An objective multi-scale model with hybrid injection

LABANDA, NICOLÁS A.; GIUSTI, SEBASTIÁN M.; LUCCIONI, BIBIANA M.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2018 vol. 101 p. 95 - 112

0020-7462

This paper presents a new semi-concurrent multi-scale model to study the behaviour of composite materials insoftening regime. A mixed formulation is used to simulate discontinuities in both scales. The traction over thecrack is included as a unknown field in the equations system of the problem, and the jump displacement acrossthe discontinuity is obtained with a cohesive constitutive relation (traction-separation law).Axiomatic variational principles and the injection concept are used and formulated to get an objective modelwith respect to the representative volume element size (RVE). The projected stress over the normal vector ofthe macro discontinuity is injected in the localized domain in the RVE, obtaining as a dual variable the jump ofthe displacement field in the macro structure. In this way, during the stable phase of the behaviour, the scaletransition is performed in the classical way injecting the strain tensor and obtaining the stress tensor as a dualvariable. At the beginning of the unstable regime, the transition between the scales is defined by injecting thetraction (stress projection on the normal vector to the crack) in the localization domain in the micro scale and thedisplacement jump at the macro scale is obtained as a dual variable. This new concept leads to a new multi-scaleapproach with an hybrid injection.The basic equations of the model are derived, and finally some numerical examples are developed, showingthe objectivity of the homogenized response of composite material problems that involve strain localization atthe macro-scale.