A non-local elasto-plastic-damaged formulation for frictional materials

The purpose of the present work is a realistic numerical description of the complex mechanical behaviour of frictional materials such as concrete through the use of an elasto-plastic-damaged formulation. In particular the plasticity model is based on Menétrey-Willam plastic surface; a three.-invariant yield function is here chosen to consider the significant role of the intermediate principal stress and the Lode parameter and a non-associated flow rule is employed to control inelastic dilatancy, a fundamental aspect of concrete post-peak behaviour. Damage enters in compliance with the plastic-damage combination theory based on the effective stress, as a scalar isotropic variable which is function of the plastic strain. In order to avoid strain localization, a phenomenon characterized by the concentration of deformations that make the constitutive model incapable to describe objectively localized material failure, a nonlocal integral-type regularization technique is here adopted. In this approach a certain state variable is replaced by its nonlocal counterpart, obtained through a space-weighted average which reflects the ability of the microstructure to transmit information to neighbouring points within a certain distance. Strict comparisons between experimental evidences and numerical results on specimens subjected to uniaxial tests have been performed, fairly proving the correctness of the suggested approach. The analyses are developed at the mesoscale level distinguishing between cement paste and aggregates (first pioneer works can be found in [6]), and a specific constitutive behaviour has been assigned to each constituent; the cement matrix is characterized as an elastic-plastic material with damage capabilities while the aggregates are assumed to behave elastically. Compelling issues for the modelling phase are also addressed, in order to obtain models as much as close as possible to the experimental samples; i.e. the accurate reproduction of the external geometry of the aggregates added to the concrete mix design and their random disposition in the sample. For this purpose, solid models are created through the adoption of 3D advanced measurement techniques, such as laser scanners or industrial computer tomography (CT), while ad-hoc random algorithm has been developed to place and orient the inclusions by satisfying their volume ratio and the grading curve.