Project P7
Project description
Numerical Relaxation Techniques for the Modeling of Microstructure Evolution in Multifunctional Magnetic Materials
The main goal of project P7 is the formulation of novel, scale-bridging models for the coupled, nonlinear and dissipative behavior of magnetostrictive materials incorporating an explicit consideration of microstructure evolution on the basis of relaxed energy potentials. First, the locally homogenized magneto-mechanical response on the single crystal level is to be simulated in a basic model. The modeling approach is based on a geometric approximation of the characteristic microstructure via second order laminates. In this approach the evolution of energetic internal state variables is determined by the relaxation of non-convex energies. Changes in dissipative variables are governed by appropriate evolution equations. The second project phase is concerned with an extended relaxation model, in which for example finite magnetocrystalline anisotropy energy formulations and relaxation with additional degrees of freedom are considered. Furthermore, generalized notions and representations of material stability in the context of coupled magnetomechanical response will be investigated. The third project phase consists of the derivation of a theoretical and algorithmic framework for the computation of effective material properties on the polycrystalline and macro-level through the implementation of the developed relaxation models into scale-bridging finite element simulations.
Publications
Kiefer, B., Buckmann, K. & Bartel, T. (2015), "Numerical Energy Relaxation to Model Microstructure Evolution in Functional Magnetic Materials", GAMM-Mitteilungen. Vol. 38(1), pp. 171-196. |
BibTeX:
@article{Kief2015, author = {Kiefer, B.B. and Buckmann, K. and Bartel, T.}, title = {Numerical Energy Relaxation to Model Microstructure Evolution in Functional Magnetic Materials}, journal = {GAMM-Mitteilungen}, year = {2015}, volume = {38}, number = {1}, pages = {171--196}, note = {P7} } |
Schröder, J., Labusch, M., Keip, M.-A., Kiefer, B., Brands, D. & Lupascu, D.C. (2015), "Computation of Magneto-Electric Product Properties for BTO-CFO 0-3 Composites", GAMM-Mitteilungen. Vol. 38(1), pp. 8-24. |
BibTeX:
@article{Sch2015, author = {Schröder, J. and Labusch, M. and Keip, M.-A. and Kiefer, B. and Brands, D. and Lupascu, D. C.}, title = {Computation of Magneto-Electric Product Properties for BTO-CFO 0-3 Composites}, journal = {GAMM-Mitteilungen}, year = {2015}, volume = {38}, number = {1}, pages = {8--24}, note = {P1, P2, P7} } |
Bartel, T., Kiefer, B., Buckmann, K. & Menzel, A. (2014), "A Kinematically-Enhanced Relaxation Scheme for the Modeling of Displacive Phase Transformations", Intelligent Material Systems and Structures. |
BibTeX:
@article{Bartel2014, author = {T. Bartel and B. Kiefer and K. Buckmann and A. Menzel}, title = {A Kinematically-Enhanced Relaxation Scheme for the Modeling of Displacive Phase Transformations}, journal = {Intelligent Material Systems and Structures}, year = {2014}, doi = {http://dx.doi.org/10.1177/1045389X14557507} } |
Buckmann, K., Kiefer, B., Bartel, T. & Menzel, A. (2014), "Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques", In Proceedings of the Second Seminar on the Mechanics of Multifunctional Materials., pp. 7-10. |
BibTeX:
@inproceedings{Buckmann2014, author = {K. Buckmann and B. Kiefer and T. Bartel and A. Menzel}, title = {Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques}, booktitle = {Proceedings of the Second Seminar on the Mechanics of Multifunctional Materials}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, pages = {7--10} } |
Buckmann, K., Kiefer, B., Bartel, T. & Menzel, A. (2014), "Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 559-560. |
BibTeX:
@article{Buckmann2014, author = {K. Buckmann and B. Kiefer and T. Bartel and A. Menzel}, title = {Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, volume = {14}, pages = {559--560} } |
Kiefer, B., Buckmann, K., Bartel, T. & Menzel, A. (2014), "Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques", Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS). , pp. Paper 7436. |
BibTeX:
@article{Kiefer2014, author = {Kiefer, B. and Buckmann, K. and Bartel, T. and Menzel, A.}, title = {Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques}, journal = {Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS)}, year = {2014}, pages = {Paper 7436}, note = {DOI:10.1115/SMASIS2014-7436 P7 and P6} } |
Labusch, M., Keip, M.-A., Kiefer, B. & Schröder, J. (2014), "Computation of Effective Non-linear Inelastic Properties of Magnetostrictive Composites", Proceedings in Applied Mathematics and Mechanics. Vol. 14, pp. 559-560. |
BibTeX:
@article{Lab2014, author = {Labusch, M. and Keip, M.-A. and Kiefer, B. and Schröder, J.}, title = {Computation of Effective Non-linear Inelastic Properties of Magnetostrictive Composites}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2014}, volume = {14}, pages = {559--560}, note = {P1 and P7} } |
