Analytical Framework
Mathematical models describing the mechanical response of composite structures allow designers to calculate the stiffness and deformation of multilayered printed circuit boards under varied loads. Use of classical lamination theory provides a way to estimate how individual layers of glass-reinforced resin and copper foil interact when subjected to heat or mechanical force. The model assumes that each layer is perfectly bonded and that the total thickness remains small relative to the lateral dimensions.
Constitutive Relation
Stresses and strains within the board are related through a series of matrices that account for the orthotropic nature of the woven glass reinforcement. By summing the stiffness of each layer relative to the mid-plane of the stackup, classical lamination theory generates the extensional, coupling and bending matrices needed for finite element analysis. These calculations determine how the board reacts to the thermal cycles encountered during reflow soldering.
An accurate model requires precise input regarding the elastic modulus and thermal expansion coefficient of every constituent material.
Board Deflection
Predicting the curvature of a panel during fabrication depends on the interaction between the internal layers and the external copper distribution. When the stackup lacks symmetry, the mathematical model identifies the specific source of potential warpage before the physical board is built. This prevents assembly errors caused by excessive planar distortion.
