Mechanics, geometry and instability (or bistability)


Zi Chen, Society in Science – Branco Weiss Fellow
Washington University in St. Louis


The fundamental questions we are trying to address include: (1) the role of mechanics in morphogenesis (the creation of forms in nature) in plant and animal development, and (2) how this information can inspire designs for nano-fabrication techniques and bio-mimetic devices (devices with intelligent, functional responses to environmental stimuli). The more specific aims of our research include understanding how mechanics and geometry can be inter-related, e.g., in spontaneous formation of helical structures which can be related to the shape of  helical seed pods and “bistable morphing structures” (structures that can switch/morph between two different stable states). These structures have important applications in a wide variety of devices ranging from bio-inspired robots to actively shape-able aeroplane wings.


Our study investigates, through both theoretical analysis and table-top experiments, the spontaneous formation of helical structures, and the geometric and mechanical conditions for bistability due to “geometric nonlinearity” (nonlinear behavior due to geometric effects).

In the table-top experiments, we pre-stretch one or two pieces of thin latex rubber sheets and attach it to an elastic strip. Upon release, the bonded two or three-layer system will spontaneously deform into either a helical shape or a doubly curved strip with or without bistability. Whether or not the system is bistable depends on the interplay between mechanics and geometry (i.e., the pre-stretch, the relative dimensions, and the geometric orientation). A typical demonstration of the bistable strip can be viewed at


In our first study, the helix angle and radius of helical ribbons are predicted with a comprehensive, three-dimensional elasticity theory. In many biological and engineered systems, helical geometry is commonplace and may be driven by surface stress, differential growth, and geometric or elastic mismatch between layers of a layered composite material. More generally, our approach can be applied to develop materials and systems with tunable helical geometries.

In our second study, we identify two dimensionless parameters controlling bistability, and we classify the conditions needed for bistability, thus defining a design space for bistable structures. These results provide a mechanical framework for studying the biological processes that lead to shape formation and will facilitate the design of multi-stable functional structures. Such multi-stable structures include artificial muscles, bio-inspired robots, and deployable, morphing structures (like shape-able wings) in aerospace applications.

We are actively studying the mechanics of bistable structures in biology, such as the Venus flytrap. The take-home message: mechanics + geometry = extreme mechanics = extreme fun!


mechanical engineering, geometry, instability, bifurcation

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