A bit of a twist for this weeks Phoenix Busines Journal blog post… “How far away are we from 3D Printing the androids on ‘Westworld?‘” In discussing this great new reboot of a classic, and yet another fantastic cautionary tale from Michael Crhichton, a couple people started wondering how far off the tech in the show is. The answer, well you will have to read the article.
How can the mechanical behavior of cellular structures (honeycombs, foams and lattices) be modeled?
This is the second in a two-part post on the modeling aspects of 3D printed cellular structures. If you haven’t already, please read the first part here, where I detail the challenges associated with modeling 3D printed cellular structures.
The literature on the 3D printing of cellular structures is vast, and growing. While the majority of the focus in this field is on the design and process aspects, there is a significant body of work on characterizing behavior for the purposes of developing analytical material models. I have found that these approaches fall into 3 different categories depending on the level of discretization at which the property is modeled: at the level of each material point, or at the level of the connecting member or finally, at the level of the cell. At the end of this article I have compiled some of the best references I could find for each of the 3 broad approaches.
1. Continuum Modeling
The most straightforward approach is to use bulk material properties to represent what is happening to the material at the cellular level [1-4]. This approach does away with the need for any cellular level characterization and in so doing, we do not have to worry about size or contact effects described in the previous post that are artifacts of having to characterize behavior at the cellular level. However, the assumption that the connecting struts/walls in a cellular structure behave the same way the bulk material does can particularly be erroneous for AM processes that can introduce significant size specific behavior and large anisotropy. It is important to keep in mind that factors that may not be significant at a bulk level (such as surface roughness, local microstructure or dimensional tolerances) can be very significant when the connecting member is under 1 mm thick, as is often the case.
The level of error introduced by a continuum assumption is likely to vary by process: processes like Fused Deposition Modeling (FDM) are already strongly anisotropic with highly geometry-specific meso-structures and an assumption like this will generate large errors as shown in Figure 1. On the other hand, it is possible that better results may be had for powder based fusion processes used for metal alloys, especially when the connecting members are large enough and the key property being solved for is mechanical stiffness (as opposed to fracture toughness or fatigue life).
2. Cell Level Homogenization
The most common approach in the literature is the use of homogenization – representing the effective property of the cellular structure without regard to the cellular geometry itself. This approach has significantly lower computational expense associated with its implementation. Additionally, it is relatively straightforward to develop a model by fitting a power law to experimental data [5-8] as shown in the equation below, relating the effective modulus E* to the bulk material property Es and their respective densities (ρ and ρs), by solving for the constants C and n.
While a homogenization approach is useful in generating comparative, qualitative data, it has some difficulties in being used as a reliable material model in analysis & simulation. This is first and foremost since the majority of the experiments do not consider size and contact effects. Secondly, even if these were considered, the homogenization of the cells only works for the specific cell in question (e.g. octet truss or hexagonal honeycomb) – so every new cell type needs to be re-characterized. Finally, the homogenization of these cells can lose insight into how structures behave in the transition region between different volume fractions, even if each cell type is calibrated at a range of volume fractions – this is likely to be exacerbated for failure modeling.
3. Member Modeling
The third approach involves describing behavior not at each material point or at the level of the cell, but at a level in-between: the connecting member (also referred to as strut or beam). This approach has been used by researchers [9-11] including us at PADT  by invoking beam theory to first describe what is happening at the level of the member and then use that information to build up to the level of the cells.
This approach, while promising, is beset with some challenges as well: it requires experimental characterization at the cellular level, which brings in the previously mentioned challenges. Additionally, from a computational standpoint, the validation of these models typically requires a modeling of the full cellular geometry, which can be prohibitively expensive. Finally, the theory involved in representing member level detail is more complex, makes assumptions of its own (e.g. modeling the “fixed” ends) and it is not proven adequately at this point if this is justified by a significant improvement in the model’s predictability compared to the above two approaches. This approach does have one significant promise: if we are able to accurately describe behavior at the level of a member, it is a first step towards a truly shape and size independent model that can bridge with ease between say, an octet truss and an auxetic structure, or different sizes of cells, as well as the transitions between them – thus enabling true freedom to the designer and analyst. It is for this reason that we are focusing on this approach.
Continuum models are easy to implement and for relatively isotropic processes and materials such as metal fusion, may be a good approximation of stiffness and deformation behavior. We know through our own experience that these models perform very poorly when the process is anisotropic (such as FDM), even when the bulk constitutive model incorporates the anisotropy.
Homogenization at the level of the cell is an intuitive improvement and the experimental insights gained are invaluable – comparison between cell type performances, or dependencies on member thickness & cell size etc. are worthy data points. However, caution needs to be exercised when developing models from them for use in analysis (simulation), though the relative ease of their computational implementation is a very powerful argument for pursuing this line of work.
Finally, the member level approach, while beset with challenges of its own, is a promising direction forward since it attempts to address behavior at a level that incorporates process and geometric detail. The approach we have taken at PADT is in line with this approach, but specifically seeks to bridge the continuum and cell level models by using cellular structure response to extract a point-wise material property. Our preliminary work has shown promise for cells of similar sizes and ongoing work, funded by America Makes, is looking to expand this into a larger, non-empirical model that can span cell types. If this is an area of interest to you, please connect with me on LinkedIn for updates. If you have questions or comments, please email us at email@example.com or drop me a message on LinkedIn.
References (by Approach)
Bulk Property Models
 C. Neff, N. Hopkinson, N.B. Crane, “Selective Laser Sintering of Diamond Lattice Structures: Experimental Results and FEA Model Comparison,” 2015 Solid Freeform Fabrication Symposium
 M. Jamshidinia, L. Wang, W. Tong, and R. Kovacevic. “The bio-compatible dental implant designed by using non-stochastic porosity produced by Electron Beam Melting®(EBM),” Journal of Materials Processing Technology214, no. 8 (2014): 1728-1739
 S. Park, D.W. Rosen, C.E. Duty, “Comparing Mechanical and Geometrical Properties of Lattice Structure Fabricated using Electron Beam Melting“, 2014 Solid Freeform Fabrication Symposium
 D.M. Correa, T. Klatt, S. Cortes, M. Haberman, D. Kovar, C. Seepersad, “Negative stiffness honeycombs for recoverable shock isolation,” Rapid Prototyping Journal, 2015, 21(2), pp.193-200.
