  Universal displacements are those displacements that can be maintained for
any member of a specific class of linear elastic materials in the absence of
body forces, solely by applying boundary tractions. For linear hyperelastic
(Green elastic) solids, it is known that the space of universal displacements
explicitly depends on the symmetry group of the material, and moreover, the
larger the symmetry group the larger the set of universal displacements. Linear
Cauchy elastic solids, which include linear hyperelastic solids as a special
case, do not necessarily have an underlying energy function. Consequently,
their elastic constants do not possess the major symmetries. In this paper, we
characterize the universal displacements of anisotropic linear Cauchy
elasticity. We prove the unexpected result that for each symmetry class, the
set of universal displacements of linear Cauchy elasticity is identical to that
of linear hyperelasticity.
