Refined explicit integration of elastoplastic models with automatic error control

Effective explicit algorithms for integrating complex elastoplastic constitutive methods such as those belonging to the Cam clay family, are described. these automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used in a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non-linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr-Coulomb, modified Cam clay and generalized Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non-linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress-strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.