Cell Homogenization Models
 C. Yan, L. Hao, A. Hussein, P. Young, and D. Raymont. “Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting,” Materials & Design 55 (2014): 533-541.
 S. Didam, B. Eidel, A. Ohrndorf, H.‐J. Christ. “Mechanical Analysis of Metallic SLM‐Lattices on Small Scales: Finite Element Simulations versus Experiments,” PAMM 15.1 (2015): 189-190.
 P. Zhang, J. Toman, Y. Yu, E. Biyikli, M. Kirca, M. Chmielus, and A.C. To. “Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: theory and validation,” Journal of Manufacturing Science and Engineering 137, no. 2 (2015): 021004.
 M. Mazur, M. Leary, S. Sun, M. Vcelka, D. Shidid, M. Brandt. “Deformation and failure behaviour of Ti-6Al-4V lattice structures manufactured by selective laser melting (SLM),” The International Journal of Advanced Manufacturing Technology 84.5 (2016): 1391-1411.
Beam Theory Models
 R. Gümrük, R.A.W. Mines, “Compressive behaviour of stainless steel micro-lattice structures,” International Journal of Mechanical Sciences 68 (2013): 125-139
 S. Ahmadi, G. Campoli, S. Amin Yavari, B. Sajadi, R. Wauthle, J. Schrooten, H. Weinans, A. Zadpoor, A. (2014), “Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells,” Journal of the Mechanical Behavior of Biomedical Materials, 34, 106-115.
 S. Zhang, S. Dilip, L. Yang, H. Miyanji, B. Stucker, “Property Evaluation of Metal Cellular Strut Structures via Powder Bed Fusion AM,” 2015 Solid Freeform Fabrication Symposium
 D. Bhate, J. Van Soest, J. Reeher, D. Patel, D. Gibson, J. Gerbasi, and M. Finfrock, “A Validated Methodology for Predicting the Mechanical Behavior of ULTEM-9085 Honeycomb Structures Manufactured by Fused Deposition Modeling,” Proceedings of the 26th Annual International Solid Freeform Fabrication, 2016, pp. 2095-2106
Our work on 3D printed honeycomb modeling that started as a Capstone project with students from ASU in September 2015 (described in a previous blog post), was published in a peer-reviewed paper released last week in the proceedings of the SFF Symposium 2016. The full title of the paper is “A Validated Methodology for Predicting the Mechanical Behavior of ULTEM-9085 Honeycomb Structures Manufactured by Fused Deposition Modeling“. This was the precursor work that led to a us winning an 18-month award to pursue this work further with America Makes.
Download the whole paper at the link below:
ULTEM-9085 has established itself as the Additive Manufacturing (AM) polymer of choice for end-use applications such as ducts, housings, brackets and shrouds. The design freedom enabled by AM processes has allowed us to build structures with complex internal lattice structures to enhance part performance. While solutions exist for designing and manufacturing cellular structures, there are no reliable ways to predict their behavior that account for both the geometric and process complexity of these structures. In this work, we first show how the use of published values of elastic modulus for ULTEM-9085 honeycomb structures in FE simulation results in 40- 60% error in the predicted elastic response. We then develop a methodology that combines experimental, analytical and numerical techniques to predict elastic response within a 5% error. We believe our methodology is extendable to other processes, materials and geometries and discuss future work in this regard.
Building on the worldwide success of previous products in the family, PADT has just released the new SCA 3600, a large capacity cleaning system for removing the support material from Stratasys FDM parts. This new system adds capacity and capability over the existing benchtop SCA-1200HT System.
A copy of the press release is below.
At the same time, we are also launching a new website for support removal: www.padtinc.com/supportremoval.
The SCA 3600 can dissolve support from all the SST-compatible materials you use – ABS, PC, and nylon. A “no heat” option provides agitation at room temperature for the removal of Polyjet SUP706 material as well. The SCA 3600’s versatility and efficient cleaning performance are built on the success of earlier models with all the features you have come to expect, in a larger and more capable model.
Since the launch of the original SCA-1200 in 2008, PADT has successfully manufactured and supported the SCA family of products for users worldwide. Common requests from desktop SCA users were for a larger system for bigger parts, the ability to clean many parts at the same time, and the option to remove supports from PolyJet parts. The SCA 3600 is the answer: Faster, larger, and more capable.
- Removes soluble support from ABS, PC, and nylon 3D printed FDM parts
- Removes soluble support from PolyJet 3D Printed parts
- User-selectable temperature presets at 50, 60, 70, and 85°C and “No Heat” for PolyJet
- User-controlled timer
- Uses cleaning solutions from Stratasys
- Unique spray nozzle optimizes flow coverage
- 230 VAC +/- 10%, 15A
- Whisper-quiet operation
- Includes rolling cart for easy movement, filling, and draining.
- Capacity: 27 gal / 102 L
- Size: 42.8″ x 22.8″ x 36.5″/ 1,086 x 578 x 927 mm
- 16” x 16” x 14” / 406 x 406 x 356 mm removable large parts basket
- Integral hinged lid and small part basket
- Stainless steel tub and basket
- Over temperature and water level alarms
- Automatic halt of operation with alarms
- Field replaceable sub-assemblies
- Regulatory Compliance: CE/cTUVus/RoHS/WEEE
You can download our new brochure for both systems:
If you are interested in learning more or adding an SCA 3600 to your additive manufacturing lab, contact your Stratasys reseller.
