A continuum mechanical gradient theory with applications to fluid mechanics

A gradient theory of grade two based on axiomatic conception of a nonlocal continuum theory for materials of grade n is presentated. The total stress tensor of rank two in the equation of linear momentum contains two higher s tress tensors of rank two and three. In the case of isotropic materials bot h the tensor of rank two and three are tenser-valued functions of the secon d order strain rate tensor and its first gradient so that the equation of m otion is of order four. The necessary boundary conditions for real boundari es are generated by using so-called porosity tensors. This theory is applie d to two experiments. To a velocity profile of a turbulent COUETTE flow of water and a POISEUILLE now of a blood like suspension. On the basis of thes e experimental data the material and porosity coefficients are identified b y numerical algorithms like evolution strategies.