The previous two chapters established the elasticity field equations related to the kinematics of small deformation theory and the equilibrium of the associated internal stress field. Based on these physical concepts, six strain-displacement relations, six compatibility equations and three equilibrium equations can be developed for the general 3D case. Because moment equilibrium simply results in symmetry of the stress tensor, it is not normally included as a separate field equation set. Also, recall that the compatibility equations actually represent only three independent relations, and these equations are needed only to ensure that a given strain field will produce single-valued continuous displacements. Because the displacements are included in the general problem formulation, the solution normally gives continuous displacements, and the compatibility equations are not formally needed for the general system. Thus, excluding the compatibility relations, nine field equations have been developed. The unknowns in these equations include three displacement components, six components of strain, and six stress components, yielding a total of fifteen unknowns. Thus, the nine equations are not sufficient to work out the fifteen unknowns, and additional field equations are needed. This result should not be surprising since| up to this point in our development we have not considered the material response.