From PDE-Constrained Design to 3D-Printed Porous Scaffolds for Soilless Agriculture

  • Speroni, Giacomo (Politecnico di Milano)
  • Mondini, Nicolò (Politecnico di Milano)
  • Ferro, Nicola (Università Ca’ Foscari)
  • Perotto, Simona (Politecnico di Milano)

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Soilless cultivation is rapidly expanding in modern agriculture, relying on engineered substrates that must provide mechanical support to roots while ensuring adequate aeration and water–nutrient transport. Yet, widely used organic and inorganic growing media offer limited tunability of their coupled mechanical and hydraulic response and can pose sustainability and reproducibility issues. This motivates the design of engineered, controllable alternatives. We present a computational-to-manufacturing framework for the design of 3D-printed porous scaffolds tailored to soilless cultivation. The substrates are modeled as periodic lattice-based architectures, where the macroscopic effective behavior is dictated by the geometry of an underlying microstructure. The design problem is cast as a multi-physics, PDE-constrained topology optimization task, targeting microstructures that satisfy coupled requirements on stiffness/support and flow/transport capability, under manufacturability constraints. Methodologically, we extend the microSIMPATY algorithm, originally introduced in a 2D setting [1], to a fully three-dimensional multi-physics formulation. The proposed approach combines density-based SIMP inverse homogenization topology optimization with anisotropic mesh adaptation to efficiently resolve complex geometrical features while maintaining robustness in the presence of coupled physics [2]. We validate the algorithm on a set of numerical benchmarks designed to assess performance under competing objectives, highlighting how directional transport and mechanical integrity can be balanced through systematic microstructural tailoring. From the optimized density fields, we derive explicit lattice geometries and STL-ready models, enabling both in silico evaluation (including root-growth simulations) and rapid 3D-printed prototyping. Overall, the pipeline links multi-physics optimization to decision-ready, manufacturable substrates for sustainable soilless cultivation. REFERENCES [1] N. Ferro, S. Micheletti and S. Perotto. Density-based inverse homogenization with anisotropically adapted elements. In: Numerical Methods for Flows. Lect. Notes Comput. Sci. Eng., Vol. 132, pp. 211–221. Springer, Cham (2020). [2] G. Speroni, N. Mondini, N. Ferro and S. Perotto. A topology optimization framework for scaffold design in soilless cultivation. MOX Report 66/2025, Politecnico di Milano.