Substrate curvature due to thin film mismatch strain in the nonlinear deformation range

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Elasticity and stability of shape-shifting structures (2018, background): “ing [20] and twisting [21] of an elastic rod, the viscous peeling of plates [22], and the buckling [23] and the wrinkling [24] of elastic sheets on water.”
Discrete approximations of the Föppl–Von Kármán shell model: From coarse to more refined models (2013, methodology): “, 2009), from instabilities of composites under thermal loads (Dano and Hyer, 1998) to residual stress analysis in thin film assemblies (Freund, 2000).”
Thin Film Materials: Stress, Defect Formation and Surface Evolution (2004, background): “where 1 2m is a normalized mismatch strain and 1 ∙ is a normalized curvature (Freund 2000).”
Multiparameter actuation for shape control of bistable composite plates (2010, background): “For example, finite element numerical simulations on rectangular plates show that the aspect ratio between the edge lengths influences the system behavior in nonlinear regimes (Freund, 2000; Gigliotti et al., 2004).”
Bio-inspired soft robotics: Material selection, actuation, and design (2018, background): “Such shape changes maybe induced in hard materials such as metals or semi-conducting thin films [41,42], or in soft materials such as PDMS [43], or in hard–soft hybrid systems [44].”