A variational, finite-deformation constitutive model for piezoelectric materials

被引：8
作者：
Mota, Alejandro [1 ]
Zimmerman, Jonathan A. [1 ]
机构：
[1] Sandia Natl Labs, Livermore, CA 94551 USA
来源：
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2011年 / 85卷 / 06期
关键词：
piezoelectric; finite deformation; variational; vector potential; SOLID SHELL ELEMENT; MATERIAL FORCES; FORMULATION; PSEUDOMOMENTUM; DIELECTRICS; EQUATIONS; FRACTURE; ENERGY; FIELDS;
D O I：
10.1002/nme.2993
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present a constitutive model for piezoelectric materials. The model is fully variational and supports finite kinematics. The postulated free energy depends on the deformation mapping and an electric vector potential, from which the strain and the electric displacement are derived, respectively. The divergence-free condition of the electric vector potential is enforced by means of a penalty method, which leads to a positive definite tangent for the system of equations that represent the problem. The performance of the formulation is demonstrated by several examples. Published in 2010 by John Wiley & Sons, Ltd.
引用
收藏
页码：752 / 767
页数：16
相关论文
共 27 条
[1]   A geometrically and materially non-linear piezoelectric three-dimensional-beam finite element formulation including warping effects [J].
Butz, A. ;
Klinkel, S. ;
Wagner, W. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 76 (05) :601-635
[2]   Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates [J].
Carrera, E. ;
Boscolo, A. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2007, 70 (10) :1135-1181
[3]  
Cimatti Giovanni., 2004, Ann. Mat. Pura Appl, V183, P495, DOI DOI 10.1007/S10231-004-0102-Z
[4]   Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics [J].
Damjanovic, D .
REPORTS ON PROGRESS IN PHYSICS, 1998, 61 (09) :1267-1324
[5]   Theory of elastic dielectrics revisited [J].
Ericksen, J. L. .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :299-313
[6]  
Holzapfel G. A., 2001, NONLINEAR SOLID MECH
[7]   A constitutive model for ferroelectric polycrystals [J].
Huber, JE ;
Fleck, NA ;
Landis, CM ;
McMeeking, RM .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1999, 47 (08) :1663-1697
[8]   A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation [J].
Klinkel, S ;
Wagner, W .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2006, 65 (03) :349-382
[9]   A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications [J].
Klinkel, Sven ;
Wagner, Werner .
COMPUTERS & STRUCTURES, 2008, 86 (1-2) :38-46
[10]   A new finite-element formulation for electromechanical boundary value problems [J].
Landis, CM .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2002, 55 (05) :613-628
123