An Efficient Return Algorithm For Non-Associated Plasticity With Linear Yield Criteria In Principal Stress Space

En effektiv returalgoritme for spæningsopdatering i numeriske plasticitetsberegninger præsenteres. Flydekriteriet skal være lineært i hovedspændingsrummet og kan bestå af en eller flere flydeplaner. Enhver af disse planer kan have en associeret eller ikke-associeret flyderegel. Spændingsreturneringen og dannelsen af den konstitutive matrix foretages i hovedspændingsrummet. I dette rum bliver manipulationerne simple og baserer sig på geometriske argumenter. Singulariteterne, som opstår hvor flydeplaner krydser hinanden, klares på en simpel måde, ligeledes baseret på geometriske overvejelser. Metoden eksemplificeres med et ikke-associeret Mohr-Coulomb materiale igennem artiklen.An efficient return algorithm for stress update in numerical plasticity computations is presented. The yield criterion must be linear in principal stress space and can be composed of any number of yield planes. Each of these yield planes may have an associated or non-associated flow rule. The stress return and the formation of the constitutive matrix is carried out in principal stress space. Here the manipulations simplify and rely on geometrical arguments. The singularities arising at the intersection of yield planes are dealt with in a straightforward way also based on geometrical considerations. The method is exemplified on non-associated Mohr-Coulomb plasticity throughout the paper