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Continuum mechanics of moving defects in growing bodies

Amit Acharya's picture

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.

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