A strain based Lipschitz regularization for materials undergoing damage - Kamasamudram, Vasudevan; Stainier, Laurent (Comptes Rendus. Mécanique)
Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use a length scale, which can be introduced into the problem in multiple ways. A few commonly used ways include the addition of the gradient of damage variable in the energy density functional, using the gradient of strain while evaluating the internal variable, and so on. However, in the context of DDCM, these techniques may not be effective as the internal variables are not explicitly defined. Hence, the current article introduces a regularization technique, where the gradient of strain is constrained to lie within some interval. This prevents strain localization within an element by introducing a length scale into the problem. This article demonstrates the effectiveness of such a regularization technique in the case of 1D problems using a constitutive model while comparing its performance with strain gradient (SG) models.