Variational formulation of dynamic problems for a nonlinear Cosserat medium

Abstract

Abstract A variational formulation of dynamic problems for a geometrically and physically nonlinear elastic Cosserat medium is obtained in the form of the problem of finding the stationary point of Hamilton's functional. Variations of the strain and rotation tensors and the linear and angular velocity vectors are calculated. The equivalence of the Euler equations with natural boundary conditions to the equations of motion with the original boundary conditions in the case of potential force and torque loads is proved. A nontrivial potentiality condition of the torque (bulk and surface) loads is obtained.