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Global solution to the full one‐dimensional Frémond model for shape memory alloys
Author(s) -
Colli Pierluigi,
Sprekels Jürgen
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180504
Subject(s) - uniqueness , energy balance , mathematics , momentum (technical analysis) , boundary value problem , variational inequality , mathematical analysis , balance (ability) , energy–momentum relation , shape memory alloy , cahn–hilliard equation , boundary (topology) , classical mechanics , statistical physics , physics , partial differential equation , thermodynamics , materials science , medicine , finance , metallurgy , economics , physical medicine and rehabilitation
In this paper, we prove the existence and uniqueness of the solution to the one‐dimensional initial‐boundary value problem resulting from the Frémond thermomechanical model of structural phase transitions in shape memory materials. In this model, the free energy is assumed to depend on temperature, macroscopic deformation and phase fractions. The resulting equilibrium equations are the balance laws of (linear) momentum and energy, coupled with an evolution variational inequality for the phase fractions. Fourth‐order regularizing terms in the quasi‐stationary momentum balance equation are not necessary, and, as far as we know for the first time, all the non‐linear terms of the energy balance equation are taken into account.