Tian Yu
Mechanics of thin structures
Exact and approximate mechanisms for pure bending of sheets
Direct measurement of the moment-curvature response of sheets or wires up to high curvatures can aid in modeling creasing, pleating, and other forming operations. We consider theoretical issues related to the geometry of pure bending. We present a linkage design that, for homogeneous deformation of the sample, results in an exact pure bending state up to arbitrarily high curvature, by combining a cochleoidal trajectory with an angle-doubling mechanism.
T. Yu, J. A. Hanna. Exact and approximate mechanisms for pure bending of sheets. Mechanism and Machine Theory, 149: 103805, 2020. [Full paper] [arXiv preprint]
Multi-stability and bifurcations of thin bands
We study the multi-stability and bifurcations of clamped thin bands subjecting to combinations of compression and shear at the two ends, through numerical continuation of a perfectly anisotropic Kirchhoff rod and experiments. We find that, despite clear physical differences between rods and strips, a naive Kirchhoff model works surprisingly well as an organizing framework for the experimental observations. In the context of this model, we observe that anisotropy creates new states and alters the connectivity between existing states. Our results are a preliminary look at relatively unstudied boundary conditions for rods and strips that may arise in a variety of engineering applications, and may guide the avoidance of jump phenomena in such settings. We also briefly comment on the limitations of current strip models.
T. Yu, J. A. Hanna. Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations, JMPS, 122: 657-685, 2019. [Full paper] [arXiv preprint]
Mechanics of pleating
Mechanical pleating is a mature industrial process making filter structures that may go into your car. However, mechanics of pleating is not well understood. In this project, we want to answer a basic question: What combinations of material and processing parameters lead to successful pleating ?
Bistability of creases under removal of singularities
Creased thin sheets exhibit bistability, with a pressed-through state possessing a localized elastic singularity. We experimentally explore the loss of bistability upon excision of the singularity and a surrounding region of material, varying the thickness and hole geometry. We examine numerical solutions of an inextensible strip model, varying hole geometry, crease angle and stiffness, and other factors, and find reasonable qualitative agreement with experimental bistability boundaries.