# Project P3

## Modelling and homogenization of magneto-mechanical material response on multiple scales

This project focuses on the construction of a compatible hierarchy of continuum physical models describing coupled magneto-mechanical
behavior on different scales, and its combination with multi-scale homogenization. The overall goal is to provide theoretical and algorithmic formulations that will enhance the understanding of time-dependent, dissipative magneto-mechanical effects in solids, thus providing a building block for describing multiferroic materials. As a first step, a variational-based micro-magneto-elastic model for the temporal evolution of magnetic domains in ferromagnetic and magnetostrictive materials is constructed.
The second step is concerned with the development of homogenization techniques that bridge the micro and macro scales by linking the the micro-magneto-elastic model to the variables at macroscale. In the third step, we deal with the complexity of modeling the constitutive jump conditions arising at grain boundaries, as well as the inclusion of fracture. This is based on the already existing work within the working group
that deals with phase-field magneto-mechanical models for the regularization of discontinuities.

## Publications

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 Ethiraj, G., Sridhar, A. & Miehe, C. (2015), "Variational Modeling and Homogenization in Dissipative Magneto-Mechanics", GAMM Mitteilungen. Vol. 38(1), pp. 75-101. BibTeX: @article{Ethiraj2015, author = {Ethiraj, G. and Sridhar, A. and Miehe, C.}, title = {Variational Modeling and Homogenization in Dissipative Magneto-Mechanics}, journal = {GAMM Mitteilungen}, year = {2015}, volume = {38}, number = {1}, pages = {75--101}, note = {P3} }  Miehe, C., Vallicotti, D. & Zäh, D. (2015), "Computational Structural and Material Stability Analysis in Finite Electro-Elasto-Statics of Electro-Active Materials", Journal of Numerical Methods in Engineering. BibTeX: @article{Miehe2015, author = {C. Miehe and D. Vallicotti and D. Zäh}, title = {Computational Structural and Material Stability Analysis in Finite Electro-Elasto-Statics of Electro-Active Materials}, journal = {Journal of Numerical Methods in Engineering}, year = {2015}, doi = {http://dx.doi.org/10.1002/nme.4855} }  Sridhar, A., M.-A.Keip & Miehe, C. (2015), "Homogenization in Micro-Magneto-Mechanics", Computational Mechanics. Vol. submitted for publication BibTeX: @article{Sridhar2015, author = {A. Sridhar and M.-A.Keip and C. Miehe}, title = {Homogenization in Micro-Magneto-Mechanics}, journal = {Computational Mechanics}, year = {2015}, volume = {submitted for publication} }  Zäh, D. & Miehe, C. (2015), "Multiplicative electro-elasticity of electroactive polymers accounting for micromechanically-based network models", Computer Methods in Applied Mechanics and Engineering. Vol. 286, pp. 394-421. BibTeX: @article{Zaeh2015, author = {D. Zäh and C. Miehe}, title = {Multiplicative electro-elasticity of electroactive polymers accounting for micromechanically-based network models}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2015}, volume = {286}, pages = {394--421} }  Ethiraj, G. & Miehe, C. (2014), "Multiplicative Magneto-Elasticity of Magnetosensitive Polymers Incorporating Micromechanically-Based Network Kernels", Acta Mechanica. Vol. submitted for publication BibTeX: @article{Ethiraj2014, author = {G. Ethiraj and C. Miehe}, title = {Multiplicative Magneto-Elasticity of Magnetosensitive Polymers Incorporating Micromechanically-Based Network Kernels}, journal = {Acta Mechanica}, year = {2014}, volume = {submitted for publication} }  Rosato, D. & Miehe, C. (2014), "Dissipative ferroelectricity at finite strains. Variational principles, constitutive assumptions and algorithms", International Journal of Engineering Science. Vol. 74, pp. 163-189. BibTeX: @article{Rosato2014, author = {Rosato, D. and Miehe, C.