Refined explicit integration of elastoplastic models with automatic error control

Abstract

Effective explicit algorithms for integrating complex elastoplastic constitutive models, 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 is 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 generalised 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.

Validation of a New Elastoplastic Constitutive Model Dedicated to the Cyclic Behaviour of Brittle Rock Materials

“…The integration of the constitutive law requires a more complex integration scheme. We recommend the explicit integration scheme with automatic control error presented in (Sloan et al, 2001).…”

Performance of mixed formulations for the particle finite element method in soil mechanics problems

“…The integration of the elasto-plastic constitutive relations is performed with an explicit scheme with adaptive sub-stepping; correction for the yield surface drift is applied [18,34].…”

A hysteretic multiscale formulation for nonlinear dynamic analysis of composite materials

“…In this work, an Euler scheme is implemented to retrieve the updated stress field at the Gauss points for brevity. However, more refined sub-stepping explicit [32,51] or implicit methods [49] can be implemented for the solution of the incremental equations of plasticity. Thus, at the end of the iterative procedure, both the current stress field and the interaction matrix [R] are evaluated.…”