REGULARIZATION OF DAMAGE AND FAILURE USING A NON-LOCAL 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. Here, a nonlocal hardening variable is introduced in a finite deformation Eulerian formulation of inelasticity. This nonlocal variable is defined over an Eulerian region of nonlocality, which is a sphere with radius equal to a characteristic length, defined in the current deformed geometry of the material. The influence of the nonlocal hardening variable is studied using an example of a plate that is loaded by a prescribed boundary displacement causing formation of a shear band. Predictions of the applied load vs. displacement curves and contour plots of the total distortional deformation of the plate and the hardening variable are studied. It is shown that the characteristic material length controls the structure of the shear band developed in the plate.