Predicting the behaviour of ubiquitous filaments
Despite the apparent differences in filamentary systems, their growth, movement and plasticity appear to follow universal physical laws. However, important gaps still exist in our understanding. With EU support of the GROWINGRODS (Mathematics and mechanics of growth and remodelling of bio-filaments) project, scientists have developed unifying mathematical frameworks correlating mechanics with growth. When a growing body attempts to expand against geometrical constraints of its environment, non-linear growth regimes can cause emergent mechanical properties of the whole to be much more than the sum of its parts. GROWINGRODS' general theory for filament growth of arbitrary material properties that explains this phenomenon was used to explain the diversity and evolution of sea shells. Structures made of bundles of filaments are another type of system for which no general theory was previously able to predict behaviours. Taking a simplified system composed of two filaments interacting elastically, scientists developed a theory of mechanics and growth allowing elucidation of the effective properties of the structure from that of the subfilaments. Significantly, the framework demonstrates that the conventional laws relating averaged forces and moments to strains for single rods (Kirchoff's laws) are not appropriate for bundles. Instead, scientists developed a definition of generalised stresses and solutions of the corresponding balance equations. Most importantly, scientists overcame a confounding barrier in descriptions of the stability of mechanical equilibria of 1D systems. Many equilibrium states can exist but, if they are not stable, they are rarely observed. Until now, theoretical descriptions could only identify a few cases of equilibrium. The team developed a formulation that now enables finding most if not all equilibrium states with ease. This opens the door to applications in engineering such that one can modify a system to stabilise particular equilibria. Researchers successfully applied the new mathematical frameworks to a natural system, a hybrid and an engineered device. GROWINGRODS has contributed important and widely useful new mathematical formulations describing the mechanics and growth of ubiquitous filamentary structures. The resulting three publications with advanced descriptions will have far-reaching implications on understanding and engineering innovative devices in many fields.
