Nonlinear Continuum Mechanics, Electrodynamics and Ether Theories
All attempts of describing fundamental physics with continuum mechanics in the 19th century have been falsified by the famous experiments by Michelson and Morley that seem to have disproved the concept of an aether. The aether theorists however never thought of particles as being topological defects creating a displacement field - which is not astonishing, since the first examples of such defects, dislocations in solids, were discovered in 1934 by Taylor, almost 30 years after aether theories had disappeared from the stage of theoretical physics. In view of the results of Frank (1949) and others, however, one must say that the wrong concept was not describing spacetime as an elastic continuum but a wrong or missing picture of particles moving in it. The hypothesis that elementary particles could be topological defects in an elastic continuum is backed by interesting results of modern nonlinear continuum mechanics (Truesdell 1960, Beatty 1987, Hayes 2000). This is discussed in the papers
What can Physics Learn from Continuum Mechanics ? (gr-qc/001164)
Topological Defects in an Elastic Continuum - A Valid Model for Particle Physics ?
(TRECOP 01 - Structured Media, pp. 293-311, ed.B. Maruszewski)
See also the talks
Einsteins Teleparallelism Attempt and its Relation to Topological Defects in an Elastic continuum (abstract),
given at the SIGRAV 02 in Rome 09/02 (abstract)
Einstein's Teleparallel Theory and its Relation to Nonlinear Continuum Mechanics with Topological Defects (abstract), given at the MG10 meeting (07/03) in Rio de Janeiro. See a review paper
A numerical treatment of a topological defect is done in the paper
'Displacement Field and Elastic Energy of a Circular Twist Disclination for Large Deformations - an Example how to Treat Nonlinear Boundary Value Problems with Computer Algebra Systems' cond-mat/0301531.