In the Fused Deposition Modeling (FDM) process, support structures are needed for features with overhang incline angle less than 45-degree from horizontal. Stratasys developed a series of support materials for different model materials: SR-30TM for ABS, SR-100TM for polycarbonate and SR-110TM for nylon. Also, they developed the Waterworks Soluble Concentrate, P400-SC, to be used to dissolve these support materials. In this blog post, I develop a theory for the chemical reaction how P400-SC Waterworks dissolves SR-30TM, SR-100TM and SR-110TM support materials. As part of this, I explain how PADT’s Support Cleaning Apparatus (SCA) tank, with its heating and unique circulation and agitation capabilities that are important for the support dissolving process.
We begin by looking at the composition of the different materials involved in the table below.
Adapted from Stratasys.com
How P400-SC Works for Support Materials Removal
Polymer can swell and then dissolve into water as a consequence of abundant hydrophilic groups, like carboxyl group (-COOH), ether group (-O-), hydroxyl group (-OH) and so on in its molecular structure. Theoretically, SR-30TM and SR-100TM /SR-110TM Soluble Support Materials including a carboxyl group (-COOH) in their repeat unit are likely to be water soluble. However, they also have a hydrophobic ester group (-COO-) in their repeat unit, which counteracts the efficacy of the hydrophilic group on the long carbon chain. Thus, the key to making SR-30TM and SR-100TM /SR-110TM soluble, is to somehow get rid of the ester group.
Hydrolysis of ester in pure water is a slow process even the system is heated. Both acid and alkaline conditions can catalyze and speed up the process. Under the acid condition, the hydrolysis is a reversible process until it reaches an equilibrium state, whereas alkaline conditions promote a thorough hydrolysis with a stirring and heating system.
P400-SC Waterworks contains sodium carbonate, sodium hydroxide, sodium lauryl sulfate and sodium metasilicate. The last two constituents, with 1-5 wt% respectively, are auxiliaries in the P400-SC Waterworks. The remaining two react with carboxylic acid and ester group per the following chemical reaction:
- R-COOH + NaOH = R-COO– Na+ + H2O (neutralization reaction)
- 2 R-COOH + Na2CO3 = 2 R-COO– Na+ + H2O + CO2
- R1–COO-R2 + NaOH ≜ R1-COO– Na+ + R2OH (ester hydrolysis under alkaline condition)
where R is the remaining carbon chain apart from carboxyl group and R1, R2 represent the two-side segments of ester group. Ester hydrolysis is the main reaction we need, which ionizes the ester group and makes it water soluble with an increased polarity. These reactions would happen when SR-30TM or SR-100TM /SR-110TM supports are dropped into a tank with P400-SC Waterworks cleaning solution inside.
From the table above, we can see that ABS-M30TM and PC-10TM don’t have hydrophilic groups, which restrains their solubility into water. Nylon is semi-crystalline polymer and difficult to dissolve into water and most organic solvent, despite the presence of the hydrophilic group acylamino (-CONH-), which still results in a nice water-absorbing ability. All these model materials are common-use engineering plastic with nice chemical resistance (depending on their functional groups), they can be safe in the cleaning solution.
The SCA tank offers an optimized environment with agitation and heating for the ester hydrolysis reaction. The tank has four preset temperature options (50 ℃, 60℃, 70℃, 85℃) for ABS-M30TM, PC-10TM, and FDMTM Nylon 12 model materials, due to their different thermal resistance. The innovative custom designed pump is key to cause the solution to effectively and efficiently dissolve and remove the support materials.
For more information on PADT’s entire line of SCA, please see http://www.supportremoval.com/
The Wake Forest Institute of Regenerative Medicine (WFIRM) hosted about 400 attendees at the annual Biofabrication conference, held this year at Winston-Salem, NC (Oct 28-Nov 1, 2016). The conference included a 2 hour tour of WFIRM’s incredible facilities, 145 posters, 200 or so presentations and a small trade show with about 30 exhibitors. As a mechanical engineer attending my first bio-related conference, I struggled to fully comprehend many concepts and terms in some of the deeper technical presentations. Nonetheless, there was a lot I DID learn, and this post serves to summarize my thoughts on the four high-level insights I gleaned amidst the pile of information on offer. I hope these are of value to the larger community that is not on the front lines of this exciting and impactful area of research.
More than Organs
To say biofabrication is all about making organs is like saying manufacturing is all about making spacecrafts carrying humans to Mars. It misses a lot of the other valid human needs that can be met and suggests organs are the end of the biofabrication R&D curve, when they only represent one manifestation (arguably the most difficult one in our current sense of the world) of the application of the science. If we take a step back, biofabrication is fundamentally about “manufacturing with living materials” – in that sense, biofabrication blurs the lines between natural and man-made entities. If you could manipulate and engineer living cells in physical constructs, what all could you do? Here is a list of some examples of the different applications that were discussed at the conference:
- Toxicology Studies – Organovo’s examples of skin, liver and kidney tissue being used to evaluate drug efficacy
- Body-on-a-Chip – A solution to aid in pre-clinical work to study whole systems (a key regulatory hurdle) and potentially displace animal studies in the future
- Tissues for Therapy – This could involve patches, stents and other such fixes of a therapeutic nature (as opposed to replacing the entire organ in question)
- Non-Medical Applications – Modern Meadow is a company that is using biofabrication techniques to make leather and thereby help reduce our dependency on animal agriculture. Biofabricated meat is another potential application.
- Functional Tissues and Organs – An interesting thought presented by Prof. Rashid Bashir is that replacing organs with matched constructs may not be optimal – we may be able to develop biological entities that get the job done without necessarily replicating every aspect of the organ being replaced. A similar thought is to to use biological materials to do engineering tasks. The challenge with this approach is living cells need to be kept alive – this is easier done when the fabricated entity is part of a living system, but harder to do when it is independent of one.
