Plastic Failure Modes of Rectangles, Triangles and Drums

A block of yield-stress fluid fails under gravity when its surface becomes too steep. In this study we examine the modes of failure of rectangular and triangular blocks leaning against a vertical wall,and of a partially filled cylindrical drum.

We present computational results for the failure modes using the augmented-Lagrangian scheme. These results are compared with analytical predictions based on the limit analysis of perfect plasticity theory. For the drum, the computational results match with the plasticity predictions, with failure arising along a circular arc and overlying material rotating rigidly out of position. For rectangular and triangular blocks against a wall, the computations demonstrate more complicated modes of failure, with the simpler geometries of the analytical failure modes providing a cruder bound.