ON ERICKSENS PROBLEM FOR PLANE DEFORMATIONS WITH UNIFORM TRANSVERSE STRETCH

Ericksen's problem[1] consists of determining static deformation fields which are producible in every isotropic, homogeneous, incompressible, elastic body under the sole action of surface traction. In this paper, we obtain the complete solution of this problem for the ease of plane deformations with uniform transverse stretch. The approach utilizes a novel and convenient parameterization of the deformation gradient field. Aside from the set of homogeneous deformations, the following four families of deformations are found to be the only ones possible: (i) Bending and stretching of a rectangular block, (ii) Straightening and stretching of a sector of a hollow cylinder, (iii) Inflation, bending and extension of an annular wedge. (iv) Inflation, bending, extension and azimuthai shearing of an annular wedge. © 1969.