- Full Organ Replacement – Replicating an organ in all its detail: structurally and functionally – WFIRM has done this for a few organs that they consider Level 1-3 in terms of complexity (see Figure 1). Level 4 organs (like the heart) are at the moment exceedingly challenging due to their needs for high vascularity and large size.
It Takes a Village (and a Vivarium)
Imagine this is the early 2000s and you are tasked with establishing a center dedicated to accelerating the progress of regenerative medicine. What are the parts this center needs to house? This was probably what Dr. Anthony Atala and others were working out prior to establishing WFIRM in 2004. To give you a sense of what goes on in WFIRM today, here is a (partial) list of the different rooms/groups we visited on our tour: decellularization, imaging, tissue maturation, bioprinting, electrospinning, lab-on-a-chip, direct writing, vivarium that cares for animals (mice, ferrets, sheep, pigs, dogs – beagles to be specific, and “non-human primates”) and a cleanroom for pre-clinical studies. Add administrative, outreach and regulatory staff. Today, about 450 people work at WFIRM and many more collaborate. Going into this conference, I was well aware this field was an inter-disciplinary one. The tour opened my eyes to just how many interdependent parts there are that make an end-to-end solution possible, some more interdisciplinary in nature than others and just how advantageous it must be to have all these capabilities under one roof dedicated to a larger mission instead of spread across a large university campus, serving many masters.
“I Have a Hammer, Where is the Nail?”
I will be honest – I justified my interest in biofabrication on the very dubious basis of my experience with 3D printing, a long standing interest in the life sciences that I had hitherto suppressed, and the fact that I am married to a cancer researching biochemist – bioprinting was my justification for finally getting my feet (close to a) wet (lab). I suspect I am not alone in this (support group, anyone?). When I described this to the only surgeon who entertains my questions, he accurately summarized my approach in the afore mentioned hammer-nail analogy. So, armed with my hammer, I headed to the biofabrication conference seeking nails. The good news is I found a couple. As in exactly two. The bad news? See the section above – this stuff is hard and multi-faceted – and there are folks with a multi-decade head start. So for those of us not on the front lines of this work or not in college planning our next move, the question becomes how best can we serve the scientists and engineers that are already in this field. Better tools are one option, and the trade show had examples of these: companies that make bioprinters (see Figure 2 below), improved nozzles for bioprinting, clean-room alternatives, biomaterials like hydrogels, and characterization and testing equipment. But solving problems that will help the biofabrication community is another approach and there were about 5-10 posters and
presentations (mine included) which attempted to do just that. What are some of the areas that could benefit from such peripheral R&D engagement? My somewhat biased feeling is that there is opportunity for bringing some of the same challenges Additive Manufacturing is going through to this area as well:
- Design for Bioprinting: fully exploiting the possibilities of bioprinting – “in Silico” has made some progress with medical devices – a similar window of value exists for biofabrication due to the design freedom of 3D printing
- Modeling: Biofabrication almost always involves multi-materials, often with varying constitutive behaviors and further are in complex, time-varying environments – getting some handle on this is a precursor to item 1 above
- Challenges of Scale: This has many elements: quality control, cost, automation, data security, bio-safety. This is one of the key drivers behind the recent DOD call for an Advanced Tissue Biofabrication Manufacturing Innovation Institute and is likely to drive several projects in this space over the next 5-7 years.
Moral of the story for me: carry your hammer with pride but take the time to learn, ask and probe to find the pain points that are either already there or are likely to arise in the future, and keep refining your hammer with input from the biofabrication community – conferences are the best place to do this – IF you go in with that intent and prepare ahead of time identifying the people you want to talk to and the questions you wish to ask them – something I hope to be better at next time around.
The Rate-of-Progress Paradox
Finally, a more abstract point. From the sidelines, we may ask how far has the field of biofabrication come and how fast is it progressing? It is one thing to sift through media hype and reconcile it with ground realities. It is quite another to discover this conflict seemingly exists even in the trenches – there are several examples of transplanted biofabricated entities, yet there is a common refrain that we have a long way to go to doing just so. And that struck me initially as a paradox as I heard the plenary talks that were alternatingly cautious and wild – but on the very last day I started to appreciate why this was not a paradox at all, it is just the nature of the science itself. Unlike a lot of engineering paradigms, there are limits to efficiencies that can be gained in the life sciences – and once these are gained (shared resources, improved methods etc.), success in one particular tissue or organ may not make the next one progress much faster. Take Wake Forest’s own commonly used approach for regenerative medicine, for example: harvest cells, culture them, build scaffold constructs, mature cells on these constructs, implant and monitor. Sounds simple, but takes 5-10 years to get to clinical implantation and another 5-10 of observation before the results are published. And just because you have shown this in one area, bladder for example, doesn’t make the next one much faster at all. All the same steps have to be followed: pathways to be re-evaluated, developmental studies to be done – prior to extensive animal and clinical trials. The solution? Pursue multiple tissues/organs in parallel, follow each step diligently and be patient. Wake Forest seems to have envisioned this over a decade ago and I expect the coming decade will show a cascade of biofabrication successes hit us with increasingly boring steadiness.
Finally, we should all be thankful to the many PhD students and post-docs from all over the world putting in the bulk of the disciplined, hard work this field demands, most of them, in my opinion, at salaries not reflective of their extensive education and societal value. We should also spare a thought for all the animals being sacrificed for this and other research, even in the context of best veterinary practices – my personal hope is that biofabrication enables us to stop all animal trials at some point in the near future – indeed, this seems to be the only technology that can. Then we can truly say with confidence, that we have first and foremost, done no harm.
Thank you WFIRM, for a wonderful conference and all the work you do everyday!
Rey Chu, one of PADT’s owners and our head of Manufacturing Technologies, is featured in the 2017 issue of AZ Business Leaders with his article “How 3D Printing is Changing Manufacturing” It is a great overview of 3D printing and how it is impacting the way we make things.
