A variational approach to the Cosserat-like continuum (Q1308891)

The exposition is intended to show an equivalent variational approach to formulation of the virtual work principle for the Cosserat-like continuum. Stationarity conditions for an action integral lead to the Euler-Lagrange equations identified with the balance equations for stresses and couple-stresses within micropolar and micromorphic continua. Vector fields as independent variables are taken so as to satisfy the known Stokes' decomposition. Based on the standard variational arguments, for a given Lagrangian function and an assumed one-parameter family of transformations of both the independent and dependent variables, the fundamental variational formula identified with the virtual work principle of the Cosserat-like continuum is obtained.