Thermal stresses in the discrete joints of sandwiched structures

A two-step solutions is used to model the stresses in the discrete joints of a sandwiched structure due to mismatched thermal expansion. In the first step, the discrete joints are modelled as elastic body with nil lateral stiffness, the stretch and shear stiffness of which are equivalent to that of the solder joints smearing across the entire layer. Through the introduction of a high-order frequency function, interfacial shear and peeling stresses with the correct free-edge effects are derived. In the second step, the interfacial stresses are integrated into forces and are applied to the discrete joints to obtain the mean stresses; this is followed by modification of the mean shear stress using the high-order frequency function to impose the nil-shear-stress condition at the free-edge of the discrete joints. The closed-form solutions have found good agreements with the numerical solutions.