UCLA

Slender structures, existing in both natural environments (tendrils) and man-made systems (soft robots), often undergo geometrically nonlinear deformations and dramatic topological changes when subjected to simple boundary conditions or moderate external actuations, which pose extensive challenges to the traditional numerical and analytical methods. This dissertation focuses on the Discrete Differential Geometry (DDG)-based numerical frameworks for simulating the mechanical response in slender structures and soft robots, and makes four major contributions:

First, we use a planar rod theory and incorporate Coulomb frictional contact, elastic/inelastic collision with ground, and inertial effects in a physically accurate manner, to simulate the dynamics of shape memory alloy (SMA)-powered soft robots. Our simulations show quantitative agreement when compared against with experiments, suggesting that our numerical approach represents a promising step toward the ultimate goal of a computational framework for soft robotic engineering. We then combine the same planar rod framework with a naive fluid-structure interaction model to perform the swimming of a seastar-inspired soft robot in water.

Secondly, we numerically explore the propulsion of bacteria flagella in a low Reynolds fluid. We study the locomotion of a bacteria-inspired soft robot. Our numerical framework uses (i) Discrete Elastic Rods (DER) method to account for the elasticity of soft filament, (ii) Lighthill's Slender Body Theory (LSBT) for the long term hydrodynamic flow by helical flagellum, and (iii) Higdon's model for the hydrodynamics from spherical head. A data-driven approach is later employed to develop a control algorithm such that our flagella-inspired robot can follow a prescribed trajectory only by changing its rotation frequency. Then, to investigate the bundling behavior between two soft helical rods rotating side by side in a viscous fluid, we implement a coupled DER and Regularized Stokeslet Segment (RSS) framework. The contact between two rods is also considered in our numerical tool. A novel bundling behavior between two nearby helical rods is uncovered, whereby the filaments come across each other above a critical angular velocity.

Our third contribution is to present a numerical method for both forward physics-based simulations and inverse form-finding problems in elastic gridshells. Our numerical framework on elastic gridshell first decomposes this special structure into multiple one dimensional rods and linkers, which can be performed by the well-established Discrete Elastic Rods (DER) algorithm. A stiffed spring between rods and linkages is later introduced to ensure the bending and twisting coupling at joint area. The inverse form finding problem -- compute the initial planar pattern from a given 3D configuration -- is directly solved by a contact-based procedure, without using any the conventional optimization-based algorithms. Several examples are used to show the effectiveness of the inverse design process.

Finally, we compare Kirchhoff rod model, Sadowsky ribbon model, and FvK plate equations, to systematically characterize a group of slender structures, from narrow strip to wide plate. We consider a pre-buckled band under lateral end translation and quantity its supercritical pitchfork bifurcation. The one dimensional anisotropic rod can give a reasonable prediction when the strip is narrow, while fails to capture its width effect. A two dimensional plate approach, on the other hand, accurately anticipates the nonlinear deformations and the critical supercritical pitchfork points for both narrow and wide plates. We finally discuss in detail the issues of traditional one dimensional ribbon models at the inflection points, and then use an extensible ribbon model to bridge the gap between the Kirchhoff rod model and the classical Sadowsky ribbon model.