Project P6

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Project description

Microstructural interaction and switching in ferroelectrics

The purpose of this project is to establish multiscale laminate- and homogenization-based models for the interactions between the grain, defect,
polarization and dislocation microstructures in ferroelectric single- and polycrystals during technological processes. These involve in particular single-, multi- and polycrystal-based modeling. At the single-crystal level, laminatebased mixture models for energetic and dissipative processes associated with the polarization, defect and dislocation microstructures and their evolution will be developed. These will then be embedded in multigrain-based grain boundary interaction models for the investigation of the eect of graingrain interactions on the polarization and defect microstructures. Finally, the single-grain model will be embedded into an orientation-distributionfunction-based single- and multi-grain-based texture model for the grain microstructure at the specimen and technological level.

Publications

JabRef References output

Dusthakar, D., Menzel, A. & Svendsen, B. (2015), "Comparison of phenomenological and laminate-based models for rate-dependent switching in ferroelectric continua", GAMM-Mitteilungen. Vol. 38(1), pp. 147-170.

[BibTeX]

BibTeX:

@article{Dust2015,
  author = {Dusthakar, D.K. and Menzel, A. and Svendsen, B.},
  title = {Comparison of phenomenological and laminate-based models for rate-dependent switching in ferroelectric continua},
  journal = {GAMM-Mitteilungen},
  year = {2015},
  volume = {38},
  number = {1},
  pages = {147--170},
  note = {P6}
}

Keip, M.-A., Schrade, D., Thai, H., Schröder, J., Svendsen, B., Müller, R. & Gross, D. (2015), "Coordinate-invariant phase-field modeling of ferroelectrics, part II: Model formulation and single-crystal simulations", GAMM-Mitteilungen. Vol. 38(1), pp. 115-131.

[BibTeX]

BibTeX:

@article{Keip2015,
  author = {Keip, M.-A. and Schrade, D. and Thai, H. and Schröder, J. and Svendsen, B. and Müller, R. and Gross, D.},
  title = {Coordinate-invariant phase-field modeling of ferroelectrics, part II: Model formulation and single-crystal simulations},
  journal = {GAMM-Mitteilungen},
  year = {2015},
  volume = {38},
  number = {1},
  pages = {115--131}
}

Schrade, D., Keip, M.-A., Thai, H., Schröder, J., Svendsen, B., Müller, R. & Gross, D. (2015), "Coordinate-invariant phase-field modeling of ferroelectrics, part I: Model formulation and single-crystal simulations", GAMM-Mitteilungen. Vol. 38(1), pp. 102-114.

[BibTeX]

BibTeX:

@article{Schrade2015,
  author = {Schrade, D. and Keip, M.-A. and Thai, H. and Schröder, J. and Svendsen, B. and Müller, R. and Gross, D.},
  title = {Coordinate-invariant phase-field modeling of ferroelectrics, part I: Model formulation and single-crystal simulations},
  journal = {GAMM-Mitteilungen},
  year = {2015},
  volume = {38},
  number = {1},
  pages = {102--114},
  note = {P4, P1, P6}
}

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] [DOI]

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]

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]

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}
}

Dusthakar, D.K., Menzel, A. & Svendsen, B. (2014), "Free energy models for ferroelectric materials with application to rate-dependent switching (Extended Abstract)", Proceedings of the 2nd Seminar on The Mechanics of Multifunctional Materials. , pp. 11-13.

[BibTeX]

BibTeX:

@article{Dust2014a,
  author = {Dusthakar, D. K. and Menzel, A. and Svendsen, B.},
  title = {Free energy models for ferroelectric materials with application to rate-dependent switching (Extended Abstract)},
  journal = {Proceedings of the 2nd Seminar on The Mechanics of Multifunctional Materials},
  year = {2014},
  pages = {11--13},
  note = {P6}
}

Dusthakar, D.K., Menzel, A. & Svendsen, B. (2014), "Rate-dependent laminate-based approach for modelling of ferroelectric single crystals", Proceedings of the 5th International Congress on Computational Mechanics and Simulation. , pp. 1324-1336.

