TY - JOUR
T1 - Emergence of Spontaneous Twist and Curvature in Non-Euclidean Rods
T2 - Application to Erodium Plant Cells
AU - Aharoni, Hillel
AU - Abraham, Yael
AU - Elbaum, Rivka
AU - Sharon, Eran
AU - Kupferman, Raz
N1 - We are grateful to U. Raviv for performing the SAXS measurements. The electron microscopy studies were conducted at the Irving and Cherna Moskowitz Center for Nano and Bio-Nano Imaging at the Weizmann Institute of Science. This research was supported by the Israel Science Foundation (Grants No. 375/09 and No. 598/10) and by the United States–Israel Binational Foundation (Grants No. 2004037 and No. 2010129). E. S. was supported by the European Research Council SoftGrowth project.
PY - 2012/6/4
Y1 - 2012/6/4
N2 - We present a limiting model for thin non-Euclidean elastic rods. Originating from the three-dimensional ( 3D) reference metric of the rod, which is determined by its internal material structure, we derive a 1D reduced rod theory. Specifically, we show how the spontaneous twist and curvature of a rod emerge from the reference metric derivatives. Thus, the model allows calculating the unconstrained equilibrium configuration of a thin rod directly from its internal structure. The model is applied to the study of cells from members of the Geraniaceae plant family and their configurational response to dehydration. We show how the geometrical arrangement of cellulose fibrils on the cell walls determines the helical shapes of isolated cells.
AB - We present a limiting model for thin non-Euclidean elastic rods. Originating from the three-dimensional ( 3D) reference metric of the rod, which is determined by its internal material structure, we derive a 1D reduced rod theory. Specifically, we show how the spontaneous twist and curvature of a rod emerge from the reference metric derivatives. Thus, the model allows calculating the unconstrained equilibrium configuration of a thin rod directly from its internal structure. The model is applied to the study of cells from members of the Geraniaceae plant family and their configurational response to dehydration. We show how the geometrical arrangement of cellulose fibrils on the cell walls determines the helical shapes of isolated cells.
UR - http://www.scopus.com/inward/record.url?scp=84861883774&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.108.238106
DO - 10.1103/PhysRevLett.108.238106
M3 - مقالة
SN - 0031-9007
VL - 108
JO - Physical review letters
JF - Physical review letters
IS - 23
M1 - 238106
ER -