Closed-form displacement field equations for a disc subjected to self-equilibrated arbitrary loads

The closed-form displacement field equations for the case of a disc subjected to self-equilibrated loads of arbitrary magnitude and direction are systematically derived from the existing closed-form stress field expressions. The proposed equations are validated with the help of numerical simulation carried out for the case of a disc under diametral compression and a disc subjected to four arbitrary loads. The derived expressions open the way for the extensive use of displacement measuring experimental techniques in the inverse analysis of granular materials for determining the particle forces. Graphical abstract: [Figure not available: see fulltext.]