Before revision: For an isotropic material: so that: This equation can also be written in terms of Young's modulus E and Poissons 's ratio υ using the standard relationships: Substituting, we obtain the following: For most metals, the left-hand side of this equation is positive, so that the elastic energy will be a minimum for those directions that minimize the term: l2m2 + m2n2 + l2n2.
After revision: For an isotropic material: so that: This equation can also be written in terms of Young's modulus E and Poisson 's ratio υ using the standard relationships: Substituting, we obtain the following: For most metals, the left-hand side of this equation is positive, so that the elastic energy will be a minimum for those directions that minimize the term: l2m2 + m2n2 + l2n2.