M. Labusch, M.-A. Keip, B.K.J.S. (2014), "Computation of the Effective Magnetostrictive Coeffcient of Magneto-mechanically Coupled Composites", In Proceedings of 11$^th$ World Congress on Computational Mechanics (WCCM XI). |
BibTeX:
@inproceedings{Labusch2014, author = {M. Labusch, M.-A. Keip, B. Kiefer, J. Schröder}, title = {Computation of the Effective Magnetostrictive Coeffcient of Magneto-mechanically Coupled Composites}, booktitle = {Proceedings of 11$^th$ World Congress on Computational Mechanics (WCCM XI)}, year = {2014} } |
Bartel, T., Buckmann, K., Kiefer, B. & Menzel, A. (2013), "An Advanced Energy Relaxation Scheme for the Modeling of Displacive Phase Transformations", Proceedings of the ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS). , pp. Paper 3041. |
BibTeX:
@article{Bartel2013, author = {Bartel, T. and Buckmann, K. and Kiefer, B. and Menzel, A.}, title = {An Advanced Energy Relaxation Scheme for the Modeling of Displacive Phase Transformations}, journal = {Proceedings of the ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems (SMASIS)}, year = {2013}, pages = {Paper 3041}, note = {P7 and P6 doi:10.1115/SMASIS2013-3041} } |
Kiefer, B., Bartel, T. & Menzel, A. (2012), "Implementation of Numerical Integration Schemes for the Simulation of Magnetic SMA Constitutive Response". |
BibTeX:
@inproceedings{KieBarMen:2012:ion, author = {Kiefer, B. and Bartel, T. and Menzel, A.}, title = {Implementation of Numerical Integration Schemes for the Simulation of Magnetic SMA Constitutive Response}, journal = {Smart Materials and Structure}, year = {2012} } |
Miehe, C., Kiefer, B. & Rosato, D. (2011), "An Incremental Variational Formulation of Dissipative Magnetostriction at the Macroscopic Continuum Level", International Journal of Solids and Structures. Vol. 48, pp. 1846-1866. |
BibTeX:
@article{Miehe2011, author = {Miehe, C. and Kiefer, B. and Rosato, D.}, title = {An Incremental Variational Formulation of Dissipative Magnetostriction at the Macroscopic Continuum Level}, journal = {International Journal of Solids and Structures}, year = {2011}, volume = {48}, pages = {1846--1866} } |
Bartel, T. & Hackl, K. (2010), "Multiscale Modeling of Martensitic Phase Transformations: On the Numerical Determination of Heterogeneous Mesostructures Within Shape-Memory Alloys Induced by Precipitates", Technische Mechanik. Vol. 30, pp. 324-342. |
BibTeX:
@article{BarHac:2010:mmo, author = {Bartel, T. and Hackl,K}, title = {Multiscale Modeling of Martensitic Phase Transformations: On the Numerical Determination of Heterogeneous Mesostructures Within Shape-Memory Alloys Induced by Precipitates}, journal = {Technische Mechanik}, year = {2010}, volume = {30}, pages = {324--342} } |
Bartel, T. & Hackl, K. (2009), "A Micromechanical Model for Martensitic Phase-Transformations in Shape-Memory Alloys Based on Energy-Relaxation", Zeitschrift für Angewandte Mathematik und Mechanik. Vol. 89, pp. 792-809. |
BibTeX:
@article{BarHac:2009:amm, author = {Bartel, T. and Hackl, K.}, title = {A Micromechanical Model for Martensitic Phase-Transformations in Shape-Memory Alloys Based on Energy-Relaxation}, journal = {Zeitschrift für Angewandte Mathematik und Mechanik}, year = {2009}, volume = {89}, pages = {792--809} } |
Kiefer, B. & Lagoudas, D. (2009), "Modeling the Coupled Strain and Magnetization Response of Magnetic Shape Memory Alloys under Magnetomechanical Loading", Journal of Intelligent Material Systems and Structures. Vol. 20, pp. 143-170. |
BibTeX:
@article{KieLag:2009:mtc, author = {Kiefer, B. and Lagoudas, D.C.}, title = {Modeling the Coupled Strain and Magnetization Response of Magnetic Shape Memory Alloys under Magnetomechanical Loading}, journal = {Journal of Intelligent Material Systems and Structures}, year = {2009}, volume = {20}, pages = {143--170} } |
Stand: 12.05.2015
Latest results
The central goal of the first funding period was to establish micromechanically-motivated constitutive models for multifunctional magnetic materials based on energy potentials. To this end, the constrained theory of magnetoelasticity proposed by DeSimone and James, which combines classical micro-magnetics modeling with the theory of energy minimizing phase mixtures by Ball and James, was considered as a theoretical point of departure. This approach has the advantage of possessing well-investigated mathematical properties, but, especially in its application to magnetic shape memory alloys, turns out to be too restrictive, so that some important features of the material response can not be captured. The extended approach therefore considers:
(i) elastic deformations on the basis of energy relaxation concepts (convexification, lamination),
(ii) finite magnetocrystalline anisotropy and additional degrees of freedom for local magnetization orientation, and
(iii) hysteretic effects via a variational approach for standard dissipative materials.
It was demonstrated through comparison with experimental data that important constitutive effects, which originally could not be captured, are properly described by the extended approach.