3D anisotropic thermo-viscous-elastic residual stress model is developed for the 3D shrinkage and warpage analysis. With these assumptions and material models described in the Shrinkage prediction method for 3D models topic, the thermo-viscous-elastic residual stress model has been implemented in a relatively simplified way. Basically the residual stresses include the initial stresses from recorded frozen pressure at each node and initial stresses due to isotropic or anisotropic thermal shrinkage.
where:
- 'g' refers o the global coordinate system
- 'l' refers to the local coordinate system
is the transformation matrix from global strains to local strains
- [
] represents the stress-strain relationship matrix
- {
g 0 } is the initial stress, i.e pressure at freeze
- {
g 0 } is the initial strain from zero pressure state, or transitional temperature to room temperature