Internal Stresses Lead to Net Forces and Torques on Extended Elastic Bodies.
A geometrically frustrated elastic body will develop residual stresses arising from the mismatch between the intrinsic geometry of the body and the geometry of the ambient space. We analyze these stresses for an ambient space with gradients in its intrinsic curvature, and show that residual stresses generate effective forces and torques on the center of mass of the body. We analytically calculate these forces in two dimensions, and experimentally demonstrate their action by the migration of a non-Euclidean gel disc in a curved Hele-Shaw cell. An extension of our analysis to higher dimensions shows that these forces are also generated in three dimensions, but are negligible compared to gravity.
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.|Department of Physics & Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Hillel
H
Aharoni
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
John M
JM
Kolinski
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.|Department of Physics, Soft matter program, Syracuse University, Syracuse, New York 13244, USA.|Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Michael
M
Moshe
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Idan
I
Meirzada
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Eran
E
Sharon