For this first part of the research 3D printed Samples of TPMS Geometries designed, produced are tested.
The Triply Periodic Minimal Surfaces (TPMS) are modeled by meshing an interpolation of points distributed according to the equation aproximation of Gyroid and PSchwartz surfaces within a specified domain of 0 to x Pi, for which Sawapan´s Millipede Component in Grasshopper is used.
DENSITY COMPARISON GRAPH
__pending__
Experimentation consists of:
 Compression tests and print tests to set base parameters: Volume, Scale of reliable and consistent prints.
 Compression tests to review differences of performance between Materials and to assess differences between simulation performance and phyiscal performance.
 Compression tests to assess differences between base tokens and algorithmically optimized tokens.
 Compression tests of bespoke matrices based on TPMS for optimal deformation and compression performance.
GYROID BASED TOKEN PERFORMANCE GRAPHS
Gyroid Based Token >> Algorithmically Optimized >> With Free Domain
Future work:
In order to advance the viability of 3d printing in architecture further research will compare printability and performance of large scale robotically augmented 3d printed fibrous structures.
Initial Tests: Scale and thickness print quality reliability: choosing the appropiate material, geometry, period and print thickness.
 C1: PLA 0.6 mm for a continuos well fused print. Deformation by collapse show clear “camel back” behaviour, corresponding with each of the layers, although a good tension distribution is initially achieved, these collapse deformations are to be held into account for a correct application to large scale architectural components.
 Best Performance before first layer collapse: 3960 N
 Deformation at N: 2.99 mm
 Best Performance before collapse: 4233 N
 T1 T5: TENAX 1.0mm wall thickness tokens show the most succesful compression results.
 T6 T7: TENAX 0.4 mm wall thickness tokens show the minimum wall thickness for a succesful layer by layer print with a 0.4 mm diamater nozzle at 60 mm/s print speed.
 Best Performance before first layer collapse: 3960 N,
 Deformation at N: 2.99 mm
 Best Performance before collapse: 4233 N
 Compression tests show a fragile noticeably more brittle token.
 Further tests should be produced to review the possibility of printing thinner succesful TPMS.
The definition of a standard case of 6cm3 size and 3pi period is chosen for next tests
1st Set of Tests: Plastic Comparison on BASE Period GEOMETRIES
Tokens with the same volume and density (as per virtual model) are modeled. The model is then deformated through a process of iteration deformation simulation for optimization.
Volume and Domain of 3pi are fixed constraints and no Deformations are produced.
Contours Standard Gyroid Token along Z axis
 Test 1: 1G11G2: TENAX PSchwartz Base Piece
 Best Performance before first layer collapse: 2150 N,
 Deformation at N: 3.69 mm
 Best Performance before collapse: 1G1:2153 N, 1G2: 4739 N
 Test 2: 2P12P2: TENAX Gyroid Base Piece
 Best Performance before first layer collapse: 4750 N
 Deformation at N: 4.54 mm
 Best Performance before collapse: 4750 N
 Test 3: 3B13B3: PLA Gyroid Base Piece
 Best Performance before first layer collapse: 2550 N
 Deformation at N: 4.05 mm
 Best Performance before collapse: 3034 N
 Test 4: 4P14P3: PLA PSchwartz Base Piece
 Best Performance before first layer collapse: 1220 N
 Deformation at N: 2.68 mm
 Best Performance before collapse: 1380 N
The presence of “camel back” humps in the graphics indicate the collapse of a level corresponding to a period. This is particularly clear among the 3Pi pieces which present three clear humps.
After the collapse of the three levels in these base cases, the piece is compacted and starts to behave more like a solid.
2nd Set of Tests: PLA Optimized Tokens with Fixed Domain.
Gyroids, as per better performance for equal material distribution compared to P Schwartz tokens are chosen for optimization studies.
Tokens with the same volume and density (as per virtual model) are modeled. The model is then deformated through a process of iteration deformation simulation for optimization.
Volume and 3 Pi Period Domain are fixed constraints.
Contours Optimized (Fixed Period) Gyroid Tokens along Z axis
(FIX DOMAIN 3 Pi TRANFORMATIONS ON BASE GEOMETRY BASED ON COMPRESSION SIMULATION)
This first optimization process only varies the distribution of material within the 3Pi constrain.
 Test 5: 501506:

 Best Performance before first layer collapse: 4294 N
 Deformation at N: 3.16 mm
 Best Performance before collapse: 4294 N
3nd Set of Tests: Optimized Tokens with NonFixed Domain.
Tokens with the same volume and density (as per virtual model) are modeled. The model is then deformated through a process of iteration deformation simulation for optimization.
Total wall volume is fixed and Period of set variable. Immedeatly the algorithm searches for a more complex material distribution that reduces the span of cells by reducing wall thickness to 0.4 mm and producing a noticeable differentiation between core and perimeter.
ContoursOptimized Gyroid Tokens along Z axis
(VARIABLE PERIOD TRANFORMATIONS ON BASE GEOMETRY BASED ON COMPRESSION SIMULATION)
:: IMAGEN DE PROCESO DE OPTIMIZACION ::
 Test 6: A1A2:
 Best Performance: 10071 N
 Deformation at N: 29.01 mm
 Test 7: B1B2:
 Best Performance: 5941 N,
 Deformation at N: 36.80 mm
Tokens present an Energy Absortion similar to that of Foams and commencte to behaves solids as it is continuosly compacted by deformation. Here a link to MIT open course by Prof. Lorna Gibson: Energy Absorption Notes on Celular Solids Structure Properties and Applications.
 Foams — roughly isotropic — can absorb energy from any direction – light and cheap
 Capacity to undergo large deformation at constant σ
 Absorb large energies with little increase in peak stress
While the number of tests conducted is not enough to be statistically conclusive, the preliminary results suggest nevertheless that optimization of specimens through the proposed workflow can lead to improved structural behaviour compared to the initial nonoptimized specimens.
Both experimental and simulation results demonstrate the benefit of material redistribution by optimization as seen in the improved peformance of 501506, A1, A2 and B1, B2.
Similarly the combined benefits of domain optimization in A1, A1 and B1,B2 eliminte the problem of hump like deformation behaviour and shows potential in the design of Additevely Manufactured spongy lattices which their solid like behaviour is triggered as deformed. A designed anisotropy shows great potential in the performance improvement of fibrous components by introducing controlled complex deformation behaviours.
 Tests have been produced in the Universal Test Machine INSTRON Type, which possess a highly sensitive system for measuering load, with a load cell whose calibration and force measurement tolerance is less than 1% and whose full scale is 100 kN (10T).
 Tokens printed with WASP 2040 Turbo 3d Printer
 With 1.75 black TreeD PLA filament
 Slic3r software with settings at 190 ºC and max print speed of 100 mm/s
 Surface Modeled in Rhino, through Millipede Component, calculated with Karamba shell FEM analysis and iterated for optimization with Galapagos, full workflow file available for download.
 More information for TPMS surface modeling approximation method here. Another interesting and very useful approach using Kangaroo here.
Download Full Set of Compression Tests Data . Click on Test Headers for additional information
Special thanks to:
Rafael Claramunt, Asocciate Professor in Mechanical Engineering Department at the Univesidad Politecnica de Madrid.
Marta Muñoz Sánchez, Laboratory Technician at the Material Resistance Laboratory at the Univesidad Politecnica de Madrid.
http://rm.mecaest.etsii.upm.es/