scholarly journals Nonuniform growth and topological defects in the shaping of elastic sheets

Soft Matter ◽  
2014 ◽  
Vol 10 (34) ◽  
pp. 6382-6386 ◽  
Author(s):  
Nakul P. Bende ◽  
Ryan C. Hayward ◽  
Christian D. Santangelo
Keyword(s):  
Gaussian Curvature ◽  
Flat Surface ◽  
Topological Defects ◽  
Elastic Sheet ◽  
Zero Gaussian Curvature ◽  
Elastic Sheets

We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified.

A representation of distributions supported on smooth hypersurfaces of Rn

1995 ◽  
Vol 117 (1) ◽  
pp. 153-160
Author(s):  
Kanghui Guo
Keyword(s):  
Gaussian Curvature ◽  
Dual Space ◽  
Smooth Hypersurface ◽  
Zero Gaussian Curvature ◽  
Schwartz Class ◽  
Image Position

Let S(Rn) be the space of Schwartz class functions. The dual space of S′(Rn), S(Rn), is called the temperate distributions. In this article, we call them distributions. For 1 ≤ p ≤ ∞, let FLp(Rn) = {f:∈ Lp(Rn)}, then we know that FLp(Rn) ⊂ S′(Rn), for 1 ≤ p ≤ ∞. Let U be open and bounded in Rn−1 and let M = {(x, ψ(x));x ∈ U} be a smooth hypersurface of Rn with non-zero Gaussian curvature. It is easy to see that any bounded measure σ on Rn−1 supported in U yields a distribution T in Rn, supported in M, given by the formula

Limit equilibrium of reinforced shells of zero gaussian curvature

1989 ◽  
Vol 25 (9) ◽  
pp. 913-919
Author(s):  
A. V. Nalimov ◽  
Yu. V. Nemirovskii
Keyword(s):  
Gaussian Curvature ◽  
Limit Equilibrium ◽  
Zero Gaussian Curvature

scholarly journals Multi-stability of free spontaneously curved anisotropic strips

2011 ◽  
Vol 468 (2138) ◽  
pp. 511-530 ◽  
Author(s):  
L. Giomi ◽  
L. Mahadevan
Keyword(s):  
Gaussian Curvature ◽  
Elastic Moduli ◽  
Composite Plates ◽  
Spontaneous Curvature ◽  
Bending Rigidity ◽  
Stable Conformation ◽  
Elastic Composite ◽  
Measuring Tape ◽  
Zero Gaussian Curvature ◽  
The Common

Multi-stable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here, we consider the energy landscape of a general class of multi-stable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, and strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multi-stability in anisotropic shells and suggests new design criteria for these structures.

Steady-state creep of shells of zero Gaussian curvature with allowance for shear stresses

1982 ◽  
Vol 18 (2) ◽  
pp. 104-109
Author(s):  
P. I. Danchak ◽  
M. S. Mikhalishin ◽  
O. N. Shablii
Keyword(s):  
Steady State ◽  
Gaussian Curvature ◽  
Steady State Creep ◽  
Shear Stresses ◽  
Zero Gaussian Curvature

Deformation of a constrained thin elastic sheet over a flat surface due to gravity

2018 ◽  
Vol 106 ◽  
pp. 155-161
Author(s):  
Maniya Maleki ◽  
S. Mahmoud Hashemi ◽  
Aboutaleb Amiri
Keyword(s):  
Flat Surface ◽  
Elastic Sheet

scholarly journals Wrinkles and splay conspire to give positive disclinations negative curvature

2015 ◽  
Vol 112 (41) ◽  
pp. 12639-12644 ◽  
Author(s):  
Elisabetta A. Matsumoto ◽  
Daniel A. Vega ◽  
Aldo D. Pezzutti ◽  
Nicolás A. García ◽  
Paul M. Chaikin ◽  
...  
Keyword(s):  
Diblock Copolymer ◽  
Gaussian Curvature ◽  
Negative Curvature ◽  
Topological Defects ◽  
Free Standing ◽  
Columnar Phase ◽  
Negative Gaussian Curvature ◽  
Positive Gaussian Curvature

Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In free-standing films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations.

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