Modelling of thin martensitic films with nonpolynomial stored energies

M Kruzik, J Zimmer

Research output: Contribution to conferencePaper

Abstract

A study of the thin film limit of martensitic materials is presented, with the film height tending to zero. The behaviour of the material is modelled by a stored elastic energy which grows to infinity if the normal to the deformed film tends to zero. We show that the macroscopic behaviour of the material can be described by gradient Young measures if Dirichlet boundary conditions are prescribed at the boundary of the film. In this situation, we also formulate a rate-independent problem describing evolution of the material. A second approach, perhaps useful in case of non-Dirichlet loading, is presented as well, relying on suitable generalised Young measures.
Original languageEnglish
Pages587-608
Number of pages22
DOIs
Publication statusPublished - 2013
Event2012 International Conference Recent Trends in Dynamical Systems - Munich, Germany
Duration: 11 Jan 201213 Jan 2012

Conference

Conference2012 International Conference Recent Trends in Dynamical Systems
CountryGermany
CityMunich
Period11/01/1213/01/12

Fingerprint

Young Measures
Energy
Modeling
Zero
Dirichlet Boundary Conditions
Thin Films
Infinity
Tend
Gradient

Cite this

Kruzik, M., & Zimmer, J. (2013). Modelling of thin martensitic films with nonpolynomial stored energies. 587-608. Paper presented at 2012 International Conference Recent Trends in Dynamical Systems, Munich, Germany. https://doi.org/10.1007/978-3-0348-0451-6_22

Modelling of thin martensitic films with nonpolynomial stored energies. / Kruzik, M; Zimmer, J.

2013. 587-608 Paper presented at 2012 International Conference Recent Trends in Dynamical Systems, Munich, Germany.

Research output: Contribution to conferencePaper

Kruzik, M & Zimmer, J 2013, 'Modelling of thin martensitic films with nonpolynomial stored energies' Paper presented at 2012 International Conference Recent Trends in Dynamical Systems, Munich, Germany, 11/01/12 - 13/01/12, pp. 587-608. https://doi.org/10.1007/978-3-0348-0451-6_22
Kruzik M, Zimmer J. Modelling of thin martensitic films with nonpolynomial stored energies. 2013. Paper presented at 2012 International Conference Recent Trends in Dynamical Systems, Munich, Germany. https://doi.org/10.1007/978-3-0348-0451-6_22
Kruzik, M ; Zimmer, J. / Modelling of thin martensitic films with nonpolynomial stored energies. Paper presented at 2012 International Conference Recent Trends in Dynamical Systems, Munich, Germany.22 p.
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