Stress invariance and redundant moduli in three-dimensional elasticity

A three-dimensional framework is established for generating invariant stres s configurations and associated shifts in the elastic compliance. Under the se shifts the stress throughout an elastic body is unaltered, while the com patibility equations for the strain are automatically satisfied. The types of invariant stress fields and translations of the compliance identified he re generalize the results of Cherkaev, Lurie & Milton (CLM) for planar elas ticity. The key to the classification is the partitioning of the fourth-ord er compliance tensor into symmetric and antisymmetric components. The CLM t heorem and its generalization are closely linked to the six-dimensional ant isymmetric part of the compliance, and several examples are given of stress invariance under shifts of these elements of the compliance tensor.