Robust and efficient handling of yield surface discontinuities in elasto-plastic finite element calculations

Purpose
– The purpose of this paper is to present several methods on how to deal with yield surface discontinuities. The explicit formulations, first presented by Koiter (1953), result in multisingular constitutive matrices which can cause numerical problems in elasto-plastic finite element calculations. These problems, however, are not documented in previous literature. In this paper an amendment to the Koiter formulation of the constitutive matrices for stress points located on discontinuities is proposed.

Design/methodology/approach
– First, a review of existing methods of handling yield surface discontinuities is given. Examples of the numerical problems of the methods are presented. Next, an augmentation of the existing methods is proposed and its robustness is demonstrated through footing bearing capacity calculations that are usually considered “hard”.

Findings
– Previous studies documented in the literature all present “easy” calculation examples, e.g. low friction angles and few elements. The amendments presented in this paper result in robust elasto-plastic computations, making the solution of “hard” problems possible without introducing approximations in the yield surfaces. Examples of “hard” problems are highly frictional soils and/or three-dimensional geometries.

Originality/value
– The proposed method makes finite element calculations using yield criteria with corners and apices, e.g. Mohr-Coulomb and Hoek-Brown, much more robust and stable.