Damage Modeling for Second Gradient Continua: Granular Micromechanics and Variational Methods

Many materials science and engineering problems require the description of collective mechanical behavior of very large number of grains. Since these problems are characterized by complexity and diversity of grain-scale mechano-morphology, modelling approaches are needed that are both representative and tractable. Continuum models, arguably, are the most feasible. However, these models must properly account for the granular nature of the material to be representative. Granular micromechanics approach (GMA) provides a paradigm that bridges the grain-scale models to appropriate continuum models [1-2]. Recently this approach has been further refined for damage modeling under finite deformations [3]. Objective kinematic descriptors have been obtained for grain-pair relative displacement in the framework of second gradient continua. Additionally, Karush–Kuhn–Tucker (KKT)-type conditions have been derived for grain-pair damage evolution using purely mechanical arguments based upon a non-standard hemivariational approach [3-4]. This presentation will discuss the salient points of the modeling approach with particular attention to damage induced anisotropy evolution including the emergence of a type of chiral behavior and formation of mesh-independent finite localization zones.