Staff Dr. Martin Lenz

Address:
Institut für Numerische Simulation
Endenicher Allee 60
53115 Bonn
Phone: +49 228 73-3416
Office: EA60 2.037
E-Mail: ed tod nnob-inu tod sni ta znel tod nitrama tod b@foo tod de

Teaching

Winter semester 2023/24

See teaching activities of the whole group.

Research Projects

Current

Numerical optimization of shape microstructures

Project C06, DFG SFB 1060.

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Completed

Mathematical modeling and simulation of microstructured magnetic-shape-memory materials

Project A6, DFG priority program 1239.

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The macroscopic behavior of magnetic shape-memory (MSM) materials is largely determined by the formation of fine-scale structures, both in the elastic and in the magnetic degrees of freedom. Most practically used samples exhibit additional inhomogeneities on the mesoscale, such as for example the grain structure in polycrystals. The interaction of the two types of microstructure is up to now only poorly understood. Focusing on two occurrences of high current experimental relevance we intend to investigate the role of microstructure for the macroscopic material behavior, and to furnish criteria to improve material production. Building upon the static continuum model developed in the first phase, which permits to resolve the magnetic and elastic structure at scales much smaller than the domain size, we plan:

1) to consider the experimentally relevant case of grains larger than the domain size, where the magnetoelastic behavior of a grain is determined by averaging over the domains;

2) to study dynamics and in particular hysteresis by formulating an evolutionary problem which resolves the motion of individual domain boundaries; and

3) to study the dynamics for grains larger than the domain size, with an averaged version of the evolution model. For each issue we shall address the development of a model, the numerical implementation of the obtained models, and the application to the study of MSM-polymer composites and MSM polycrystals.

Publications

  1. Geometry of needle-like microstructures in shape-memory alloys. S. Conti, M. Lenz, M. Rumpf, J. Verhülsdonk, and B. Zwicknagl. Shap. Mem. Superelasticity, 2023. BibTeX DOI
  2. Microstructure of macrointerfaces in shape-memory alloys. S. Conti, M. Lenz, M. Rumpf, J. Verhülsdonk, and B. Zwicknagl. J. Mech. Phys. Solids, 179:105343, 2023. BibTeX DOI
  3. Geometry of martensite needles in shape memory alloys. S. Conti, M. Lenz, N. Lüthen, M. Rumpf, and B. Zwicknagl. C. R. Math. Acad. Sci. Paris, 358(9-10):1047–1057, 2020. BibTeX DOI arXiv
  4. A posteriori modeling error estimates in the optimization of two-scale elastic composite materials. S. Conti, B. Geihe, M. Lenz, and M. Rumpf. ESAIM: Mathematical Modelling and Numerical Analysis, 52(4):1457–14761, July–August 2018. BibTeX PDF DOI arXiv
  5. Homogenization in magnetic-shape-memory polymer composites. S. Conti, M. Lenz, M. Pawelczyk, and M. Rumpf. In V. Schulz and D. Seck, editors, Shape Optimization, Homogenization and Optimal Control : DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017, pages 1–17. Springer International Publishing, Cham, 2018. BibTeX DOI
  6. Hysteresis in magnetic shape memory composites: modeling and simulation. S. Conti, M. Lenz, and M. Rumpf. J. Mech. Phys. Solids, 89:272–286, 2016. BibTeX PDF DOI arXiv
  7. Risk averse elastic shape optimization with parametrized fine scale geometry. B. Geihe, M. Lenz, M. Rumpf, and R. Schultz. Mathematical Programming, 141(1-2):383–403, 2013. BibTeX PDF DOI
  8. Modeling and simulation of large microstructured particles in magnetic-shape-memory. S. Conti, M. Lenz, and M. Rumpf. Advanced Engineering Materials, 14(8):582–588, 2012. BibTeX PDF DOI
  9. A convergent finite volume scheme for diffusion on evolving surfaces. M. Lenz, S. F. Nemadjieu, and M. Rumpf. SIAM Journal on Numerical Analysis, 49(1):15–37, 2011. BibTeX PDF DOI
  10. Macroscopic behaviour of magnetic shape-memory polycrystals and polymer composites. S. Conti, M. Lenz, and M. Rumpf. In 7th European Symposium on Martensitic Transformations and Shape Memory Alloys, volume 481–482 of Materials Science and Engineering: A, 351–355. 2008. BibTeX PDF DOI
  11. Finite volume method on moving surfaces. M. Lenz, S. F. Nemadjieu, and M. Rumpf. In R. Eymard and J.-M. Hérald, editors, Finite Volumes for Complex Applications V, 561–576. Wiley, 2008. BibTeX PDF
  12. Modeling and simulation of magnetic shape-memory polymer composites. S. Conti, M. Lenz, and M. Rumpf. Journal of Mechanics and Physics of Solids, 55:1462–1486, 2007. BibTeX PDF DOI
  13. Modellierung und Simulation des effektiven Verhaltens von Grenzflächen in Metalllegierungen. M. Lenz. Dissertation, University Bonn, 2007. BibTeX PDF Read
  14. Multiple scales in phase separating systems with elastic misfit. H. Garcke, M. Lenz, B. Niethammer, M. Rumpf, and U. Weikard. In A. Mielke, editor, Analysis, Modeling and Simulation of Multiscale Problems. Springer, 2006. BibTeX PDF Publisher
  15. Numerical methods for fourth order nonlinear degenerate diffusion problems. J. Becker, G. Grün, M. Lenz, and M. Rumpf. Applications of Mathematics, 47(6):517–543, 2002. BibTeX DOI
  16. A finite volume scheme for surfactant driven thin film flow. G. Grün, M. Lenz, and M. Rumpf. In R. Herbin and D. Kröner, editors, Finite Volumes for Complex Applications III, 567–574. Hermes Penton Sciences, 2002. BibTeX PDF
  17. Finite Volumen Methoden für degenerierte parabolische Systeme – Ausbreitung eines Surfactant auf einem dünnen Flüssigkeitsfilm. M. Lenz. Diploma thesis, University Bonn, 2002. BibTeX PDF
  18. A procedural interface to hierarchical grids. T. Geßner, B. Haasdonk, R. Kende, M. Lenz, R. Neubauer, M. Metscher, M. Ohlberger, W. Rosenbaum, M. Rumpf, R. Schwörer, M. Spielberg, and U. Weikard. Technical Report, SFB 256, University Bonn, 1999. BibTeX PDF Link