ABSTRACT
For the formulation of the constitutive relationships we need deformation measures which are invariant with respect to rigid body motions which are the conventional strain tensor namely the strain tensor
the relative rotation
and the gradient of the Cosserat rotation which is called the curvature of the deformation
It is usual to combine equations (2) and (3) to a single, tensorial deformation measure (see Muhlhaus 1993, Vardoulakis and Sulem 1995)
The six deformation quantities (equations 4 and 5) are conjugate in energy to six stress quantities. First we have the four components of the non symmetric stress tensor GtJ which is conjugate to the non symmetric deformation tensor jv and second we have two moment stresses (moment per unit area) mi and m?, which are conjugate to the two curvatures K/ and K^. Force and moment equilibrium at the element (<3xi,dxi) lead to
In the above equations dynamic effects are included through inertial forces and moment. The stress-strain relationships for a 2D anisotropic Cosserat continuum are (see Schaefer 1962)
where a is a parameter of anisotropy.
