Collisions in shape memory alloys

authored by: Michel Frémond, Michele Marino, Elisabetta Rocca
Abstract: We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by a hammer stroke.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Tor Vergata University of Rome
University of Pavia
Type: Article
Journal: GAMM Mitteilungen
Volume: 40
Pages: 157-183
No. of pages: 27
ISSN: 0936-7195
Publication date: 16.04.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General Materials Science, General Physics and Astronomy, Applied Mathematics
Electronic version(s): http://arxiv.org/pdf/1705.11121 (Access: Open)
https://doi.org/10.1002/gamm.201730002 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{95ebf11e4069488baa4d542fb99f56d8,
title = "Collisions in shape memory alloys",
abstract = "We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by a hammer stroke.",
keywords = "collisions, existence and uniqueness result, numerical examples, Shape memory alloys",
author = "Michel Fr{\'e}mond and Michele Marino and Elisabetta Rocca",
note = "Funding information: The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR “Matematica d{\textquoteright}Eccellenza in biologia ed ingegneria come acceleratore di una nuova strateGia per l{\textquoteright}ATtRattivit{\`a} dell{\textquoteright}ateneo pavese” is gratefully acknowledged. The paper also benefited from the support of the GNAMPA (Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) for ER. The financial support of the State of Lower Saxony (Germany) in the framework of the Masterplan “Smart Biotecs” is acknowledged by MM.",
year = "2018",
month = apr,
day = "16",
doi = "10.1002/gamm.201730002",
language = "English",
volume = "40",
pages = "157--183",
journal = "GAMM Mitteilungen",
issn = "0936-7195",
publisher = "Wiley-VCH Verlag",
number = "3",
}