What do you get when you combine a motivated student leader, enthusiastic classmates, a worldwide online community, and the latest 3D Printing technology from Stratasys? You give children around the world a cool way to hold things again. That is what happened when high school student Rahul Jayaraman of Basis Chandler decided to take part in a project called Enabling The Future. They describe themselves as “A global network of passionate volunteers using 3D Printing to give the world a ‘helping hand'” by designing a wide variety of prosthetic hands for kids that can be printed and assembled by volunteers.
Local news station, KSAZ FOX 10 Phoenix stopped by PADT while we were printing three hands in our Stratasys FORTUS 450 to interview Rahul and talk to us about the project. It gives a great summary:
And Channel 3, KTVK, came to the assembly event at Basis Chandler:>
As did Channel 12, KPNX:
3D Printing is a fantastic technology for one simple reason, it enables almost anyone to manufacture parts. All you need is a good design. And that is where the people at Enabling the Future come in. Check out their website to see some great examples of how their volunteer work changes so many lives. Have a box of tissue handy if you watch the videos…
This is how the project works. A leader like Rahul takes the initiative to sign up for the project. He then chooses which of the many designs he wants to make. For this first go around, he picked a general design from Thingiverse called the Raptor Reloaded. Next they needed the hardware you could not 3D Print – screws springs, velcro, and bits and pieces that hold the design together. For this they needed to raise $25 per hand so Rahul was given the opportunity to learn how to raise money, a very useful skill.
PADT’s Dhruv Bhate and the rest of our 3D Printing team worked with Rahul to get the design just right and then 3D Print the hands. That will be done this week and this weekend the next phase will take place. Rahul and a large number of his classmates from Basis Chandler will get together at the school this weekend to put thirty or so hands together. They will then box them up and another volunteer group, www.HandChallenge.com, will ship them to kids in the developing world that need them.
Here is a video from Tom Fergus from Fox10 showing a closeup of the hand in action:
— Tom Fergus (@TomFergusFox10) October 14, 2016
We at PADT love projects like this because it is win-win-win. The students get a chance to run a complicated project by themselves, learning the skills they will need later in life to organize, manage, and finish a project. PADT wins because we can contribute to our chosen area of charity, STEM education, in a way that benefits others beyond a given school. And the big winners are the kids around the world that receive a new and cool way to grab hold of life.
We will have sample hands at our open house next Thursday: Nerdtoberfest as well as an update when we get feedback from the distribution of the hands.
Noticed an interesting email in my inbox the other day with the subject line:
“Oktoberfest Time: 3D Print a Beer Stein in Beer Filament”
Marketing gold, you have my attention!
After reading the reviews from the filament manufacturer, I dove in and got some of the hoppy, malty filament on order from 3D Fuel. I was very excited when it came in and couldn’t wait to print PADT’s own beer stein for our upcoming Nerdtoberfest event. Meanwhile I found a nice starting point with a file from GrabCad and added my own additions and alterations.
I quickly went to load the beer filament into one of our 3D printers, when I noticed that the roll size was not compatible with the spool holder on the printer. It was this disconnect that would have previously stopped this experiment in it’s track, however, the future is NOW!
I popped onto the Thingiverse, and alas, I was not alone in having this issue and a plethora of solution were populated before me. I was about to 3D print and adapter to allow my 3D printer to accept a new roll size that was found to be incompatible just moments before. Disaster averted, I was now cooking with gas, er, beer.
The printing process was uneventful and the beer filament printed well. We now have a beer mug printed out of beer filament for PADT’s annual Nerdtoberfest!
In this post, I discuss six challenges that make the modeling of 3D printed cellular structures (such as honeycombs and lattices) a non-trivial matter. In a following post, I will present how some of these problems have been addressed with different approaches.
At the outset, I need to clarify that by modeling I mean the analytical representation of material behavior, primarily for use in predictive analysis (simulation). Here are some reasons why this is a challenging endeavor for 3D printed cellular solids – some of these reasons are unique to 3D printing, others are a result of aspects that are specific to cellular solids, independent of how they are manufactured. I show examples with honeycombs since that is the majority of the work we have data for, but I expect that these ideas apply to foams and lattices as well, just with varying degrees of sensitivity.
1. Complex Geometry with Non-Uniform Local Conditions
I state the most well-appreciated challenge with cellular structures first: they are NOT fully-dense solid materials that have relatively predictable responses governed by straightforward analytical expressions. Consider a dogbone-shaped specimen of solid material under tension: it’s stress-strain response can be described fairly well using continuum expressions that do not account for geometrical features beyond the size of the dogbone (area and length for stress and strain computations respectively). However, as shown in Figure 1, such is not the case for cellular structures, where local stress and strain distributions are non-uniform. Further, they may have variable distributions of bending, stretching and shear in the connecting members that constitute the structure. So the first question becomes: how does one represent such complex geometry – both analytically and numerically?
2. Size Effects
A size effect is said to be significant when an observed behavior varies as a function of the size of the sample whose response is being characterized even after normalization (dividing force by area to get stress, for example). Here I limit myself to size effects that are purely a mathematical artifact of the cellular geometry itself, independent of the manufacturing process used to make them – in other words this effect would persist even if the material in the cellular structure was a mathematically precise, homogeneous and isotropic material.
It is common in the field of cellular structure modeling to extract an “effective” property – a property that represents a homogenized behavior without explicitly modeling the cellular detail. This is an elegant concept but introduces some practical challenges in implementation – inherent in the assumption is that this property, modulus for example, is equivalent to a continuum property valid at every material point. The reality is the extraction of this property is strongly dependent on the number of cells involved in the experimental characterization process. Consider experimental work done by us at PADT, and shown in Figure 2 below, where we varied both the number of axial and longitudinal cells (see inset for definition) when testing hexagonal honeycomb samples made of ULTEM-9085 with FDM. The predicted effective modulus increases with increasing number of cells in the axial direction, but reduces (at a lower rate) for increasing number of cells in the longitudinal direction.
