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.
|Original language||English (US)|
|State||Published - Jun 19 2019|
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