Design and Characterization of Cellular Solids from Modeling through Solid Freeform Fabrication Matthew Wettergreen a , Br...
<ul><li>Introduction </li></ul><ul><li>Cellular Solids </li></ul><ul><li>Computer Modeling </li></ul><ul><li>Solid Freefor...
Introduction <ul><li>From mechanical standpoint, density is primary controlling factor of strength of objects </li></ul><u...
<ul><li>Architectures of minimum weight maximum strength </li></ul><ul><li>Exhibit power law relationship between modulus ...
<ul><li>CAD </li></ul><ul><li>Morphological Characterization </li></ul><ul><li>FEA </li></ul><ul><li>Curve Fitting </li></...
Computer Aided Design of Polyhedra <ul><li>Four architectures generated: Hexahedron (H), Truncated Hexahedron (TH), Rhombi...
Morphological Characterization <ul><li>Strut length and strut diameter are linearly related to volume fraction for any sin...
<ul><li>Meshed with ABAQUS/CAE with greater than 20,000 elements determined from convergence study </li></ul><ul><li>Mater...
Finite Element Results <ul><li>Architectures of same material volume exhibit significantly different mechanical properties...
Stress Distribution In Polyhedra With  Respect To Volume Fraction <ul><li>Elemental stress distribution demonstrates a str...
Stress Distribution In Polyhedra With  Respect To Volume Fraction, 80% porosity <ul><li>Compressive Mode values are higher...
Curve Fitting <ul><li>Stated power law relationship between volume fraction and modulus </li></ul><ul><li>C is constant de...
Curve Fitting
Curve Fitting <ul><li>Hexahedron exhibits cell wall stretching </li></ul><ul><li>All other architectures exhibit deformati...
<ul><li>Four architectures printed at 80 and 90% porosity </li></ul><ul><li>DTM Sinterstation 2500plus used to fabricate a...
Mechanical Testing <ul><li>Uniaxial compression with MTS Machine, 1mm/min to fracture </li></ul><ul><li>Bulk sample evalua...
Modulus Results <ul><li>TO shows higher modulus than H at 80% porosity </li></ul><ul><li>FEA better predictor at low modul...
Correlations <ul><li>Strength roughly linear to Stiffness </li></ul><ul><li>Regression analysis indicates a linear relatio...
<ul><li>We detail a characterization of architectures which contain the same material volume but differing architectural a...
Acknowledgements CEBL Lab Members Brandon Bucklen Jeremy Lemoine CATE Lab Members   Lauren Shor Bobby Chang  Binil Starly ...
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Design and Characterization of Cellular Solids from Modeling through Solid Freeform Fabrication, 8/2006

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Presentation given to the Solid Freeform Fabrication Conference, Austin, TX 8/2006

ABSTRACT
Cellular solids studies the mechanical effects of the material arrangement of architectures for the goal of designing materials which are lightweight and possess high structural integrity. These architectures present themselves frequently in structural members in nature (bone, plant stalks, and porous rock) and are now used frequently in design (tissue engineering scaffolds, mechanical design). Until now however, physical studies of these architectures have been completed using molding techniques (for 2D) and random models (for 3D). Rapid prototyping (RP) provides high repeatability during replication which decreases error in studied samples and can serve to reduce the number of conflicting variables which confound the development of structural relationships. In this study we designed and characterized four geometric solids from the Platonic and Archimedean set of polyhedra, the simplest architectures that exist in nature which exhibit symmetry and order. Multiple models of these polyhedra were generated using computer aided design at similar topologies but with varying volume fractions. Employing finite element analysis we analyzed the structures with simulated uni-axial linear compressive tests. We then built actual models of the architectures using solid laser sintering (SLS) with a Sinterstation 2500Plus. The architectures were printed at porosities of 80% and 90% by volume with a bounding box of 2cm x 2cm x 2cm. After printing of the models, they were scanned with micro-computed tomography (µCT) as a validation of the use of SLS for fabrication of computer modeled architectures. Finally, the architectures were compressed to fracture using an MTS, validating the modeling component of the design and providing information which will allow for the determination of relationships which govern the material arrangement and resulting mechanical properties. These results of this study are useful in the development of models which directly relate complex architecture to mechanical properties; these models can be used to develop any architecture based on given input parameters such as porosity, surface area, connectivity and fracture pattern.

