A New Simple Equation for Obtaining The Strain Distribution of a Granular Bed

Abstract

A new simple equation to estimate the strain distribution of a granular bed is derived based on the mechanics of an elastic body and the hydrodynamics. A new assumption introduced is that stresses caused by strains depend on both the strains and the average stress in the granular bed. As a simple but typical example to verify the new theory, the strain distribution of a powder bed sandwiched between two parallel plates is discussed. The distribution caused by the slow movement of the upper or lower plate is represented not by a straight line, but a curved line. The simple equation based on the new theory gives a good estimation for the strain distribution.