Mechanics OfLaminated Structures WithMultifield Coupling

Film/substrate structures have been widely used in flexible electronics, electronic packaging, and Micro/Nano-Electro-Mechanical-Systems. During the processes of production and packaging, the thermal residual stresses are built up due to the mismatch of thermal and mechanical properties between the film and substrate, which can finally lead to deformations and defects. These deformations and defects usually provide the driving force for the mechanical failure of the structures. The thermal stresses in film/substrate structures play an important role in the design and service lifetime, and their distribution and magnitude is a subject of perennial interest.Film/substrate bil-/trilayers with weak interface are investigated based on the Euler-Bernoulli beam theory, and the weak interfaces between the layers are examined by adopting the Newmark’s model. The closed-form analytical solutions of thermal stresses, deflection, curvature and interfacial shear stresses are presented, which can be degenerated to the classical results when the interface stiffness tends to infinity.The state space method is employed to analyze film/substrate multilayers. The state equation governing the multilayer structure subjected to a uniform temperature variation is obtained. The thermal stresses, deflection and interfacial shear stresses can be calculated based on the state equation exactly.A new Bernoulli-Euler beam model based on the modified couple stress theory is developed and applied to the analysis of a nanosized film/substrate bi-/multilayer structure subject to temperature variation. A modified Stoney’s formula for bilayer is obtained in the framework of the modified couple stress theory. The analytical solutions of the thermal stresses and curvature of the bilayer structure with perfect or weak interface are derived. A state-space formulation for the multilayer structure is presented, and the axial force, deflection and interfacial shear stress are predicted. The results show that nano-sized structures can exhibit a significant size-dependent phenomenon, and the presence of weak interfaces may alter strikingly the response of a layered structure.A bilayer system composed of a piezoelectric thin film bonded to an elastomeric substrate is studied. Exact solutions for stress distribution with perfect or weak interface are derived. A state-space formulation for the magneto-electro-elastic laminated structures is developed considering the couplings among the elastic, electric, magnetic, and thermal fields.The bending of multilayer graphene nanoribbons incorporating the effect of interlayer shear is analyzed. An improved beam theory is adopted and extended in which the in-plane extension of each layer is taken into account. Exact solutions for cantilever multilayer graphene nanoribbons are derived. Comparisons with the molecular dynamics (MD) simulations show that the current study provides a strong evidence to include the in-plane extension effect in the continuum modeling of multilayer graphene structures. The free vibration of multilayer graphene nanoribbons is investigated. The frequency equations for different boundary conditions are obtained via the state space method.