Chromatin in the nucleus undergoes mechanical stresses from different sources during the various stages of cell life. Here a trinucleosome array is used as the minimal model to study the mechanical response to applied stress at the molecular level. By using large-scale, all-atom steered-molecular dynamics simulations, we show that the largest part of mechanical stress in compression is accommodated by the DNA linkers joining pairs of nucleosomes, which store the elastic energy accumulated by the applied force. Different mechanical instabilities (Euler bending, Brazier kinking, twist-bending) can deform the DNA canonical structure, as a function of the increasing force load. An important role of the histone tails in assisting the DNA deformation is highlighted. The overall response of the smallest chromatin fragment to compressive stress leaves the nucleosome assembly with a substantial plastic deformation and localised defects, which can have a potential impact on DNA transcription, downstream signaling pathways, the regulation of gene expression, and DNA repair.