Regularization of localization due to material softening using a nonlocal hardening variable in an Eulerian formulation of inelasticity

It is known that damage or inelastic softening can cause an ill-posed problem leading to localization and mesh-dependence in finite element simulations. In this paper, a nonlocal hardening variable, κ̄, introduced deformation Eulerian formulation of inelasticity with rate-independent smooth elastic–inelastic transition. This variable defined over region nonlocality, which sphere radius equal the characteristic length, Lc, current deformed geometry material. Two models are explored. One model where κ̄ minimum value local κ within another average same region. The influence studied using example plate loaded by prescribed boundary displacement causing formation shear band. Predictions applied load vs. curves contour plots total distortional studied. based on predicts mesh-independent post-peak response curve. Also, it shown material controls structure band developed plate.