Publication 19-CNA-010

Continuum mechanics of moving defects in growing bodies

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Shankar C. Venkataramani
Department of Mathematics
University of Arizona
Tucson, AZ 85721
shankar@math.arizona.edu

Abstract: 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 exibility 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.

Get the paper in its entirety as  19-CNA-010.pdf

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