Efficient finite element modeling across optical length scales

Abstract

Optical engineers frequently rely on finite element analysis (FEA) to predict the thermal and mechanical performance of an optic before it is produced. These analyses are usually performed by modeling a simplified version of the real structure to obtain the global deformations of the surface of the mirror. This method eliminates the ability to represent localized deformations and strain gradients, resulting from thermal and mechanical loading, which may exceed the mechanical limit of the materials or material interfaces in coated mirrors causing delamination or cracking. The goal of this study is first to improve optical performance modeling by incorporating localized strain behavior within material layers and at material interfaces, bond strengths between mirror coatings and substrates, gravitational deformations, and effects of size scaling on deformation and strain magnitudes. Second, these methods will be used to investigate viability for constructing a coated mirror with mismatched coefficients of thermal expansion (CTE) with an interlayer of a polymer with a designable CTE to improve thermal deformation and reduce the risk of structural failure. Modeling localized regions of an optic requires incorporating length scales differing by nine orders of magnitude.

In order to precisely predict localized effects of the loading conditions, combinations of shell and continuum elements were used to minimize model size and computational time while localized accuracy is retained. Tie constraints were used to connect different elements and meshes and zero-thickness cohesive zones were created to predict delamination at material interfaces. Material properties for each material were specified to appropriate regions within the model, enabling realistic representation of deformation within mirror layers. This process was demonstrated on 3-D and axisymmetric models of a three-component mirror comprised of a coating, substrate, and an intermediate polymer layer with a designable CTE. Deformation and strain results were shown to change as the intermediate layer CTE was varied. Inclusion of the polymer layer was shown to have a slight effect on deformation resulting from gravity loading. Cohesive zone modeling techniques were used to investigate the strength of material interfaces after qualitative experimental verification. Parametric studies performed using axisymmetric cohesive zone models show that delamination resistance can be improved by tuning the polymer CTE.