Two gradient-dependent combinations of isotropic plasticity and scalar damage are proposed. The gradient enhancements of either the plasticity or the damage component of the theory are performed by introducing the Laplacian of a strain measure and an internal length parameter. This makes the constitutive models applicable to localization analyses.
The models are used for finite element simulations of localization in a one-dimensional tensile bar problem. The coupling of hardening/softening plasticity with damage governed by different damage evolution functions is discussed. Then, attention is focused on the response of the models in unloading from localized deformation states. The model of gradient damage combined with hardening plasticity is used to predict progressive damage of concrete in a beam subjected to four-point bending. The simulated stiffness degradation is compared with experimental results.
Gradient-dependent continuum, plasticity, damage, strain localization, finite elements.