THERMAL CONTROL OF A RATE-INDEPENDENT MODEL FOR PERMANENT INELASTIC EFFECTS IN SHAPE MEMORY MATERIALS

被引：6

作者：

Eleuteri, Michela ^{[1
]}

Lussardi, Luca ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Informat, I-50134 Florence, Italy

[2] Univ Cattolica Sacro Cuore, Dipartimento Matemat & Fis N Tartaglia, I-25121 Brescia, Italy

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2014年 / 3卷 / 03期

关键词：

Shape memory alloys; optimal control; rate-independent; quasi-static evolution; permanent inelasticity; SOLID-PHASE TRANSFORMATIONS; SOUZA-AURICCHIO MODEL; 3-DIMENSIONAL MODEL; THERMOMECHANICAL EVOLUTION; CONSTITUTIVE MODEL; STATE CONSTRAINTS; ALLOYS; STRESS; EXISTENCE; TEMPERATURE;

D O I：

10.3934/eect.2014.3.411

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We address the thermal control of the quasi-static evolution of a polycrystalline shape memory alloy specimen. The thermomechanical evolution of the body is described by means of an extension of the phenomenological SOUZA-AURICCHIO model [6, 7, 8, 57] accounting also for permanent inelastic effects [9, 11, 2]. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energetic sense. In a similar way as in [28], using results by RINDLER [49, 50] we prove the existence of optimal controls for a suitably large class of cost functionals.

引用

页码：411 / 427

页数：17

共 62 条

[1] Aiki T., 2002, GAKUTO INT SER MATH, V17, P144
[2] [Anonymous], SMST 2003 P INT C SH
[3] [Anonymous], 2007, ADV MATH SCI APPL
[4] Modelling and numerical simulation of martensitic transformation in shape memory alloys
Arndt, M
Griebel, M
Roubícek, T
[J]. CONTINUUM MECHANICS AND THERMODYNAMICS, 2003, 15 (05) : 463 - 485
[5] A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity
Auricchio, F.
Reali, A.
Stefanelli, U.
[J]. INTERNATIONAL JOURNAL OF PLASTICITY, 2007, 23 (02) : 207 - 226
[6] A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications
Auricchio, F
Petrini, L
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2004, 61 (05) : 716 - 737
[7] A three-dimensional model describing stress-temperature induced solid phase transformations: solution algorithm and boundary value problems
Auricchio, F
Petrini, L
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2004, 61 (06) : 807 - 836
[8] Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations
Auricchio, F
Petrini, L
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2002, 55 (11) : 1255 - 1284
[9] A macroscopic 1D model for shape memory alloys including asymmetric behaviors and transformation-dependent elastic properties
Auricchio, F.
Reali, A.
Stefanelli, U.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2009, 198 (17-20) : 1631 - 1637
[10] Auricchio F., 2013, 3PV1330 IMATICNR

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