We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for geometric model thin flexible rods with arbitrary cross section undeformed configuration. Our approach differs from existing simulation techniques in graphics mechanics literature both kinematic description---we represent material frame by its angular deviation natural Bishop frame---as well as dynamical treatment---we treat centerline dynamic quasistatic....

1. Introduction 2. Three-dimensional elasticity I: RODS 3. Equations for elastic rods 4. Mechanics of the human hair 5. Rippled leaves, uncoiled springs II: PLATES 6. The equations plates 7. End effects in plate buckling 8. Finite amplitude a strip 9. Crumpled paper 10. Fractal near edges III: SHELLS 11. Geometric rigidity surfaces 12. Shells revolution 13. torus 14. Spherical shell pushed by wall Appendix A: Calculus variations: worked example B: Boundary and interior layers C: geometry...

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on role time-parallel transport eliminating---without approximation---all but an O ( n ) band entries physical system's energy Hessian. The result is fast, unified, implicit treatment rods that closely reproduces variety...

Simulating human hair is recognized as one of the most difficult tasks in computer animation. In this paper, we show that Kirchhoff equations for dynamic, inextensible elastic rods can be used accurately predicting motion. These fully account nonlinear behavior strands with respect to bending and twisting. We introduce a novel deformable model solving them: each strand represented by Super-Helix , i.e., piecewise helical rod which animated using principles Lagrangian mechanics. This results...

We consider the buckle-driven delamination of biaxially compressed thin films. Telephone-cord-like patterns observed in experiments are explained as a result buckling behavior film. perform stability analysis straight blister. A mechanism instability causing undulations an advancing finger is pointed out, which we claim to be basic phenomenon explaining zigzag pattern. predict transition varicose (unobserved yet) pattern at low Poisson ratios.

We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays tiles connected by flexible hinges. demonstrate a non-periodic pattern can cause sheet to buckle into three-dimensional shapes, such as domes or wrinkles, when pulled at specific boundary points. These global buckling modes are observed experiments and rationalized an in-plane kinematic analysis highlights role geometric frustration arising from...

Actuation remains a significant challenge in soft robotics. by light has important advantages: Objects can be actuated from distance, distinct frequencies used to actuate and control modes with minimal interference, power transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photochemical processes that directly convert photons configurational changes are particularly attractive for actuation. Various works have reported light-induced actuation liquid...

We investigate how natural curvature affects the configuration of a thin elastic rod suspended under its own weight, as when single strand hair hangs gravity. combine precision desktop experiments, numerics, and theoretical analysis to explore equilibrium shapes set by coupled effects elasticity, curvature, nonlinear geometry, A phase diagram is constructed in terms control parameters system, namely dimensionless where we identify three distinct regions: planar curls, localized helices,...

A drop impacting a target cutout in thin polymer film is wrapped by the dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from given slightly varying impact parameters. simplified model for nonlinear Elastica coupled with successfully explains this shape selection yields detailed quantitative agreement experiments. This first venture into largely unexplored dynamics of elastocapillary assemblies opens up perspective mass production packages...

Thin, viscous fluid threads falling onto a moving belt behave in way reminiscent of sewing machine, generating rich variety periodic stitchlike patterns including meanders, W patterns, alternating loops, and translated coiling. These form to accommodate the difference between speed terminal velocity at which thread strikes belt. Using direct numerical simulations, we show that inertia is not required produce aforementioned patterns. We introduce quasistatic geometrical model captures...

Under the effect of surface tension, a blob liquid adopts spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit similar behavior: into liquid, gel having low modulus undergoes large, reversible deformations. analyze three fundamental types deformations slender solid driven by stress, depending on its cross section: circular cylinder shortens longitudinal direction and stretches transversally; sharp edges square...

We present the first reduced-dimensional technique to simulate dynamics of thin sheets viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic shells, we apply Stokes-Rayleigh analogy derive simple yet consistent forces. incorporate nonlinear surface tension forces with formulation based on minimizing area, and preserve quality triangular mesh elements through local remeshing operations. Simultaneously, track evolve thickness each triangle...

We study the buckling of thin elastic plates caused by residual strains concentrated near a free edge. This is model for plant leaves and torn plastic sheet morphologies. derive new governing equations explaining self-similar patterns reported earlier in experiments. reveal cascade mechanism, determine bounds its wavelengths, predict similarity factor 3 agreement with confirmed numerical solutions up to five generations wrinkles.

We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for geometric model thin flexible rods with arbitrary cross section undeformed configuration. Our approach differs from existing simulation techniques in graphics mechanics literature both kinematic description---we represent material frame by its angular deviation natural Bishop frame---as well as dynamical treatment---we treat centerline dynamic quasistatic....