Matter in bulk can be distorted in many different ways: stretching, shearing, bending, twisting, etc. Each kind of distortion contributes to the elastic energy of a deformed material. In orthogonal coordinates, the elastic energy per unit volume due to strain is thus a sum of contributions: U = 1 2 C i j k l ε ε i j ε ε k l , where C i j k l is a 4th rank tensor, called the elastic tensor or stiffness tensor which is a generalization of the elastic moduli of mechanical systems, and ε ε i j is the strain tensor (Einstein summation notation has been used to imply summation over repeated indices). The values of C i j k l depend upon the crystal structure of the material: in the general case, due to symmetric nature of σ σ and ε ε , the elastic tensor consists of 21 independent elastic coefficients. This number can be further reduced by the symmetry of the material: 9 for an orthorhombic crystal, 5 for an hexagonal structure, and 3 for a cubic symmetry. Finally, for an isotropic material, there are only two independent parameters, with C i j k l = λ λ δ δ i j δ δ k l + μ μ ( δ δ i k δ δ j l + δ δ i l δ δ j k ) , where λ λ and μ μ are the Lamé constants, and δ δ i j is the Kronecker delta.