Despite of the progress made to engineer structured microtissues such as BioMEMS and 3D bioprinting, little control exists how microtissues transform as they mature, as the misbalance between cell-generated forces and the strength of cell-cell and cell-substrate contacts can result in unintended tissue deformations and ruptures. To develop a quantitative perspective on how cellular contractility, scaffold curvature and cell-substrate adhesion control such rupture processes, human aortic smooth muscle cells were grown on glass substrates with submillimeter semichannels. We quantified cell sheet detachment from 3D confocal image stacks as a function of channel curvature and cell sheet tension by adding different amounts of Blebbistatin and TGF-β to inhibit or enhance cell contractility, respectively. We found that both higher curvature and higher contractility increased the detachment probability. Variations of the adhesive strength of the protein coating on the substrate revealed that the rupture plane was localized along the substrate-extracellular matrix interface for non-covalently adsorbed adhesion proteins, while the collagen-integrin interface ruptured when collagen I was covalently crosslinked to the substrate. Finally, a simple mechanical model is introduced that quantitatively explains how the tuning of substrate curvature, cell sheet contractility and adhesive strength can be used as tunable parameters as summarized in a first semi-quantitative phase diagram. These parameters can thus be exploited to either inhibit or purposefully induce a collective detachment of sheet-like microtissues for the use in tissue engineering and regenerative therapies.Despite of the significant progress in 3D tissue fabrication technologies at the microscale, there is still no quantitative model that can predict if cells seeded on a 3D structure maintain the imposed geometry while they form a continuous microtissue. Especially, detachment or loss of shape control of growing tissue is a major concern when designing 3D-structured scaffolds. Utilizing semi-cylindrical channels and vascular smooth muscle cells, we characterized how geometrical and mechanical parameters such as curvature of the substrate, cellular contractility, or protein-substrate adhesion strength tune the catastrophic detachment of microtissue. Observed results were rationalized by a theoretical model. The phase diagram showing how unintended tissue detachment progresses would help in designing of mechanically-balanced 3D scaffolds in future tissue engineering applications.