Localization of deformations in elastic‐plastic solids

Localization of deformation in elastic‐plastic solids subject to plane strain deformation are investigated numerically. It is shown that the localization may be captured accurately in finite element models by employing (1) the elastic‐plastic material stiffness to form the global stiffness, (2) in the case of symmetrical configurations, an imperfection in the form of a weak element, and (3) in the case of incompressible materials, a reduced selective integration scheme which alleviates mesh ‘locking’. Accuracy of the technique is demonstrated by applying it to analyse the classical punch and slope stability problems. Its versatility is illustrated by applying it to analyse finite deformation problems and shear bands formations in associative and non‐associative elastic‐plastic solids.