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

Cover image for Vol. 93 Issue 10‐11

Special Issue: Mathematical Modeling: Contact Mechanics, Phase Transitions, Multiscale Problems. In Memory of Christof Eck

October 2013

Volume 93, Issue 10-11

Pages 713–840

Issue edited by: Tomás Roubíček

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. You have free access to this content
      Cover Picture: ZAMM 10–11 / 2013

      Article first published online: 7 OCT 2013 | DOI: 10.1002/zamm.201390018

      Thumbnail image of graphical abstract

      A micro-scale phase field modeling of dendritic growth due to phase transition during solidification processes in binary mixtures; for more details about the mathematical model and computations see M. Redeker & C. Eck: A fast and accurate adaptive solution strategy for two-scale models with continuous inter-scale dependencies, J. Comput. Phys. 240, 268–283 (2013).

  2. Issue Information

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. You have free access to this content
      Issue Information: ZAMM 10–11 / 2013

      Article first published online: 7 OCT 2013 | DOI: 10.1002/zamm.201390019

  3. Contents

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. You have free access to this content
      Contents: ZAMM 10–11 / 2013 (pages 713–716)

      Article first published online: 7 OCT 2013 | DOI: 10.1002/zamm.201309310

  4. Editorial

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. You have free access to this content
      Editorial: Christof Eck 24.04.1968–14.09.2011 (pages 717–718)

      Jiří Jarušek, Christian Rohde, Tomás Roubíček, Anna-Margarete Sändig, Kunibert G. Siebert and Wolfgang L. Wendland

      Article first published online: 7 OCT 2013 | DOI: 10.1002/zamm.201393011

  5. Original Papers

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. On the stable discretization of strongly anisotropic phase field models with applications to crystal growth (pages 719–732)

      J.W. Barrett, H. Garcke and R. Nürnberg

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201200147

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      The authors introduce unconditionally stable finite element approximations for anisotropic Allen–Cahn and Cahn--Hilliard equations. These equations frequently feature in phase field models that appear in materials science. On introducing the novel fully practical finite element approximations they prove their stability and demonstrate their applicability with some numerical results.

    2. Dynamic contact problem for a von Kármán–Donnell shell (pages 733–744)

      I. Bock and J. Jarušek

      Article first published online: 30 JAN 2013 | DOI: 10.1002/zamm.201200152

      The existence of solutions is proved for the unilateral dynamic contact of a von Kármán-Donnell shell with a rigid obstacle. Both purely elastic material and a material with a singular memory are treated.

    3. A two scale model for liquid phase epitaxy with elasticity: An iterative procedure (pages 745–761)

      Ch. Eck, M. Kutter, A.-M. Sändig and Ch. Rohde

      Article first published online: 2 JUL 2013 | DOI: 10.1002/zamm.201200238

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      Epitaxy is a technically relevant process since it gives the possibility to generate microstructures of different morphologies. These microstructures can be influenced by elastic effects in the epitaxial layer. The authors consider a two scale model including elasticity, introduced by Eck and Emmerich. The coupling of the microscopic and the macroscopic equations is described by an iterative procedure. They concentrate on the microscopic equations and study their solvability in appropriate function spaces. As the main results they prove the existence and uniqueness of solutions of the three single parts of the microscopic problem.

    4. Layer potential analysis for a Dirichlet-transmission problem in Lipschitz domains in ℝn (pages 762–776)

      D. Fericean and W.L. Wendland

      Article first published online: 25 FEB 2013 | DOI: 10.1002/zamm.201200185

      The authors obtain the existence and uniqueness in some Sobolev and Lp spaces for a Dirichlet-transmission problem for the Stokes and Brinkman equations on Lipschitz domains in ℝn, n > 3. In the particular case n = 3 this problem describes the Stokes flow of a viscous incompressible fluid past a porous particle and in presence of a solid core. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, they use an indirect boundary integral formulation based on the layer potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the Stokes flow past a porous particle with large permeability, respectively low permeability, are also analyzed.

