Ericksen’s problem: existence of additional inhomogeneous constant-invariant universal deformations

Determine whether there exist additional inhomogeneous universal deformations with constant principal invariants in incompressible isotropic elastic solids.

Background

Classical results identify six families of universal deformations in incompressible isotropic elastic solids. The fifth family is inhomogeneous and characterized by constant principal invariants, disproving the earlier conjecture that constant-invariant deformations must be homogeneous.

Despite extensive efforts, it remains unresolved whether further inhomogeneous universal deformations with constant principal invariants exist beyond the known examples. This long-standing question is commonly referred to as Ericksen’s problem.