This is a significant challenge and deserves a full form post to do justice (and is forthcoming), but the key to remember is that testing a particular cellular structure does not suffice in the extraction of effective properties. So the second question here becomes: what is the correct specimen design for characterizing cellular properties?
3. Contact Effects
In the compression test shown in the inset in Figure 2, there is physical contact between the platen and the specimen that creates a local effect at the top and bottom that is different from the experience of the cells closer the center. This is tied to the size effect discussed above – if you have large enough cells in the axial direction, the contribution of this effect should reduce – but I have called it out as a separate effect here for two reasons: Firstly, it raises the question of how best to design the interface for the specimen: should the top and bottom cells terminate in a flat plate, or should the cells extend to the surface of contact (the latter is the case in the above image). Secondly, it raises the question of how best to model the interface, especially if one is seeking to match simulation results to experimentally observed behavior. Both these ideas are shown in Figure 3 below. This also has implications for product design – how do we characterize and model the lattice-skin interface? As such, independent of addressing size effects, there is a need to account for contact behavior in characterization, modeling and analysis.
4. Macrostructure Effects
Another consideration related to specimen design is demonstrated in an exaggerated manner in the slowed down video below, showing a specimen flying off the platens under compression – the point being that for certain dimensions of the specimen being characterized (typically very tall aspect ratios), deformation in the macrostructure can influence what is perceived as cellular behavior. In the video below, there is some induced bending on a macro-level.
5. Dimensional Errors
While all manufacturing processes introduce some error in dimensional tolerances, the error can have a very significant effect for cellular structures – a typical industrial 3D printing process has tolerances within 75 microns (0.003″) – cellular structures (micro-lattices in particular) very often are 250-750 microns in thickness, meaning the tolerances on dimensional error can be in the 10% and higher error range for thickness of these members. This was our finding when working with Fused Deposition Modeling (FDM), where on a 0.006″ thick wall we saw about a 10% larger true measurement when we scanned the samples optically, as shown in Figure 4. Such large errors in thickness can yield a significant error in measured behavior such as elastic modulus, which often goes by some power to the thickness, amplifying the error. This drives the need for some independent measurement of the manufactured cellular structure – made challenging itself by the need to penetrate the structure for internal measurements. X-ray scanning is a popular, if expensive approach. But the modeler than has the challenge of devising an average thickness for analytical calculations and furthermore, the challenge of representation of geometry in simulation software for efficient analysis.
6. Mesostructural Effects
The layerwise nature of Additive Manufacturing introduces a set of challenges that are somewhat unique to 3D Printed parts. Chief among these is the resulting sensitivity to orientation, as shown for the laser-based powder bed fusion process in Figure 5 with standard materials and parameter sets. Overhang surfaces (unsupported) tend to have down-facing surfaces with different morphology compared to up-facing ones. In the context of cellular structures, this is likely to result in different thickness effects depending on direction measured.
For the FDM process, in addition to orientation, the toolpaths that effectively determine the internal meso-structure of the part (discussed in a previous blog post in greater detail) have a very strong influence on observed stiffness behavior, as shown in Figure 6. Thus orientation and process parameters are variables that need to be comprehended in the modeling of cellular structures – or set as constants for the range of applicability of the model parameters that are derived from a certain set of process conditions.
Modeling cellular structures has the above mentioned challenges – most have practical implications in determining what is the correct specimen design – it is our mission over the next 18 months to address some of these challenges to a satisfactory level through an America Makes grant we have been awarded. While these ideas have been explored in other manufacturing contexts, much remains to be done for the AM community, where cellular structures have a singular potential in application.
In future posts, I will discuss some of these challenges in detail and also discuss different approaches to modeling 3D printed cellular structures – they do not always address all the challenges here satisfactorily but each has its pros and cons. Until then, feel free to send us an email at firstname.lastname@example.org citing this blog post, or connect with me on LinkedIn so you get notified whenever I write a post on this, or similar subjects in Additive Manufacturing (1-2 times/month).
This year’s IMTS show in Chicago saw the introduction of some great new 3D Printing technology that makes the creation of end-use parts from additive manufacturing even more feasible. “3D printing takes a giant step forward toward production manufacturing” shares my observations on the subject.
As 3D Printing makes it’s long awaited move from being dominated by prototyping to manufacturing production parts, companies need to consider a few key issues. In “Five Unique Considerations for 3D Printing Production Parts” I share what we have learned at PADT as we have helped customers make this transition.
Updated (8/30/2016): Two corrections made following suggestions by Gilbert Peters: the first corrects the use of honeycomb structures in radiator grille applications as being for flow conditioning, the second corrects the use of the Maxwell stability criterion, replacing the space frame example with an octet truss.
This is my first detailed post in a series on cellular structures for additive manufacturing, following an introductory post I wrote where I classified the research landscape in this area into four elements: design, analysis, manufacturing and implementation.
Within the design element, the first step in implementing cellular structures in Additive Manufacturing (AM) is selecting the appropriate unit cell(s). The unit cell is selected based on the performance desired of it as well as the manufacturability of the cells. In this post, I wish to delve deeper into the different types of cellular structures and why the classification is important. This will set the stage for defining criteria for why certain unit cell designs are preferable over others, which I will attempt in future posts. This post will also explain in greater detail what a “lattice” structure, a term that is often erroneously used to describe all cellular solids, truly is.
Honeycombs are prismatic, 2-dimensional cellular designs extruded in the 3rd dimension, like the well-known hexagonal honeycomb shown in Figure 1. All cross-sections through the 3rd dimension are thus identical, making honeycombs somewhat easy to model. Though the hexagonal honeycomb is most well known, the term applies to all designs that have this prismatic property, including square and triangular honeycombs. Honeycombs have a strong anisotropy in the 3rd dimension – in fact, the modulus of regular hexagonal and triangular honeycombs is transversely isotropic – equal in all directions in the plane but very different out-of-plane.
