Cosserat rods have been used to model a wide range of different physical systems. These systems can consist of a single rod undergoing deformation or assemblies of multiple rods connected together to create more complex systems. The case studies below illustrate the flexible and versatile capabilities of Cosserat rods in analyzing a wide range of both naturally occurring and artificial systems to provide insight into mechanics, dynamics, and control using Elastica.
Swimming and Slithering
Cosserat rods can be used to understand how different gaits affect swimming and slithering speed. Snakes and slender swimmers, such as eels, can be modeled either as a single rod or as the interaction of multiple rods representing different muscle groups. Then, the torque profiles applied can be optimized to identify the gait that yield the fastest forward speed.
Zhang, Naughton, Parthasarathy, Gazzola, Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains, Nature Communications, 2021.
Zhang, Chan, Parthasarathy, Gazzola, Modeling and simulation of complex dynamic musculoskeletal architectures, Nature Communications, 2019.
Gazzola, Dudte, McCormick, Mahadevan, Forward and inverse problems in the mechanics of soft filaments, Royal Society Open Science, 2018.
Control of Soft Matter Structures
Soft, flexible structures have many more degrees of freedom than rigid structures, making the development of control strategies for such systems difficult. Cosserat rod theory can be used model soft slender structures allowing a framework within which novel control strategies for these difficult problems can be developed.
Wang, Halder, Gribkova, Gazzola, Mehta, Control-oriented modeling of bend propagation in an octopus arm, arXiv:2110.07211.
Chang, Halder, Gribkova, Tekinalp, Naughton, Gazzola, Mehta, Controlling a CyberOctopus soft arm with muscle-like actuation, arXiv:2010.03368.
Wang, Halder, Chang, Gazzola, Mehta, Optimal control of a soft CyberOctopus arm, American Control Conference (ACC), 2021.
Chang, Halder, Shih, Tekinalp, Parthasarathy, Gribkova, Chowdhary, Gillette, Gazzola, Mehta, Energy shaping control of a CyberOctopus soft arm, IEEE Conference on Decision and Control (CDC), 2020.
Solenoids and Plectonomes
When a long, slender fiber is twisted, it will eventually curl up on itself. This behavior has been observed across a wide range of spatial scales, from DNA to metal wires. Understanding these modes of deformation is important in the future development of slender elastomeric structures such as artificial muscles.
Charles, Gazzola, Mahadevan, Topology, geometry, and mechanics of strongly stretched and twisted filaments: solenoids, plectonemes, and artificial muscle fibers, Physical Review Letters, 2019.
Gazzola, Dudte, McCormick, Mahadevan, Forward and inverse problems in the mechanics of soft filaments, Royal Society Open Science, 2018.
Complex Musculoskeletal Architectures
Skeletal muscles are long, thin fibers that work together to generate force and allow movement. By combining multiple Cosserat rods together, this behavior of muscles can be simulated. Because Cosserat rods can incorporate both extension and shearing, they are well equipped to handle the complex deformations that muscles undergo during contraction.
Zhang, Chan, Parthasarathy, Gazzola, Modeling and simulation of complex dynamic musculoskeletal architectures, Nature Communications, 2019.
Soft Robotics and Bio-robotics
New generations of robotics are seeking to develop both soft and biohybrid robots. Biohybrid machines have been developed using muscles to actuate soft robotic structures. Soft, flexible robots have been developed to allow maneuverability in small spaces and simulations of these robots allow in silico optimization of their designs prior to fabrication, reducing development time and cost.
Naughton, Sun, Tekinalp, Chowdhary, Gazzola, Elastica: A compliant mechanics environment for soft robotic control, IEEE Robotics and Automation Letters, 2021.
Aydin, Zhang, Nuethong, Pagan-Diaz, Bashir, Gazzola, Saif, Neuromuscular actuation of biohybrid motile bots, Proceedings of the National Academy of Sciences, 2019.
Chowdhary, Gazzola, Krishnan, Soman, Lovell, Soft robotics as an enabling technology for agroforestry practice and research, Sustainability, 2019.
Pagan‐Diaz, Zhang, Grant, Kim, Aydin, Cvetkovic, Ko, Solomon, Hollis, Kong, Saif, Gazzola, Bashir, Simulation and fabrication of stronger, larger and faster walking biohybrid machines, Advanced Functional Materials, 2018.
Birds Nest Meta-materials
Birds create complex structures with desirable mechanical properties. These randomly packed systems exhibit forms of self-assembly. Understanding the characteristics of such meta-material systems can yield insights into next generation fabrication techniques and material properties.
Bhosale, Weiner, Butler, Kim, Gazzola, King, Micromechanical origin of plasticity and hysteresis in nest-like packings, arXiv:2112.00784.
Weiner, Bhosale, Gazzola, King, Mechanics of randomly packed filaments – the ‘bird nest’ as meta-material, Journal of Applied Physics, 2020.