Discontinuous deformation analysis based on the multiplicative decomposition of the displacement

Abstract

SummaryUpdating the block configuration on the basis of additive decomposition and its linearized expression of the displacement increment leads to the low calculation accuracy of the original discontinuous deformation analysis (DDA) and false volume expansion. In this study, the displacement expressions of a small deformation, a large rotation, and the corresponding velocity and acceleration terms on the basis of the initial configuration are presented using multiplicative decomposition. With the use of the principle of virtual work, the stiffness matrix, mass matrix, and force vector of blocks are obtained. Compared with the original DDA, each of the block deformation parameters has obvious physical meaning as a parameter of mechanics, which can be obtained by adding the incremental deformation components of each time step directly without co‐ordinate transformation. Moreover, the proposed modification automatically considers the block deformation produced by centrifugal and Coriolis forces. The analysis of some typical numerical examples have verified the accuracy of the strain and stress calculated by the proposed method, and the current configuration is updated by the total displacements, which completely overcomes the false volume expansion and provides reasonable linear strains.