Estimating forces during ploughing of a granular bed

Abstract

We present a method for predicting forces on a plough – modelled as a flat, rigid plate inclined in the direction of motion – as it moves through a granular bed. Our method combines coarse, but representative, discrete element (DE) simulations with continuum mechanics. We first homogenize the kinematic information obtained from DE simulations to obtain a continuum strain field. The strain field is then combined with an appropriate continuum constitutive law for the granular material being ploughed and linear momentum balance to obtain forces acting on the plough. Our method has the advantage that it does not require (i) detailed DE simulations nor (ii) extensive calibration of grain parameters to match experiments which, in turn, requires significant effort and may be system dependent. Both (i) and (ii) are necessary if forces are to be estimated directly from simulations. We confirm the effectiveness of our approach by comparing our predictions with results from calibrated DE simulations and experiments.