After injury, while regeneration can be observed in hydra, planaria and some vertebrates,regeneration is rare in mammals and particularly in humans. In this paper, we investigatethe mechanisms by which biological tissues recover after injury. We explore this question onadipose tissue, using the mathematical framework recently developed in Peurichard et al.,J. Theoret. Biol. 429 (2017), pp. 61-81. Our assumption is that simple mechanical cuesbetween the Extra-Cellular Matrix (ECM) and differentiated cells can explain adipose tissuemorphogenesis and that regeneration requires after injury the same mechanisms. We validatethis hypothesis by means of a two-dimensional Individual Based Model (IBM) of interactingadipocytes and ECM fiber elements. The model successfully generates regeneration or scarformation as functions of few key parameters, and seems to indicate that the fate of injuryoutcome could be mainly due to ECM rigidity.