Substepping schemes for the numerical integration of elastoplastic stress–strain relations

Abstract

SUMMARYThis paper describes two substepping schemes for integrating elastoplastic stress-strain relations. The schemes are designed for use in finite element plasticity calculations and solve for the stress increments assuming that the strain increments are known. Both methods are applicable to a general type of constitutive law and control the error in the integration process by adjusting the size of each substep automatically. The first method is ba5ed on the well-known modified Euler scheme, whereas the second technique employs a high order Runge-Kutta formula. The procedures outlined do not require any form of stress correction to prevent drift from the yield surface. Their utility is illustrated by analysis of typical boundary value problems.

Parameter determination in field and laboratory tests

“…Due to the strong non-linearity of the volumetric plastic potential, P , the evolution of p is badly approximated and solution diverges. The only possibility to overcome this drawback is to reduce the step size or to subintegrate, (Sloan 1987). The implicit curves with sub-integration are given in Figures 5 and 6. …”

Application of an Anisotropic Constitutive Model for Structured Clay to Seismic Slope Stability

“…Various numerical techniques-explicit, refined explicit, and implicit-have already been proposed and extensively discussed in the literature (e.g., see Potts and Gens 1985;Sloan 1987; Borja and Lee 1990; Crisfield 1991; Borja 1991; Jeremić and Sture 1997; Sloan et al 2001). Implicit integration is the most accurate approach, and in most cases, a robust integration of a constitutive model dictates the use of an implicit algorithm.…”

“…Given such a requirement in the main algorithm of this code, it has been decided to use a compatible stress update algorithm. To enhance the numerical accuracy, an explicit integration scheme with a drift-correction method and an optional substepping technique (Sloan 1987;Sloan et al 2001) have been adopted for the model implementation in the current work.…”

Consistent tangent matrices for substepping schemes

“…Another approach, also successfully applied in various situations, is substepping [4,5]. The time-step is subdivided into a number of substeps (which can be different for each Gauss point), and a single-step integration rule is employed within each one.…”