Reduction of the Cosserat-type nonlinear equations to the system of Godunov's form

Vladimir M. Sadovskii

Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation

Abstract: The complete system of equations for the dynamics of a Cosserat-type continuum with finite strains and particle rotations in Lagrangian variables is reduced to a compatible system of conservation laws in the Godunov sense. This system allows one to analyse generalized solutions with surfaces of strong discontinuity of stresses and velocities and admits integral estimates. They guarantee the uniqueness and continuity of solutions of the Cauchy problem and boundary-value problems with dissipative boundary conditions in relation to initial data.

Keywords: elasticity, Cosserat continuum, couple stress tensor, curvature tensor.

UDC: 539.371

Received: 31.10.2023
Received in revised form: 07.11.2023
Accepted: 27.12.2023

Language: English