STRESS-STRAIN RELATIONS FOR ANISOTROPIC MATERIALS

The generalized Hooke s law relating stresses to strains can be written in contracted notation as 

The stiffness matrix, Cy, has 36 constants in Equation (2.1). However, less than 36 of the constants can be shown to actually be independent for elastic materials when important characteristics of the strain energy are considered. Elastic materials for which an elastic potential or strain energy density function exists have incremental work per unit volume of 

Upon integration for all strains, the work per unit of volume is 

However, Hooke s law, Equation (2.1), can be derived from Equation (2.5)  

the stiffness matrix is symmetric, so only 21 of the constants are independent. 

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