Development of a plane stress projected non-local plasticity model with Tikhonov regularisation

Conventional local plasticity models with a softening slope exhibit a mesh dependency phenomenon, in which outcome parameters (e.g. equivalent plastic strain) depend on the mesh size. This behaviour has prompted the development of non-local plasticity models. The existing non-local models use a radial return algorithm to return the stress to the yield surface. These methods, however, cannot be used for plane stress condition models because the out-of-plane direction is not defined, making the radial return algorithm not uniquely defined. This paper presents a novel non-local model explicitly designed for the two-dimensional (2D) plane stress condition, with the objective of solving models that exhibit strain softening. The proposed model tackles the challenge of an ill-posed softening equation by utilising Tikhonov regularisation within the plane stress projected subspace. A numerical example demonstrates the proposed approach’s effectiveness in providing a stable and efficient solution for strain-softening problems. The results show that the width of the localisation zone is independent of the mesh size and is mainly controlled by the internal length scale parameter. The constant localisation width and the equivalent plastic strain provide reliable results for problems of plasticity with strain softening.