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Design and Characterization of Cellular Solids from Modeling through Solid Freeform Fabrication, 8/2006

  1. 1. Design and Characterization of Cellular Solids from Modeling through Solid Freeform Fabrication Matthew Wettergreen a , Brandon Bucklen a , Michael Liebschner a , Wei Sun b a Rice University, b Drexel University Solid Freeform Fabrication Symposium August 15, 2006
  2. 2. <ul><li>Introduction </li></ul><ul><li>Cellular Solids </li></ul><ul><li>Computer Modeling </li></ul><ul><li>Solid Freeform Fabrication </li></ul><ul><li>Correlative Relationships </li></ul><ul><li>Conclusions </li></ul>Outline
  3. 3. Introduction <ul><li>From mechanical standpoint, density is primary controlling factor of strength of objects </li></ul><ul><li>Minor topological differences result in gross property variations </li></ul><ul><ul><li>Osteoporosis, 80 vs. 90 percent porosity </li></ul></ul><ul><li>Apparent density cannot describe anisotropy or directionally dependent materials </li></ul><ul><li>No previous systematic exploration on variations in mech. properties with respect to density </li></ul>
  4. 4. <ul><li>Architectures of minimum weight maximum strength </li></ul><ul><li>Exhibit power law relationship between modulus and volume fraction demonstrated by Gibson and others </li></ul><ul><li>Models relating structure to strength have been derived for 2D case (honeycombs, etc.) </li></ul><ul><li>3D model must be as simple and regular as 2D </li></ul><ul><ul><li>Regular polyhedra </li></ul></ul><ul><li>Platonic and Archimedean solids </li></ul><ul><ul><li>Simplest geometric architectures which exhibit symmetry </li></ul></ul><ul><li>Structural relationships can be drawn between architecture and mechanical properties independent of material </li></ul>Cellular Solids
  5. 5. <ul><li>CAD </li></ul><ul><li>Morphological Characterization </li></ul><ul><li>FEA </li></ul><ul><li>Curve Fitting </li></ul><ul><li>Rapid Prototyping </li></ul><ul><li>Mechanical Testing </li></ul><ul><li>Statistical Analysis </li></ul>Methodology
  6. 6. Computer Aided Design of Polyhedra <ul><li>Four architectures generated: Hexahedron (H), Truncated Hexahedron (TH), Rhombitruncated Cuboctahedron, Truncated Octahedron (TO) </li></ul><ul><li>All architectures created in same bounding box </li></ul><ul><li>Porosities sized to 50-90% volumetric porosity </li></ul>
  7. 7. Morphological Characterization <ul><li>Strut length and strut diameter are linearly related to volume fraction for any single architecture </li></ul><ul><ul><li>Slope of H is -1.0 compared to similar slopes (ranged between -0.26 and -0.38) for remaining three </li></ul></ul><ul><li>Range of the truncated octahedron is 25% greater than the remaining shapes. </li></ul><ul><li>Simple architectures (hexahedron, truncated hexahedron) exhibited decrease in surface area with increasing porosity </li></ul><ul><li>Complex shapes exhibited a maxima for surface area at or around 70% porosity </li></ul>
  8. 8. <ul><li>Meshed with ABAQUS/CAE with greater than 20,000 elements determined from convergence study </li></ul><ul><li>Material properties: Isotropic, E=2GPa, v=.3 </li></ul><ul><li>Single step, linear, elastic finite element analysis with ABAQUS Standard, unconfined uniaxial compression with 1% prescribed displacement </li></ul><ul><li>Apparent (structural) Modulus calculated for each polyhedra </li></ul>Finite Element Analysis
  9. 9. Finite Element Results <ul><li>Architectures of same material volume exhibit significantly different mechanical properties </li></ul><ul><li>Modulus of the hexahedron is between 19 – 88% > any architecture over the entire porosity range. </li></ul><ul><li>TH and RC have similar moduli, second and third strongest shapes at 50% porosity and weakest architectures at porosities >50% </li></ul>
