Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity | Zendy

Sergio Conti | Zendy; Matthias Klar | Zendy; Barbara Zwicknagl | Zendy

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Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity

Author(s) -

Sergio Conti,

Matthias Klar,

Barbara Zwicknagl

Publication year - 2017

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2017.0235

Subject(s) - oblique case , affine transformation , nonlinear system , austenite , elasticity (physics) , martensite , piecewise , planar , phase transition , materials science , mathematics , hysteresis , mathematical analysis , geometry , condensed matter physics , microstructure , physics , composite material , computer science , philosophy , linguistics , computer graphics (images) , quantum mechanics

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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