1 A nonlinear field theory of deformable dielectric s Zhigang Suo Harvard University rk with Zhao, W. Greene, Wei Hong, J. Zhou in Session 21-2-2, 10:00 am - 12:00 pm, Wednesday, 6 June 2007, McMat 2007, Austin, Texas are available at http://imechanica.org/node/635
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A nonlinear field theory of deformable dielectrics
A nonlinear field theory of deformable dielectrics. Zhigang Suo Harvard University. Work with X. Zhao, W. Greene, Wei Hong, J. Zhou. Talk 1 in Session 21-2-2, 10:00 am - 12:00 pm , Wednesday, 6 June 2007, McMat 2007, Austin, Texas Slides are available at http://imechanica.org/node/635. - PowerPoint PPT Presentation
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1
A nonlinear field theory of deformable dielectrics
Zhigang Suo
Harvard University
Work withX. Zhao, W. Greene, Wei Hong, J. Zhou
Talk 1 in Session 21-2-2, 10:00 am - 12:00 pm, Wednesday, 6 June 2007, McMat 2007, Austin, TexasSlides are available at http://imechanica.org/node/635
In a vacuum, force between charges can be measuredDefine electric field by E = F/Q
+Q +Q
+Q +Q
In a solid,force between charges is NOT an operational concept
iiE ,
ii ED
qD ii ,
ii qEF
5
Maxwell stress in vacuum (1864?)
jijjijijjii EDEDEDqEF ,,,
ijijji EE ,,, ikkijjjij EEEEED ,0
,0, 2
jijkkiji EEEEF
,
00 2
ijkkijij EEEE 20
0
iiE , ii ED 0qD ii ,
Q
Q
20
2E
P
P
6
Trouble with Maxwell stress in dielectrics
+ + + + + + + + +
- - - - - - - - - - - - - - - - - - - - - - - -
+ + + + + + + + +
+-
Maxwell stressElectrostriction2
33 2E
In solid, Maxwell stress has NO theoretical basis
Maxwell said that he didn’t make progress with dielectrics, but his qualms have not prevented people from using his name anyway…
•In dielectrics, electric force is not an operational concept.• varies with deformation in general.•Why E2 dependence?•How about the sign of the Maxwell stress?
7
All troubles are goneif we focus on measurable quantities
Pground
Q
l
electrode
dielectric
Work done by the weight lPWork done by the battery Q
QlPU
Q
QlUQl
l
QlUQlP
,,,
,,
A system of elastic conductors and dielectricsis specified by a free-energy function QlU ,