We study the mechanical response of non-cohesive granular materials under monotonic and cyclic loading using a discrete model of polygonal particles. Three asymptotic states are studied: The first is the so-called critical state in which dense and loose media achieve the same void ratio at large strains independently of their initial density state. The second is related to the loss of memory when the granular media is compressed using constant strain rates. The third state is observed under cyclic loading. Thisis given by constant accumulation of permanent deformation that is called ratcheting. These asymptotic states are studied at the micro-mechanical level by following the evolution of the fabric tensor of the contact network.