  10. 10. Stress Distribution In Polyhedra With Respect To Volume Fraction <ul><li>Elemental stress distribution demonstrates a stress dependence related to architecture and porosity </li></ul><ul><li>The ratio of tensile/compressive stress over the dynamic range is always the same ~ 16.5% </li></ul><ul><li>Stress values shift towards higher compressive values with increasing porosity </li></ul>
  11. 11. Stress Distribution In Polyhedra With Respect To Volume Fraction, 80% porosity <ul><li>Compressive Mode values are higher than Tensile Mode values for all polyhedra </li></ul><ul><li>Compressive modes may not be related to modulus values </li></ul><ul><li>Peak stresses can be identified as specific architectural features </li></ul>
  12. 12. Curve Fitting <ul><li>Stated power law relationship between volume fraction and modulus </li></ul><ul><li>C is constant dependent upon structure </li></ul><ul><li>n illustrates mechanism of deformation (1<n<4) </li></ul><ul><ul><li>n=1, cell wall stretching </li></ul></ul><ul><ul><li>n=2, deformation through edge bending </li></ul></ul><ul><ul><li>n=3, cell wall bending </li></ul></ul>
  13. 13. Curve Fitting
  14. 14. Curve Fitting <ul><li>Hexahedron exhibits cell wall stretching </li></ul><ul><li>All other architectures exhibit deformation through edge bending </li></ul><ul><li>RC and TO deform in the exact same way </li></ul>
  15. 15. <ul><li>Four architectures printed at 80 and 90% porosity </li></ul><ul><li>DTM Sinterstation 2500plus used to fabricate architectures </li></ul><ul><li>2cm bounding box for all architectures </li></ul>Rapid Prototyping
  16. 16. Mechanical Testing <ul><li>Uniaxial compression with MTS Machine, 1mm/min to fracture </li></ul><ul><li>Bulk sample evaluated for bulk Modulus </li></ul><ul><li>Complicated architectures exhibit densification region </li></ul>
  17. 17. Modulus Results <ul><li>TO shows higher modulus than H at 80% porosity </li></ul><ul><li>FEA better predictor at low modulus values </li></ul>
  18. 18. Correlations <ul><li>Strength roughly linear to Stiffness </li></ul><ul><li>Regression analysis indicates a linear relationship between strength and one or more of surveyed architectural parameters </li></ul><ul><li>Surface area exhibits little or no correlation to strength </li></ul>
  19. 19. <ul><li>We detail a characterization of architectures which contain the same material volume but differing architectural arrangements </li></ul><ul><li>Complex material arrangements can result in a maxima of surface area for a specific porosity, centered around 65% </li></ul><ul><li>The hexahedron is the strongest shape throughout all porosities via FEA results </li></ul><ul><li>Specific architectures are favored at specific porosities </li></ul><ul><li>Even at the same material volume, minor topological differences result in gross mechanical property variations. </li></ul><ul><li>Cursory regression analysis indicates factors relating to architecture have greater correlations to strength than surface area </li></ul><ul><li>This study represents the first step in an analysis of architecture for the goal of creating a logic set of rules which can explain the structural properties of an architecture based solely upon its material arrangement </li></ul><ul><li>We plan to exploit this system for the decomposition of bone and the simplification of its structure for the ease of calculation of its structural properties. </li></ul>Conclusions
  20. 20. Acknowledgements CEBL Lab Members Brandon Bucklen Jeremy Lemoine CATE Lab Members Lauren Shor Bobby Chang Binil Starly Eda Yildirim Connie Gomez Kalyani Nair Advisor Dr. Wei Sun Dr. Michael Liebschner Chris Peters – Aid with statistics

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