Third-Order Polynomials Model for Analyzing Multilayer Hard/Soft Materials in Flexible Electronics

In flexible electronics, multilayer hard/soft materials are widely used to utilize both the superior electrical properties of inorganic semiconductors and robust mechanical properties of polymers simultaneously. However, the huge mismatch in mechanical properties of the hard and soft materials makes mechanics analysis challenging. We here present an analytical model to study the mechanics of multilayer hard/soft materials in flexible electronics. Third-order polynomials are adopted to describe the displacement field, which can be used to easily derive both strain and stress fields. Then, the principle of virtual work was used to derive the governing equations and boundary conditions, which can be solved numerically. Two types of loadings, pure bending and transverse shear, are studied. The normal strain distributions along thickness direction in the bimaterial regions clearly show zigzag profiles, due to the huge mismatch in the mechanical properties of the hard and soft materials. The effect of very different mechanical properties of the hard and soft materials on shear stress distributions can also be predicted by this model. The results from this analytical mode show good agreement with finite-element modeling (FEM). This model can be useful in systems with multilayer hard/soft materials, to predict mechanical behavior and to guide design and optimization.