On thermodynamic active control of shape memory alloy wires

We propose a model for the control of high-frequency oscillations in shape memory alloy wires. We introduce a notion of generalized solution for a generalized control and in this context prove a local exact controllability result effectively corresponding to an approximate controllability result for the nonconvex pseudoelastic material system.

[1]  Mitchell Luskin,et al.  On the computation of crystalline microstructure , 1996, Acta Numerica.

[2]  Avner Friedman,et al.  Systems of nonlinear wave equations with nonlinear viscosity. , 1988 .

[3]  J. Nývlt Nucleation , 1991 .

[4]  L. Schetky Shape memory alloy applications in space systems , 1991 .

[5]  Stuart S. Antman,et al.  Quasilinear Hyperbolic–Parabolic Equations of One-Dimensional Viscoelasticity , 1996 .

[6]  P. Klouček,et al.  The computational modeling of nonequilibrium thermodynamics of the martensitic transformations , 1998 .

[7]  Manfred Wuttig Some Notes on Mechanical Damping of Shape Memory Alloys , 1990 .

[8]  P. Klouček,et al.  The computation of the dynamics of the martensitic transformation , 1994 .

[9]  Gero Friesecke,et al.  Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy , 1997 .

[10]  Philip Holmes,et al.  On the dynamics of fine structure , 1991 .

[11]  F. D. Fischer,et al.  Kinetics on the micro- and macro-levels in polycrystalline alloy materials during martensitic transformation , 1996 .

[12]  S. Antman Physically unacceptable viscous stresses , 1998 .

[13]  D. Lagoudas,et al.  A UNIFIED THERMODYNAMIC CONSTITUTIVE MODEL FOR SMA AND FINITE ELEMENT ANALYSIS OF ACTIVE METAL MATRIX COMPOSITES , 1996 .

[14]  Stuart S. Antman,et al.  The Parabolic-Hyperbolic System Governing the Spatial Motion of Nonlinearly Viscoelastic Rods , 2005 .

[15]  James K. Knowles,et al.  On the driving traction acting on a surface of strain discontinuity in a continuum , 1990 .

[16]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[17]  J. Ball,et al.  Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity , 1982 .

[18]  Piotr Rybka,et al.  Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[19]  J. K. Knowles,et al.  Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids , 1991 .

[20]  L. C. Brinson,et al.  Localized and Diffuse Thermoinduced Phase Transformation in 1-D Shape Memory Alloys , 1998 .

[21]  James K. Knowles,et al.  Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries , 1993 .