[BibTeX]

BibTeX:

@article{Dust2014b,
  author = {Dusthakar, D. K. and Menzel, A. and Svendsen, B.},
  title = {Rate-dependent laminate-based approach for modelling of ferroelectric single crystals},
  journal = {Proceedings of the 5th International Congress on Computational Mechanics and Simulation},
  year = {2014},
  pages = {1324--1336},
  note = {ISBN:978-981-09-1139-3, DOI:10.3850/978-981-09-1139-3 378 P6}
}

Dusthakar, D.K., Menzel, A. & Svendsen, B. (2014), "Laminate-based modelling of microstructure and switching in ferroelectrics", Proceedings in Applied Mathematics and Mechanics (PAMM)., In Proceedings in Applied Mathematics and Mechanics (PAMM). Vol. 4(1), pp. 407-408.

[BibTeX]

BibTeX:

@article{Dusthakar2014,
  author = {Dusthakar, D. K. and Menzel, A. and Svendsen, B.},
  title = {Laminate-based modelling of microstructure and switching in ferroelectrics},
  booktitle = {Proceedings in Applied Mathematics and Mechanics (PAMM)},
  journal = {Proceedings in Applied Mathematics and Mechanics (PAMM)},
  year = {2014},
  volume = {4},
  number = {1},
  pages = {407--408},
  note = {P6}
}

Kaliappan, J. & Menzel, A. (2014), "Modelling of non-linear switching effects in piezoceramics - A three-dimensional polygonal finite element based approach applied to oligo-crystals", Journal of Intelligent Material Systems and Structures.

[BibTeX]

BibTeX:

@article{Kaliappan2014,
  author = {Kaliappan, J. and Menzel, A.},
  title = {Modelling of non-linear switching effects in piezoceramics - A three-dimensional polygonal finite element based approach applied to oligo-crystals},
  journal = {Journal of Intelligent Material Systems and Structures},
  year = {2014},
  note = {P6 DOI: 10.1177/1045389X14554135, 2014}
}

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). Vol. Paper 7436

[BibTeX]

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},
  volume = {Paper 7436},
  note = {DOI:10.1115/SMASIS2014-7436 P7 and P6}
}

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). Vol. Paper 3041

[BibTeX]

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},
  volume = {Paper 3041},
  note = {P7 and P6 doi:10.1115/SMASIS2013-3041}
}

Stand: 12.05.2015

Latest results

Sequential laminate-based models were the focus of development during the first funding period. The single crystal models established here are able to describe the rate-dependent dissipative behaviour on a micromechanically motivated basis, thereby enabling the simulation of polarisation evolution.

Under electromechanical loading, the ferroelectric crystal forms compatible domain configurations that minimise the total energy state of the crystal.
Considering the kinematic and polarisation compatibility conditions between any two tetragonal variants, the macroscopic transformation strains and polarisation could - based on a mixture-type theory - be expressed in terms of the laminate volume fractions of the multi-rank laminate system.The evolution of these volume fractions, as derived from a rate-type dissipation function, was solved by considering the Fischer-Burmeister complementarity functions in order to algorithmically fulfil the underlying inequality constraints related to the limits of the laminate volume fractions. The model formulation was - by means of representative numerical examples - compared to an incremental and variational macroscopic modelling approach for ferroelectric ceramics established in the literature. The proposed laminate-based approach nicely captures the onset of switching behaviour and the rate-dependent dissipative response. For the single crystal BaTiO_3 studied here, the sequential laminate-based model accurately captures the effect of 90° switching phenomena that is predominant when a single crystals is subjected to compressive mechanical loading together with a cyclic electric field. Moreover, the model has been embedded into a Finite Element formulation to simulate inhomogeneous boundary value problems. The examples studied refer to both, the single- and polycrystalline case, whereby the latter is approximated by randomly generated crystallographic orientations within each finite element.