Morphorods: A Modelling Framework for Active Slender Structures

ABSTRACT

Elastic filamentary structures are ubiquitous in nature and can be found at all scales, from microscopic chains of molecules to hairs, vines, umbilical cords, and elephant trunks. Our interest in this talk is active slender elastic structures, which are capable of changing their properties in response to their environment and/or to accomplish a task. For biological structures, this may be achieved through some combination of growth, remodelling, or muscle activity. For instance, a vine searching for a pole to climb actively generates a helical shape through a directed change in growth hormone, while an elephant modulates the shape of its trunk by contraction of muscle groups. Active filamentary structures also have strong relevance in engineering applications, with great potential in biomedical devices and in the expanding field of soft robotics.

Due to their inherent slenderness, the mechanical behaviour of growing filaments is well-characterised by a one-dimensional continuum representation. In this talk, I will outline a modelling framework for describing the mechanical behavior of active slender elastic structures, which we term morphoelastic rods, or simply morphorods. I will demonstrate the utility of the theory via a number of diverse applications, from pattern formation in seashells to tropic growth of plants to the remarkable dexterity of an elephant's trunk and the applicability to soft robotics.

BIOGRAPHY

Dr. Derek Moulton is a Professor of Applied Mathematics at the Mathematical Institute at the University of Oxford. He received his PhD in Mathematical Sciences from the University of Delaware in 2008. He was a postdoc at the University of Arizona and then at Oxford, before taking his current faculty position in 2013. His research focuses on the development and analysis of physics-based mathematical models, applying and adapting tools from continuum mechanics to investigate morphogenesis, growth, pattern formation, physiology, biomimetics, and biomedical devices.