Details
| Original language | English |
|---|---|
| Pages (from-to) | 157-183 |
| Number of pages | 27 |
| Journal | GAMM Mitteilungen |
| Volume | 40 |
| Issue number | 3 |
| Publication status | Published - 16 Apr 2018 |
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
ASJC Scopus subject areas
- Materials Science(all)
- General Materials Science
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Applied Mathematics
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In: GAMM Mitteilungen, Vol. 40, No. 3, 16.04.2018, p. 157-183.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Collisions in shape memory alloys
AU - Frémond, Michel
AU - Marino, Michele
AU - Rocca, Elisabetta
N1 - Funding information: The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR “Matematica d’Eccellenza in biologia ed ingegneria come acceleratore di una nuova strateGia per l’ATtRattività dell’ateneo pavese” is gratefully acknowledged. The paper also benefited from the support of the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità 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.
PY - 2018/4/16
Y1 - 2018/4/16
N2 - 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.
AB - 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.
KW - collisions
KW - existence and uniqueness result
KW - numerical examples
KW - Shape memory alloys
UR - http://www.scopus.com/inward/record.url?scp=85045515733&partnerID=8YFLogxK
U2 - 10.1002/gamm.201730002
DO - 10.1002/gamm.201730002
M3 - Article
AN - SCOPUS:85045515733
VL - 40
SP - 157
EP - 183
JO - GAMM Mitteilungen
JF - GAMM Mitteilungen
SN - 0936-7195
IS - 3
ER -