüler, R. Manke, R. Jänicke, M. Radenberg and H. Steeb

      Version of Record online: 26 NOV 2012 | DOI: 10.1002/zamm.201200055

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      In this study, a multi-scale approach for elastic/viscoelastic compounds such as bituminous asphalt concret is presented. The focus is on the modelling aspects due to upscaling routines based on volume averaging. A simplified compound is introduced consisting of homogeneous viscoelastic binder phase and spherical filler particles with a volume fraction low compared to realistic asphalt concrete. Depending on the chosen boundary condition, stress-relaxation and creep tests are considered. After transformation of the effective stress-strain-relations from time- to frequency space, the viscoelastic properties of the compound are discussed in frequency domain.

    3. Infiltration processes in cohesionless soils (pages 138–146)

      A. Schaufler, C. Becker and H. Steeb

      Version of Record online: 6 AUG 2012 | DOI: 10.1002/zamm.201200047

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      In this paper, a thermodynamically consistent four-phase continuum model in the framework of the mixture theory is presented describing infiltration processes of suspensions in cohesionless granular material. To this end a constitutive equation describing infiltration phenomena is proposed which includes only one material parameter. Therefore a boundary value problem is studied numerically, which is characterized by a homogeneous field of the hydraulic gradient at the time t0 = 0. Infiltration affects the distribution of the hydraulic properties and the consequences of the proposed constitutive equation are illustrated for specific parameter choices. Furthermore it is shown how the material parameter can be estimated without explicit numerical calculations.

    4. Simulation of the abrasive flow machining process (pages 147–153)

      J. Schmitt and S. Diebels

      Version of Record online: 1 FEB 2013 | DOI: 10.1002/zamm.201200111

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      During the last decade the abrasive flow machining process became an accepted technique to smooth and to round inner edges in badly contactable regions of complex geometries, e.g. grooves in rails of common rail systems. The process is based on the flow of a highly viscous silicone oil which is charged by abrasive particles. This leads to an efficient rounding of the egdes. In the present article a material model for the non-Newtonian behaviour of the abrasive paste is proposed, the material parameters are identified according to experiments and, finally, a simulation of the abrasive flow machining process is presented based on a model implementation in the software package COMSOL Multiphysics®.

    5. An infinite element for the solution of Galbrun equation (pages 154–162)

      S. Retka and S. Marburg

      Version of Record online: 24 SEP 2012 | DOI: 10.1002/zamm.201200021

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      In this article a method is presented for the three-dimensional numerical simulation of the propagation of acoustic radiation inside and in the near field of long, slender, and hollow objects. While the fluid inside and close to the radiating body is meshed by Taylor-Hood tetrahedral finite elements, complex conjugated Astley-Leis infinite elements are added on the outer finite element boundary to present the effects in the far field. Flow is considered in the modal analysis, with the goal to determine the influence a moving fluid has on the eigenfrequencies of the model. Galbrun equation in a mixed, i.e. pressure and displacement based, formulation is used for the numerical realization and its weak form is presented for the finite element domain as well as for the infinite element domain.

    6. High-order finite elements compared to low-order mixed element formulations (pages 163–176)

      T. Netz, A. Düster and S. Hartmann

      Version of Record online: 24 SEP 2012 | DOI: 10.1002/zamm.201200040

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      This article compares high-order finite elements based on hierarchic shape functions with low-order mixed element formulations using finite strain hyperelasticity. These comparisons are conducted from the point of view of both accuracy and efficiency as well as highly deformed structures. It also investigates improvements to minimize the overall computational effort such as parallelizing the element assemblage procedure, choosing a starting vector estimator for Newton's method, and investigating the Newton-Chord method. The advantages and disadvantages of both finite element approaches are also discussed.

    7. Higher order accurate discontinuous and continuous p-Galerkin methods for linear elastodynamics (pages 177–194)

      T. Gleim and D. Kuhl

      Version of Record online: 11 JAN 2013 | DOI: 10.1002/zamm.201200044

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      The present paper is concerned with the numerical integration of linear structural dynamics by means of different higher order accurate discontinous and continous Galerkin time integration schemes. Single and two field formulations are investigated. In both algorithmic classes continuous Galerkin schemes are obtained by the strong enforcement of the continuity condition as special case of the discontinuous Galerkin schemes. The related time integration schemes are conditioned in an algorithmic set-up in such a manner that the implementation is similar to the classical Newmark scheme and its α derivates. Selected benchmark examples demonstrate the excellent dissipation and dispersion behavior and the robustness of the present Galerkin integration schemes. In particular the order of accuracy for each class of Galerkin integration schemes is specified. The comparison of the numerical effort for the classical Newmark scheme and the family of Galerkin schemes indicates advantages for Galerkin schemes: For a prescribed error level higher order Galerkin schemes are more effective than the Newmark scheme.

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