A PRIORI BOUNDS ON SPATIAL MOTIONS OF INCOMPRESSIBLE NONLINEARLY ELASTIC RODS.

The geometrically exact quasilinear evolution equations governing the spatial motion of incompressible rods and their specializations to the hyperbolic equations governing nonlinearly elastic rods have novel mathematical structures strikingly different from those for the equations governing the motion of compressible rods. The main objectives of this paper are to formulate the governing equations, an exercise requiring the solution of a sequence of semilinear hyperbolic equations of first order, and to derive a priori estimates for certain strain variables, ensuring that they cannot reach geometrically prohibited ranges in finite time. This process exhibits a new system of physically important quasilinear equations worthy of careful analysis. [ABSTRACT FROM AUTHOR]