Acceleration Waves in Nonlinear Thermoelastic Micropolar Media
By the term “acceleration wave”, we mean an isolated geometric surface that moves relative to the material points, across which the acceleration is discontinuous but the displacement and velocity are continuous. More generally, we call an acceleration wave a propagating surface across which second derivatives of some fields undergo discontinuity jump. In the theory of the nonlinear thermoelastic micropolar continuum (called also Cosserat continuum), acceleration waves relate with some jumps of linear and angular accelerations as well as second derivatives of temperature. Acceleration waves are similar to sound waves in solids; they also relate with the localization of deformations in solids.
Analytic solutions in the theory of the propagation of nonlinear waves are exceptional, and acceleration waves present one of the exceptions. An acceleration wave (or a wave of weak discontinuityof order 2)...
- 1.Truesdell C, Noll W (1965) The nonlinear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, vol III/3. Springer, Berlin, pp 1–602Google Scholar
- 5.Eremeyev VA (2005) Acceleration waves in micropolar elastic media. Doklady Phys 50:204–206Google Scholar
- 7.Eremeyev VA, Lebedev LP, Altenbach H (2012) Foundations of microplar mechanics. Springer, HeidelbergGoogle Scholar
- 10.Eringen AC (1999) Microcontinuum field theory. I. Foundations and solids. Springer, New YorkGoogle Scholar