Masao Satake

On distortion of tensor and yield criteria of granular materials

Abstract The distortion of tensor defined by use of normals on the tensor ellipsoid and the mean distortion are introduced. It is explained that the distortion represents the unit shear strain for the finite strain tensor, and the shear-normal stress ratio for the stress tensor. The spatial mobilized plane which plays a very important role in the mechanics of granular materials is regarded as a plane on which the distortion of stress tensor coincides with its mean distortion, and the yield criteria of granular materials are considered applying the concept of the distortion of stress tensor.

Stress analysis of a penny-shaped crack locted between two oblate spheroidal cavities in an infinite solid

Abstract The problem of a penny-shaped crack located between two oblate spheroidal cavities in an infinite solid subjected to uniaxial loads is considered. Using transformations between harmonic functions in cylindrical coordinates and those in oblate spheroidal ones, the problem is reduced to non-homogeneous linear equations. The obtained equations are solved numerically and the stress intensity factors at the penny-shaped crack tip under the influence of the two oblate spheroidal cavities are shown graphically.