Dynamics of Patterns on Elastic Hypersurfaces. Part I. Shear Waves in the Middle Surface

摘要

The shear motions in an incompressible elastic continuum are considered and it is shown that, when linearized, the governing equations can be rendered into Maxwell's form. The trace of the deviator stress tensor is analogous to the electric field, while the vorticity (the curl of the velocity field) is interpreted as the magnetic field. We show that the analogy can be extended further to incorporate the so-called Lorentz force as the counterpart of the advective nonlinearity of the elastic model. Localized shear dislocations are considered and shown to undergo Lorentz contraction in the direction of motion. Thus an interesting and far reaching analogy between the elastic continuum and the electrodynamics is established.