S1E4
Episode 4 (August 2, 2020)
Teng Zhang
Syracuse University
Bianca Giovanardi
MIT
Liu Wang
MIT
Counting wrinkles to understand the pattern of patterns
Abstract:
Wrinkling patterns in soft materials have been extensively studied due to their important roles in determining surface morphologies in biological structures and developing multifunctional devices. Most existing work focuses on relatively simple geometries, such as flat structures and curved structures with constant curvature such as the cylinder and 2-sphere. In this talk I discuss wrinkling patterns on a torus, the Gaussian and mean curvatures of which vary along the poloidal direction. We observe eight different wrinkling patterns from large-scale finite element simulations and construct a phase diagram for these patterns. We further show that the non-uniform curvature and anisotropic deformation play critical roles in determining the formation and evolution of these wrinkling patterns. The anisotropic deformation along the toroidal and poloidal directions controls pattern transitions from stripes to hexagons and the non-uniform curvatures determine the nucleation sites of the wrinkling patterns. Our results show that global deformations of a torus lead to strong coupling between elasticity and curvature which may enlarge the design space as well as the dynamically control of wrinkling patterns. If time permitted, I will discuss our ongoing work on the wrinkles on a cone.
A path-following simulation-based study of elastic instabilities in nearly-incompressible confined cylinders under tension
Abstract:
Recent experiments on hydrogels subjected to large elongations have shown elastic instabilities resulting in the formation of geometrically intricate fringe and fingering deformation patterns on the specimens boundaries. I will present a robust computational framework addressing the challenges that emerge in the simulation of this complex material response from the onset of instability to the post-bifurcation behavior. The numerical difficulties stem from the non-convexity of the strain energy density in the near-incompressible, large-deformation regime, which is responsible for the coexistence of multiple equilibrium paths with vastly-different, sinuous deformation patterns immediately after bifurcation. The ingredients to overcome these challenges include: a high order of interpolation in the finite element approximation, an arc-length-based nonlinear solution procedure that follows the entire equilibrium path of the system, and an implementation enabling parallel, large-scale simulations. The resulting computational approach provides the ability to conduct highly-resolved, truly quasi-static simulations of complex elastic instabilities. I will show numerical results illustrating the ability of the path-following approach to describe the full evolution of the fringe and fingering instabilities observed experimentally.
Hard-magnetic Elastica
Abstract:
Recently, ferromagnetic soft continuum robots – a type of slender, thread-like robots that can be steered magnetically – have demonstrated the capability to navigate through the brain's narrow and winding vasculature, offering a range of captivating applications such as robotic endovascular neurosurgery. Composed of soft polymers with embedded hard-magnetic particles as distributed actuation sources, ferromagnetic soft continuum robots produce large-scale elastic deflections through magnetic torques and/or forces generated from the intrinsic magnetic dipoles under the influence of external magnetic fields. This unique actuation mechanism based on distributed intrinsic dipoles yields better steering and navigational capabilities at much smaller scales, which differentiate them from previously developed continuum robots. To account for the presence of intrinsic magnetic polarities, this emerging class of magnetic continuum robots provides a new type of active structure – hard-magnetic elastica – which means a thin, elastic strip or rod with hard-magnetic properties. In this work, we present a nonlinear theory for hard-magnetic elastica, which allows accurate prediction of large deflections induced by the magnetic body torque and force in the presence of an external magnetic field. From our model, explicit analytical solutions can be readily obtained when the applied magnetic field is spatially uniform. Our model is validated by comparing the obtained solutions with both experimental results and finite element simulations. The validated model is then used to calculate required magnetic fields for the robot’s end tip to reach a target point in space, which essentially is an inverse problem challenging to solve with a linear theory or finite-element simulation. Providing facile routes to analyze nonlinear behavior of hard-magnetic elastica, the presented theory can be used to guide the design and control of the emerging class of magnetically steerable soft continuum robots.