Plane-Strain Problems for a Class of Gradient Elasticity Models-A Stress Function Approach

The plane strain problem is analyzed in detail for a class of isotropic, compressible, linearly elastic materials with a strain energy density function that depends on both the Strain tensor epsilon and its spatial gradient del epsilon. The appropriate Airy stress-functions and doublestress-functions are identified and the corresponding boundary value problem is formulated. The problem of an annulus loaded by an internal and an external pressure is solved.