Disclosed herein are induction heating cells and methods of using these cells for processing. An induction heating cell may be used for processing (e.g., consolidating and/or curing a composite layup having a non-planar portion. The induction heating cell comprises a caul, configured to position over and conform to this non-planar portion. Furthermore, the cell comprises a mandrel, configured to position over the caul and force the caul again the surface of the feature. The CTE of the caul may be closer to the CTE of the composite layup than to the CTE of the mandrel. As such, the caul isolates the composite layup from the dimensional changes of the mandrel, driven by temperature fluctuations. At the same time, the caul may conform to the surface of the mandrel, which can be used to define the shape and transfer pressure to the non-planar portion.