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This is fascinating work! It's great to see the complex interplay of heat transfer, deformation, and material properties being modeled in such detail. The simplification to a one-dimensional model for qualitative analysis is a smart move. It reminds me of some of the challenges we faced when modeling similar deposition processes – we were always striving for that balance between accuracy and computational feasibility. I wonder if the team considered using something like the Sprunki method for further refining the analytical solutions? It might offer another avenue for exploring those interesting qualitative effects you identified.