Global existence to a three-dimensional non-linear thermoelasticity system arising in shape memory materials

2005 ◽  
Vol 28 (4) ◽  
pp. 407-442 ◽  
Author(s):  
Irena Paw?ow ◽  
Wojciech M. Zaj??czkowski
Keyword(s):  
Global Existence ◽  
Shape Memory ◽  
Three Dimensional ◽  
Non Linear ◽  
Shape Memory Materials ◽  
Linear Thermoelasticity

Quasi‐Linear Thermoelasticity System Arising in Shape Memory Materials

2007 ◽  
Vol 38 (6) ◽  
pp. 1733-1759 ◽  
Author(s):  
Shuji Yoshikawa ◽  
Irena Pawłow ◽  
Wojciech M. Zajczkowski
Keyword(s):  
Shape Memory ◽  
Shape Memory Materials ◽  
Linear Thermoelasticity

scholarly journals A RATE-INDEPENDENT MODEL FOR THE ISOTHERMAL QUASI-STATIC EVOLUTION OF SHAPE-MEMORY MATERIALS

2008 ◽  
Vol 18 (01) ◽  
pp. 125-164 ◽  
Author(s):  
FERDINANDO AURICCHIO ◽  
ALEXANDER MIELKE ◽  
ULISSE STEFANELLI
Keyword(s):  
Shape Memory ◽  
Constitutive Relation ◽  
Continuous Dependence ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Energetic Formulation ◽  
Shape Memory Materials ◽  
Independent Model

This paper addresses a three-dimensional model for isothermal stress-induced transformation in shape-memory polycrystalline materials. We treat the problem within the framework of the energetic formulation of rate-independent processes and investigate existence and continuous dependence issues at both the constitutive relation and quasi-static evolution level. Moreover, we focus on time and space approximation as well as on regularization and parameter asymptotics.

MAGNETIC SHAPE MEMORY ALLOYS: THREE-DIMENSIONAL MODELING AND ANALYSIS

2011 ◽  
Vol 21 (05) ◽  
pp. 1043-1069 ◽  
Author(s):  
A.-L. BESSOUD ◽  
U. STEFANELLI
Keyword(s):  
Shape Memory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Magnetic Shape Memory ◽  
Magnetic Shape Memory Alloys ◽  
Modeling And Analysis ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Shape Memory Materials ◽  
Γ Convergence

We present a three-dimensional phenomenological model for the magneto-mechanical behavior of magnetic shape memory materials such as Ni2MnGa . Moving from micromagnetic considerations, we advance to some thermodynamically consistent constitutive relations describing the magnetically-induced cubic-to-tetragonal martensitic transformation in a single crystal. We present an existence analysis for both the constitutive relation problem and the three-dimensional quasi-static evolution problem. Finally, we discuss the reduction of this model to some simpler one by means of a rigorous Γ-convergence analysis.

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