1.2 Design Implications
The 2D nature of honeycomb structures means that their use is beneficial when the environmental conditions are predictable and the honeycomb design can be oriented in such a way to extract maximum benefit. One such example is the crash structure in Figure 2 as well as a range of sandwich panels. Several automotive radiator grilles are also of a honeycomb design to condition the flow of air. In both cases, the direction of the environmental stimulus is known – in the former, the impact load, in the latter, airflow.
2. Open-Cell Foam
Freeing up the prismatic requirement on the honeycomb brings us to a fully 3-dimensional open-cell foam design as shown in one representation of a unit cell in Figure 3. Typically, open-cell foams are bending-dominated, distinguishing them from stretch-dominated lattices, which are discussed in more detail in a following section on lattices.
2.2 Design Implications
Unlike the honeycomb, open cell foam designs are more useful when the environmental stimulus (stress, flow, heat) is not as predictable and unidirectional. The bending dominated mechanism of deformation make open-cell foams ideal for energy absorption – stretch dominated structures tend to be stiffer. As a result of this, applications that require energy absorption such as mattresses and crumple zones in complex structures. The interconnectivity of open-cell foams also makes them a candidate for applications requiring fluid flow through the structure.
3. Closed-Cell Foam
As the name suggests, closed cell foams are open-cell foams with enclosed cells, such as the representation shown in Figure 6. This typically involves a membrane like structure that may be of varying thickness from the strut-like structures, though this is not necessary. Closed-cell foams arise from a lot of natural processes and are commonly found in nature. In man-made entities, they are commonly found in the food industry (bread, chocolate) and in engineering applications where the enclosed cell is filled with some fluid (like air in bubble wrap, foam for bicycle helmets and fragile packaging).
3.2 Design Implications
The primary benefit of closed cell foams is the ability to encapsulate a fluid of different properties for compressive resilience. From a structural standpoint, while the membrane is a load-bearing part of the structure under certain loads, the additional material and manufacturing burden can be hard to justify. Within the AM context, this is a key area of interest for those exploring 3D printing food products in particular but may also have value for biomimetic applications.
Lattices are in appearance very similar to open cell foams but differ in that lattice member deformation is stretch-dominated, as opposed to bending*. This is important since for the same material allocation, structures tend to be stiffer in tension and/or compression compared to bending – by contrast, bending dominated structures typically absorb more energy and are more compliant.
So the question is – when does an open cell foam become stretch dominated and therefore, a lattice? Fortunately, there is an
app equation for that.
Maxwell’s Stability Criterion
Maxwell’s stability criterion involves the computation of a metric M for a lattice-like structure with b struts and j joints as follows:
In 2D structures: M = b – 2j + 3
In 3D structures: M = b – 3j + 6
Per Maxwell’s criterion, for our purposes here where the joints are locked (and not pinned), if M < 0, we get a structure that is bending dominated. If M >= 0, the structure is stretch dominated. The former constitutes an open-cell foam, the latter a lattice.
There are several approaches to establishing the appropriateness of a lattice design for a structural applications (connectivity, static and kinematic determinism etc.) and how they are applied to periodic structures and space frames. It is easy for one (including for this author) to confuse these ideas and their applicability. For the purposes of AM, Maxwell’s Stability Criterion for 3D structures is a sufficient condition for static determinancy. Further, for a periodic structure to be truly space-filling (as we need for AM applications), there is no simple rigid polyhedron that fits the bill – we need a combination of polyhedra (such as an octahedron and tetrahedron in the octet truss shown in the video below) to generate true space filling, and rigid structures. The 2001 papers by Deshpande, Ashby and Fleck illustrate these ideas in greater detail and are referenced at the end of this post.
Video: The octet truss is a classic stretch-dominated structure, with b = 36 struts, j = 14 joints and M = 0 [Attr. Lawrence Livermore National Labs]
4.2 Design Implications
Lattices are the most common cellular solid studied in AM – this is primarily on account of their strong structural performance in applications where high stiffness-to-weight ratio is desired (such as aerospace), or where stiffness modulation is important (such as in medical implants). However, it is important to realize that there are other cellular representations that have a range of other benefits that lattice designs cannot provide.
Conclusion: Why this matters
It is a fair question to ask why this matters – is this all just semantics? I would like to argue that the above classification is vital since it represents the first stage of selecting a unit cell for a particular function. Generally speaking, the following guidelines apply:
- Honeycomb structures for predictable, unidirectional loading or flow
- Open cell foams where energy absorption and compliance is important
- Closed cell foams for fluid-filled and hydrostatic applications
- Lattice structures where stiffness and resistance to bending is critical
Finally, another reason it is important to retain the bigger picture on all cellular solids is it ensures that the discussion of what we can do with AM and cellular solids includes all the possibilities and is not limited to only stiffness driven lattice designs.
Note: This blog post is part of a series on “Additive Manufacturing of Cellular Solids” that I am writing over the coming year, diving deep into the fundamentals of this exciting and fast evolving topic. To ensure you get each post (~2 a month) or to give me feedback for improvement, please connect with me on LinkedIn.
 Ashby, “Materials Selection in Mechanical Design,” Fourth Edition, 2011
 Gibson & Ashby, “Cellular Solids: Structure & Properties,” Second Edition, 1997
 Gibson, Ashby & Harley, “Cellular Materials in Nature & Medicine,” First Edition, 2010
 Ashby, Evans, Fleck, Gibson, Hutchinson, Wadley, “Metal Foams: A Design Guide,” First Edition, 2000
 Deshpande, Ashby, Fleck, “Foam Topology Bending versus Stretching Dominated Architectures,” Acta Materialia 49, 2001
 Deshpande, Fleck, Ashby, “Effective properties of the octet-truss lattice material,” Journal of the Mechanics and Physics of Solids, 49, 2001
* We defer to reference  in distinguishing lattice structures as separate from foams – this is NOT the approach used in  and  where lattices are treated implicitly as a subset of open-cell foams. The distinction is useful from a structural perspective and as such is retained here.
