Modeling of smart materials with thermal effects: Dynamic and quasi-static evolution

被引：9
|
作者：
Bonaldi, Francesco [1 ]
Geymonat, Giuseppe [2 ]
Krasucki, Francoise [1 ]
机构：
[1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, UMR CNRS 5149, F-34095 Montpellier 5, France
[2] Ecole Polytech, Mecan Solides Lab, UMR CNRS 7649, F-91128 Palaiseau, France
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2015年 / 25卷 / 14期
关键词：
Piezoelectricity; magnetostriction; pyroelectricity; pyromagnetism; smart structures; sensors; actuators; nondimensionalization; multiscale problems; semigroups; MICROMECHANICAL ANALYSIS; MULTIMATERIAL;
D O I：
10.1142/S0218202515500578
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a mathematical model for linear magneto-electro-thermo-elastic continua, as sensors and actuators can be thought of, and prove the well-posedness of the dynamic and quasi-static problems. The two proofs are accomplished, respectively, by means of the Hille-Yosida theory and of the Faedo-Galerkin method. A validation of the quasi-static hypothesis is provided by a nondimensionalization of the dynamic problem equations. We also hint at the study of the convergence of the solution to the dynamic problem to that to the quasi-static problem as a small parameter - the ratio of the largest propagation speed for an elastic wave in the body to the speed of light - tends to zero.
引用
收藏
页码：2633 / 2667
页数：35
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