Derivation of analytical expressions for the stress/strain distributions, bending plane and curvature radius in multilayer thin-film composites

Recent paradigms, such as smart cities/homes, Internet of Things or portable and implantable healthcare systems, require the use of flexible and conformal sensors that can be assembled to arbitrarily 3D complex shapes. A good set of simple and available models is of paramount importance to help designing and fabricating such devices. In this work, analytical expressions for the bending plane, the curvature radii and the stress/strain distributions of multilayer composite devices are derived for the cases of uniaxial and biaxial plane stress and plane strain and generalised plane strain. The analytical results are summarized, and two case-studies are analysed and compared with the help of these models: bilayer and trilayer hinges for self-assembled structures and rolled up flexible substrates with sensors on top. The dependence of the curvature radii and strain and stress distributions on several mechanical properties of the composite is assessed. The applicability of these models to support the design of flexible sensors, electronics or haptic devices is discussed and their practical limitations analysed.