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In this thesis we describe the results of simulations at the atomic level of a simple model of a metallic glass under cyclic shear deformation. We show that under oscillatory cyclic load, systems of Lennard-Jones particles exhibit a non-equilibrium transition as a function of the oscillation amplitude. At low amplitudes samples evolve at a microscopic level so to reach states which are unchanged by further oscillations, whereas above some threshold amplitude γ_c they evolve indefinitely. Similarly to what is observed in noncolloidal suspensions, samples are able, for small oscillation amplitudes, to retain a memory of the oscillation amplitude(s). Such amplitude(s) can be subsequently read by performing additional deformation experiments. We employ and develop simple models that are able to describe qualitatively such phenomenology, thus suggesting that a wider class of systems could be able to show the same transition and memory behavior. Separately, we study by means of computer simulation the behavior under deformation of a newly found class of soft matter systems, namely bigels, and compare it with that of single-component particle gels.