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This paper is concerned with the determination of the distribution of stresses and displacements in an infinite three-dimensional, linear, elastic, isotropic, homogeneous layer subjected to concentrated body forces acting upon an arbitrary internal point.

The method of caustics, as developed and applied to fracture mechanics over the last twenty years, contains several approximations which limit its applicability. In this paper the development of caustics is reviewed and the implicit assumptions made in the past are clarified and discussed. The exact equations are derived for caustics formed by the reflection of light from a general surface. In addition, the conditions for the formation of a caustic curve are derived and explained in detail. Numerically generated shadow spots are given for the case of light reflected from a surface deformed due to the presence of a plane stress, mode-I, elastic crack. Attention is focused on the near tip region where severe deformation gradients violate the assumptions made by previous approximate analyses. The results demonstrate significant deviation from the approximate analyses resulting in errors as large as 15% in the determination of the stress intensity factor from shadow spot measurements.

The jump conditions arising in the formulation of dislocation problems in finite elastostatics are discussed and a full field solution of the anti-plane shear type is given for the screw dislocation problem. The solution is valid for the most general homogeneous isotropic incompressible nonlinear elastic solid. The level of nonlinearity is defined for this solution and compared to "dislocation core" estimates in materials science.