Vol. 3, No. 3, 2015

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Comprehensive description of deformation of solids as wave dynamics

Sanichiro Yoshida

Vol. 3 (2015), No. 3, 243–272
DOI: 10.2140/memocs.2015.3.243

Deformation and fracture of solids are discussed as comprehensive dynamics based on a field theory. Applying the principle of local symmetry to the law of elasticity and using the Lagrangian formalism, this theory derives field equations that govern dynamics of all stages of deformation and fracture on the same theoretical foundation. Formulaically, these field equations are analogous to the Maxwell equations of electrodynamics, yielding wave solutions. Different stages of deformation are characterized by differences in the restoring mechanisms responsible for the oscillatory nature of the wave dynamics. Elastic deformation is characterized by normal restoring force generating longitudinal waves; plastic deformation is characterized by shear restoring force and normal energy-dissipative force generating transverse, decaying waves. Fracture is characterized by the final stage of plastic deformation where the solid has lost both restoring and energy-dissipative force mechanisms. In the transitional stage from the elastic regime to the plastic regime where both restoring and energy-dissipative normal force mechanisms are active, the wave can take the form of a solitary wave. Experimental observations of transverse, decaying waves and solitary waves are presented and discussed based on the field theory.

deformation of solids, plastic deformation transverse-wave, elasto-plastic solitary-wave
Physics and Astronomy Classification Scheme 2010
Primary: 46
Received: 6 February 2015
Revised: 24 May 2015
Accepted: 18 July 2015
Published: 11 October 2015

Communicated by Francesco dell'Isola
Sanichiro Yoshida
Department of Chemistry and Physics
Southeastern Louisiana University
Hammond, LA 70402
United States