}, title = {Dissipative ferroelectricity at finite strains. Variational principles, constitutive assumptions and algorithms}, journal = {International Journal of Engineering Science}, year = {2014}, volume = {74}, pages = {163--189}, note = {P3} }  Zäh, D. & Miehe, C. (2013), "Computational Homogenization in Dissipative Electro-Mechanics of Functional Materials", Computer Methods in Applied Mechanics and Engineering. Vol. 267, pp. 487-510. BibTeX: @article{Zaeh2013, author = {Zäh, D. and Miehe, C.}, title = {Computational Homogenization in Dissipative Electro-Mechanics of Functional Materials}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2013}, volume = {267}, pages = {487--510} }  Linder, C. & Miehe, C. (2012), "Effect of Electric Displacement Saturation on the Hysteretic Behavior of Ferroelectric Ceramics and the Initiation and Propagation of Cracks in piezoelectric Ceramics", Journal of the Mechanics and Physics of Solids. Vol. 60, pp. 882-903. BibTeX: @article{Linder2012, author = {Linder, C. and Miehe, C.}, title = {Effect of Electric Displacement Saturation on the Hysteretic Behavior of Ferroelectric Ceramics and the Initiation and Propagation of Cracks in piezoelectric Ceramics}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2012}, volume = {60}, pages = {882--903}, note = {P3} }  Miehe, C. & Ethiraj, G. (2012), "A Geometrically Consistent Incremental Variational Formulation for Phase Field Models in Micromagnetics", Computer Methods in Applied Mechanics and Engineering. Vol. 245--246, pp. 331-347. BibTeX: @article{miehe+ethiraj12, author = {Miehe, C. and Ethiraj, G.}, title = {A Geometrically Consistent Incremental Variational Formulation for Phase Field Models in Micromagnetics}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2012}, volume = {245--246}, pages = {331--347} }  Miehe, C., Zäh, D. & Rosato, D. (2012), "Variational-based modeling of micro-electro-elasticity with electric field-driven and stress-driven domain evolutions", International Journal for Numerical Methods in Engineering. Vol. 91, pp. 115-141. BibTeX: @article{miehe+zaeh+rosato12, author = {Miehe, C. and Zäh, D. and Rosato, D.}, title = {Variational-based modeling of micro-electro-elasticity with electric field-driven and stress-driven domain evolutions}, journal = {International Journal for Numerical Methods in Engineering}, year = {2012}, volume = {91}, pages = {115--141} }  Miehe, C. & Ethiraj, G. (2012), "A Geometrically Exact Incremental Variational Formulation for phase-Field Models in Micromagnetics", Computer Methods in Applied Mechanics and Engineering. Vol. 245, pp. 331-347. BibTeX: @article{Miehe2012, author = {Miehe, C. and Ethiraj, G.}, title = {A Geometrically Exact Incremental Variational Formulation for phase-Field Models in Micromagnetics}, journal = {Computer Methods in Applied Mechanics and Engineering}, year = {2012}, volume = {245}, pages = {331--347}, note = {P3} }  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{miehe+kiefer+rosato11, 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} }  Miehe, C., Rosato, D. & Kiefer, B. (2011), "Variational principles in dissipative electro-magneto-mechanics: A framework for the macro-modeling of functional materials", International Journal for Numerical Methods in Engineering. Vol. 86, pp. 1225-1276. BibTeX: @article{miehe+rosato+kiefer11, author = {Miehe, C. and Rosato, D. and Kiefer, B.}, title = {Variational principles in dissipative electro-magneto-mechanics: A framework for the macro-modeling of functional materials}, journal = {International Journal for Numerical Methods in Engineering}, year = {2011}, volume = {86}, pages = {1225--1276} } 

Stand: 12.05.2015

## Latest results

Prof. Dr.-Ing. Christian Miehe
Institute of Applied Mechanics

cm @ mechbau.uni-stuttgart.de
Tel.: +49-(0)711-685 66379
Room: 3.167

M. Sc. Gautam Ethiraj
Institut für Mechanik (Lehrstuhl I)

gautam.ethiraj @ mechbau.uni-stuttgart.de
Tel.: +49-(0)711-685 66131
Room: 3.169