Extrema of the strain energy density for anisotropic micropolar solids

The paper deals with any 2D solid of prescribed shape and elastic properties, consisting of an orthotropic micropolar material. The conditions are determined under which the global stiffness of the solid is maximized, taking the orientation  of the material symmetry axes to the local extreme strains as design variable. Unlike Cauchy solids, it is shown that the maximum stiffness problem for micropolar solids is not fulfilled by ‘trivial’ solutions, at which full collinearity of the material symmetry axes and the directions of the extreme strains is achieved. The paper closes with the determination of the optimal orientations for a special elasticity problem.