Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

S Conti; M. Klar; B. Zwicknagl

doi:10.1098/rspa.2017.0235

Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

S Conti, M. Klar, B. Zwicknagl

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

15 Citations (SciVal)

Abstract

We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.

Original language	English
Article number	0235
Journal	Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
Volume	473
Issue number	2203
DOIs	https://doi.org/10.1098/rspa.2017.0235
Publication status	Published - 1 Jul 2017

Keywords

Low hysteresis
Martensitic phase transition
Nonlinear elasticity
Partial diferential inclusion

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.2017.0235

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abstract = "We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.",

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AU - Conti, S

AU - Klar, M.

AU - Zwicknagl, B.

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N2 - We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.

AB - We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.

KW - Low hysteresis

KW - Martensitic phase transition

KW - Nonlinear elasticity

KW - Partial diferential inclusion

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UR - http://dx.doi.org/10.1098/rspa.2017.0235

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JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

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Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

Abstract

Keywords

ASJC Scopus subject areas

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