A model of shape memory alloys taking into account plasticity

Martin Kruižík; Johannes Zimmer

doi:10.1093/imamat/hxq058

A model of shape memory alloys taking into account plasticity

Martin Kruižík
, Johannes Zimmer

Institute of Information Theory and Automation of the ASCR
Faculty of Civil Engineering
University of Bath, Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We propose a phenomenological model for the evolutionary behaviour of shape memory alloys, where the possibility of plastic deformation is taken in to account. Two dissipative mechanisms are considered, namely the dissipation associated with solid-solid (martensitic) phase transformations and plastic dissipation. The plastic contribution may lead to an irreversibility of the evolution. The existence of a so-called energetic solution is established for a suitable relaxation of the problem in the spaceof Young measures.

Original language	English
Pages (from-to)	193-216
Number of pages	24
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	76
Issue number	1
DOIs	https://doi.org/10.1093/imamat/hxq058
State	Published - Feb 2011
Externally published	Yes

Keywords

elasto-plasticity
energetic solution
plastic strain gradients

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10.1093/imamat/hxq058

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title = "A model of shape memory alloys taking into account plasticity",

abstract = "We propose a phenomenological model for the evolutionary behaviour of shape memory alloys, where the possibility of plastic deformation is taken in to account. Two dissipative mechanisms are considered, namely the dissipation associated with solid-solid (martensitic) phase transformations and plastic dissipation. The plastic contribution may lead to an irreversibility of the evolution. The existence of a so-called energetic solution is established for a suitable relaxation of the problem in the spaceof Young measures.",

keywords = "elasto-plasticity, energetic solution, plastic strain gradients",

author = "Martin Krui{\v z}{\'i}k and Johannes Zimmer",

note = "Funding Information: This work was supported by the Royal Society (JP080789); the Ministry of Education, Youth and Sports of the Czech Republic (VZ6840770021 to M.K.); the Academy of Sciences of the Czech Republic (IAA100750802 to M.K.), Grant Agency of the Czech Republic (P201/10/0357 to M.K.) and the Engineering and Physical Sciences Research Council (GR/S99037/1 to J.Z.).",

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AU - Zimmer, Johannes

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PY - 2011/2

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N2 - We propose a phenomenological model for the evolutionary behaviour of shape memory alloys, where the possibility of plastic deformation is taken in to account. Two dissipative mechanisms are considered, namely the dissipation associated with solid-solid (martensitic) phase transformations and plastic dissipation. The plastic contribution may lead to an irreversibility of the evolution. The existence of a so-called energetic solution is established for a suitable relaxation of the problem in the spaceof Young measures.

AB - We propose a phenomenological model for the evolutionary behaviour of shape memory alloys, where the possibility of plastic deformation is taken in to account. Two dissipative mechanisms are considered, namely the dissipation associated with solid-solid (martensitic) phase transformations and plastic dissipation. The plastic contribution may lead to an irreversibility of the evolution. The existence of a so-called energetic solution is established for a suitable relaxation of the problem in the spaceof Young measures.

KW - elasto-plasticity

KW - energetic solution

KW - plastic strain gradients

UR - https://www.scopus.com/pages/publications/79551531114

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DO - 10.1093/imamat/hxq058

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JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 1

ER -

A model of shape memory alloys taking into account plasticity

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Keywords

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