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Wave Momentum and Radiative Stresses in Elastic Solids

Mechanical Engineering Institute of the Russian Academy of Sciences, 85 Belinsky Str., Nizhny Novgorod, 603024, Russia

G. A. Maugin

Laboratoire de Modélisation en Mécanique, Université Pierre-et-Marie Curie/CNRS UMR 7607, Case 162, 4 place Jussieu, 75252 Paris 05, France

C. Trimarco

Instituto di Matematica Applicata "U. Dini", Universita di Pisa, Via Bonnano 25B, 56126 Pisa, Italy

The physical meaning of the notions of wave momentum and radiative stress in elastic bodies is considered. Of great importance for defining and calculating these quantities are the variables in which the wave processes in the medium are described. In Euler variables, the radiative stress is defined as the time average of the momentum flux of the medium across the boundary of a volume that is stationary in space. It differs from the radiative stress calculated in Lagrangian variables by the value of the convective component of momentum flux involved with the motion of particles in the medium. It is shown that, physically, the wave momentum can be defined only in Euler variables. In the linear approximation of the small perturbation theory the wave momentum is a quadratic component of the total mechanical momentum of the medium. The integrals of motion of linear acoustic equations correspond to it, as well as to energy. In the second approximation of the perturbation theory, the wave momentum no longer has a rigorous definition. However, the concept of wave momentum borrowed from the linear approximation can be used for the calculation of average values of stresses and deformations, provided the body is not moving as a whole.

Key Words: elasticity • radiative stress • wave momentum • wave pressure

Mathematics and Mechanics of Solids, Vol. 10, No. 4, 441-460 (2005)
DOI: 10.1177/1081286505036414


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