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During epithelial wound healing, cell morphology near the healed wound and the healing rate vary strongly among different developmental stages even for a single species like Drosophila. We develop deformable particle (DP) model simulations to understand how variations in cell mechanics give rise to distinct wound closure phenotypes in the Drosophila embryonic ectoderm and larval wing disc epithelium. We find that plastic deformation of the cell membrane can generate large changes in cell shape consistent with wound closure in the embryonic ectoderm. Our results show that the embryonic ectoderm is best described by cell membranes with an elasto-plastic response, whereas the larval wing disc is best described by cell membranes with an exclusively elastic response. By varying the mechanical response of cell membranes in DP simulations, we recapitulate the wound closure behavior of both the embryonic ectoderm and the larval wing disc.