Stress Concentration in Strain-Gradient Bodies

An analytical solution is presented to a boundary-value problem in the linear elasticity in which potential energy depends on strains and strain gradients. The problem considered is that of an infinite medium, containing a spherical cavity, subjected to uniaxial tension at infinity. For an isotropic, centrosymmetric material, the strain-gradient theory contains five additional material constants (micro-constants), which may be related to Lame' constants by means of two material lengths. The range of the micro-constants is determined on the basis of positive definiteness of the potential energy, and under this condition no difficulty is encountered in reducing the strain-gradient solution to either the couple-stress or the classical solution. A reduction to the classical result does not have to employ the couple-stress solution as an intermediate step. Numerical calculations are performed for various values of nondimensionalized, independent parameters. The results show that, in contrast to predictions of couple-stress theory, the stress concentration factor can exceed the classical value.