Amit Acharya Shankar Venkataramani
(In Materials Theory)
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic
geometry. These objects support novel types of mesoscopic defects - discontinuity lines
for the second derivative and branch points - terminating defects for these line discontinuities.
These higher-order defects move "easily", and thus confer a great degree of
flexibility to thin hyperbolic elastic sheets. We develop a general, higher-order, continuum mechanical framework
from which we can derive the dynamics of higher order defects in a thermodynamically consistent
manner. We illustrate our framework by obtaining the explicit equations for the dynamics
of branch points in an elastic body.