An attempt to separate elastic strain energy density of linear elastic anisotropic materials based on strain considerations (Q368161)

The authors offer an original approach to the expression of the elastic strain energy density of anisotropic materials in the form of the sum of volume and shape changes. They introduce a new strain parameter which characterizes the material anisotropy and is a linear combination of strain tensor components. Under the assumption that any change of volume leaves the symmetry of the material undistorted, the authors obtain by a rigorous mathematical deduction explicit expressions for the introduced parameter for different classes of anisotropy: cubic; hexagonal, trigonal and tetragonal; orthotropic; monoclinic; triclinic. The authors show that dilatational and distortional parts of the elastic strain energy expressed in terms of the strain parameter describe the directional sensitivity of the material. For the particular case of an isotropic material, they analyze the consistency of the obtained results. The authors also give a physical interpretation of the introduced strain parameter.