Generalized proper states for anisotropic elastic materials (Q2774054)

The aim is to formulate clear criteria for controlling the properties of composite materials by proper choices of stiffness or compliance tensor at a given material point. The criteria presented are based on the determination of directions for which Young modulus reaches its minimal and maximal values, as well as on the determination of planes of minimal and maximal shear moduli. Two cases are considered which are uniaxial tension and pure shear. The problem of seeking for all unit stress states for which the stored elastic energy has a local extremum is solved by Lagrange's method. The necessary condition for extremum defines the generalized proper states for the compliance tensor. The results derived in the paper can be used to give optimal description of the internal structure of materials, e.g. the direction of fibres in fibre-reinforced composites.