Singular stress concentrations in second-grade materials

The problems of a second-grade elastic half-space deformed in plane strain and subject to a concentrated load, a discontinuous load, and a double force, acting at a point on the free surface are solved. The nature of the stress singularity is found in each case. Although the strengths of the stress singularities are the same as for both classical elasticity and conventional couple-stress materials, the detailed forms are different and depend on a certain combination of the five new elastic constants. The displacement field produced by a point load is bounded in the neighbourhood of the point of application of the force, in contrast to both earlier theories where it is singular.