Plastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol 19(6):2525–2551, 2020). In this manusctipt, we consider a more physics-based formulation that is based on morphoelasticity. We firstly introduce the morphoelasticity approach and investigate the impact of various input variables on the output parameters by sensitivity analysis. A comparison of both model formulations shows that both models give similar computational results. Furthermore, we carry out Monte Carlo simulations of the skin contraction model containing the morphoelasticity approach. Most statistical correlations from the two models are similar, however, the impact of the collagen density on the severeness of contraction is larger for the morphoelasticity model than for the phenomenological model.