    5. On uniqueness results for an elliptic-parabolic-system of partial differential equations arising in dynamic electrowetting (pages 777–788)

      M.A. Fontelos and G. Grün

      Article first published online: 8 APR 2013 | DOI: 10.1002/zamm.201200200

      The authors prove regularity results and, as a consequence, uniqueness for a system of partial differential equations arising in the study of dynamic electrowetting phenomena and more general electrokinetic processes in three space dimensions. The system consists of Stokes equations coupled with equations for the motion of electric charges, Poisson equation for computing the electric field generated by such charges and a Cahn-Hilliard equation for a phase field describing two fluids with different material parameters. The deduction and existence of weak solutions for this system was established in an earlier paper (Christof Eck et al., On a phase-field model for electrowetting, Interfaces Free Bound. 11(2),259–290, (2009)).

    6. A contact problem for electro-elastic materials (pages 789–800)

      S. Hüeber, A. Matei and B. Wohlmuth

      Article first published online: 29 JUL 2013 | DOI: 10.1002/zamm.201200235

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      The authors analyze the frictionless unilateral contact between an electro-elastic body and a rigid electrically conductive foundation. On the potential contact zone, they use the Signorini condition with non-zero gap and an electric contact condition with a conductivity depending on the Cauchy vector. They provide a weak variationally consistent formulation and show existence, uniqueness and stability of the solution. Their analysis is based on fixed point techniques for weakly sequentially continuous maps.

    7. Spatial decay for several phase-field models (pages 801–810)

      A. Miranville and R. Quintanilla

      Article first published online: 30 JAN 2013 | DOI: 10.1002/zamm.201200131

      The authors study the spatial behavior of three phase-field models. First, they consider the Cahn-Hilliard equation and they obtain the exponential decay of solutions under suitable assumptions on the data. Then, for the classical isothermal phase-field equation (i.e., the Allen-Cahn equation), they prove the nonexistence and the fast decay of solutions and, for the nonisothermal case governed by the Fourier law, they obtain a Phragmén-Lindelöf alternative of exponential type, respectively.

  6. Editor's Choice

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. You have free access to this content
      Drug release from collagen matrices including an evolving microstructure (pages 811–822)

      N. Ray, T. van Noorden, F.A. Radu, W. Friess and P. Knabner

      Article first published online: 28 FEB 2013 | DOI: 10.1002/zamm.201200196

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      Biodegradable collagen matrices have become a~promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled drug release are the diffusion of water into the collagen matrix, the swelling of the matrix coming along with drug release, and enzymatic degradation of the matrix with additional simultaneous drug release. These phenomena have been extensively studied in the past experimentally, via numerical simulations as well as analytically. However, a rigorous derivation of the macroscopic model description, which includes the evolving microstructure due to the degradation process, is still lacking. Since matrix degradation leads to the release of physically entrapped active agent, a~good understanding of these phenomena is very important. The authors present such a~derivation using formal twoscale asymptotic expansion in a~level set framework and complete their results with numerical simulations in comparison with experimental data.

  7. Original Paper

    1. Top of page
    2. Cover Picture
    3. Issue Information
    4. Contents
    5. Editorial
    6. Original Papers
    7. Editor's Choice
    8. Original Paper
    1. Quasistatic adhesive contact of visco-elastic bodies and its numerical treatment for very small viscosity (pages 823–840)

      T. Roubíček, C.G. Panagiotopoulos and V. Mantič

      Article first published online: 9 APR 2013 | DOI: 10.1002/zamm.201200239

      Thumbnail image of graphical abstract

      An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional, and inertia is neglected. The asymptotics for the viscosity approaching zero towards purely elastic material involves a certain defect-like measure recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity, which is demonstrated on particular 2-dimensional computational simulations based on a semi-implicit time discretisation and a spacial discretisation implemented by boundary-element method.

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