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• The variables are: section shape, fibers type and amount, loading protocol. • FRCM-confined concrete exhibits a multi-stage stress–strain curve. • Fibers strain exploitation ratio and volumetric dilation are evaluated. • FRCM jackets are activated after a certain amount of dilatancy has already occurred. • The envelope curve of the cyclic response is equivalent to the monotonic curve. In this work, the experimental behavior of confined concrete specimens subject to axial cyclic load is analyzed in terms of compressive strength, ductility, stress deterioration, plastic strain development, stiffness deterioration, fibers strain exploitation ratio and volumetric dilation. The following variables were considered, and their influence is discussed along the work: geometry of the cross-section (circular, square and two rectangular ones), fiber material (carbon and glass fibers) and number of layers (up to four for carbon-FRCM jackets), loading protocol (cyclic and monotonic). Results demonstrate that the envelope of the stress–strain curves obtained with cyclic loading coincides with the monotonic curve, for the range of variables analyzed here. Further, the stress–strain curve of FRCM-confined concrete has been modeled according to three different behaviors exhibited in this experimental campaign, being purely softening, softening with plateau, and hardening. [ABSTRACT FROM AUTHOR]