• elastic characterization
• lattice structures
• TPMS structures

In this work, after a general introduction to Lattice structures, the elastic properties of Triply Periodic Minimal Surface (TPMS) structures are investigated, given their natural and biological topological affinity.
In particular, the main goal of this study is to give designers a simple tool for analyzing TPMS lattices, which requires only the cell geometric parameters as input, being them the typical constraint for AM feasibility.
This result is achieved by analysing TPMS cells elastic proprieties through the Homogenization technique, which extracts the stiffness matrix from the complex cell geometry and uses it as a new FEM element with equivalent elastic proprieties.
A further step in this procedure is made with the Asymptotic Homogenization technique, which allows to simulate the behaviour of an infinite lattice with minimum computational cost, by enforcing periodicity conditions.
Homogenization is proposed through two different FEM approaches, a Shell and a Solid modelling of the cells.
The differences between the two methods are analyzed to define the limits of Shell modelling, which is simpler and faster than the Solid one, used as reference result. In fact, this comparison highlights a variable normal thickness of the cells, which cannot be easily implemented with Shell elements. The main effect of the combination of Shell elements and a thickness approximation is a limitation of the field of application of the Shell modelling.
The results obtained are the Elastic proprieties of a generic TPMS cell, as function of the cell geometric parameters.
These parameters are finally analyzed with the present state-of-art AM SLS 3D printing to identify their technological limits.