Divalent cations have a strong impact on the properties of phospholipid membranes, where amyloid-beta peptides exert effects related to possible functional or pathological roles. In this work, we use an atomistic computational model of dimyristoyl-phosphatidylcholine (DMPC) membrane bilayers. We perturb this model with a simple model of divalent cations (Mg2+) and with a single amyloid-beta (A beta) peptide of 42 residues, both with and without a single Cu-2+ ion bound to the N-terminus. In agreement with the experimental results reported in the literature, the model confirms that divalent cations locally destabilize the DMPC membrane bilayer and, for the first time, that the monomeric form of A beta helps in avoiding the interactions between divalent cations and DMPC, preventing significant effects on the DMPC bilayer properties. These results are discussed in the frame of a protective role of the diluted A beta peptide floating around phospholipid membranes.