An evaluation of substepping and implicit stress point algorithms Original Research Article

Elasto-plastic finite element analyses of geotechnical boundary value problems involve the use of a non-linear solution strategy. A popular and efficient strategy is the modified Newton Raphson approach of which a key element is the integration of the constitutive laws over a finite strain step. Two algorithms for performing such an integration are the ‘substepping’ and ‘return’ methods. In this paper the basic assumptions behind these methods are described and the associated errors compared. This comparative study is undertaken both at a fundamental level and when applied to a typical boundary value problem. The errors associated with both methods are increment size dependent. It is shown in the problems considered that for a particular increment size, the ‘substepping’ method is the more accurate.