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Collisions in shape memory alloys
Author(s) -
Frémond Michel,
Marino Michele,
Rocca Elisabetta
Publication year - 2018
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201730002
Subject(s) - classification of discontinuities , sma* , shape memory alloy , austenite , uniqueness , constitutive equation , mechanics , materials science , phase (matter) , mathematical analysis , thermodynamics , physics , mathematics , metallurgy , microstructure , finite element method , combinatorics , quantum mechanics
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.