I am writing this post after visiting the 27th SFF Symposium, a 3-day Additive Manufacturing (AM) conference held annually at the University of Texas at Austin. The SFF Symposium stands apart from other 3D printing conferences held in the US (such as AMUG, RAPID and Inside3D) in the fact that about 90% of the attendees and presenters are from academia. This year had 339 talks in 8 concurrent tracks and 54 posters, with an estimated 470 attendees from 20 countries – an overall 50% increase over the past year.
As one would expect from a predominantly academic conference, the talks were deeper in their content and tracks were more specialized. The track I presented in (Lattice Structures) had a total of 15 talks – 300 minutes of lattice talk, which pretty much made the conference for me!
In this post, I wish to summarize the research landscape in AM cellular solids at a high level: this classification dawned on me as I was listening to the talks over two days and taking in all the different work going on across several universities. My attempt in this post is to wrap my arms around the big picture and show how all these elements are needed to make cellular solids a routine design feature in production AM parts.
Classification of Cellular Solids
First, I feel the need to clarify a technicality that bothered me a wee bit at the conference: I prefer the term “cellular solids” to “lattices” since it is more inclusive of honeycomb and all foam-like structures, following Gibson and Ashby’s 1997 seminal text of the same name. Lattices are generally associated with “open-cell foam” type structures only – but there is a lot of room for honeycomb structures and close-cell foams, each having different advantages and behaviors, which get excluded when we use the term “lattice”.
The AM Cellular Solids Research Landscape
The 15 papers at the symposium, and indeed all my prior literature reviews and conference visits, suggested to me that all of the work in this space falls into one or more of four categories shown in Figure 2. For each of the four categories (design, analysis, manufacturing & implementation), I have listed below the current list of capabilities (not comprehensive), many of which were discussed in the talks at SFF. Further down I list the current challenges from my point of view, based on what I have learned studying this area over the past year.
Over the coming weeks I plan to publish a post with more detail on each of the four areas above, summarizing the commercial and academic research that is ongoing (to the best of my knowledge) in each area. For now, I provide below a brief elaboration of each area and highlight some important research questions.
1. Representation (Design)
This deals with how we incorporate cellular structures into our designs for all downstream activities. This involves two aspects: the selection of the specific cellular design (honeycomb or octet truss, for example) and its implementation in the CAD framework. For the former, a key question is: what is the optimum unit cell to select relative to performance requirements, manufacturability and other constraints? The second set of challenges arises from the CAD implementation: how does one allow for rapid iteration with minimal computational expense, how do cellular structures cover the space and merge with the external skin geometry seamlessly?
2. Optimization (Analysis)
Having tools to incorporate cellular designs is not enough – the next question is how to arrange these structures for optimum performance relative to specified requirements? The two most significant challenges in this area are performing the analysis at reasonable computational expense and the development of material models that accurately represent behavior at the cellular structure level, which may be significantly different from the bulk.
3. Realization (Manufacturing)
Manufacturing cellular structures is non-trivial, primarily due to the small size of the connecting members (struts, walls). The dimensions required are often in the order of a few hundred microns and lower, which tends to push the capabilities of the AM equipment under consideration. Additionally, in most cases, the cellular structure needs to be self-supporting and specifically for powder bed fusion, must allow for removal of trapped powder after completion of the build. One way to address this is to develop a map that identifies acceptable sizes of both the connecting members and the pores they enclose. For this, we need robust ways of monitoring quality of AM cellular solids by using in-situ and Non-Destructive techniques to guard against voids and other defects.
4. Application (Implementation)
Cellular solids have a range of potential applications. The well established ones include increasing stiffness-to-weight ratios, energy absorption and thermal performance. More recent applications include improving bone integration for implants and modulating stiffness to match biological distributions of material (biomimicry), as well as a host of ideas involving meta-materials. The key questions here include how do we ensure long term reliability of cellular structures in their use condition? How do we accurately identify and validate these conditions? How do we monitor quality in the field? And how do we ensure the entire life cycle of the product is cost-effective?
I wrote this post for two reasons: I love to classify information and couldn’t help myself after 5 hours of hearing and thinking about this area. But secondly, I hope it helps give all of us working in this space context to engage and communicate more seamlessly and see how our own work fits in the bigger picture.
A lot of us have a singular passion for the overlapping zone of AM and cellular solids and I can imagine in a few years we may well have a conference, an online journal or a forum of some sort just dedicated to this field – in fact, I’d love to assess interest in such an effort or an equivalent collaborative exercise. If this idea resonates with you, please connect with me on LinkedIn and drop me a note, or send us an email (email@example.com) and cite this blog post so it finds its way to me.
The other day, I saw a post on Engadget about a special case for Pokemon Go users to solve the problem of missing your prized Jigglypuff that you have happened across in the wild (or let’s face it, probably a CP 10 Rattata who is going to break out multiple times before disappearing in a puff of smoke…). The case is designed to give the user access to on screen controls and a nice channel to keep your Pokeball flinging finger straight and true.
As pointed out in the article on Engadget, this case is only useful in the capture screen. This caveat aside, the other issue with the case is that it obscures the screen. Here at PADT, we are fortunate to sell a wide variety of 3D Printing machines, some of which are capable of multiple colors and material durometers. I decided to design my own take on the case from Jon Clever to be prototyped on our Stratasys Connex 3.
The case was made with black and clear material. The black material can be combined to produce a custom stiffness, so we made that part soft and rubber like and kept the clear portion rigid. The clear has good optical quality, which could be increased with a layer of “clearcoat.”
If you have a Stratasys Connex 3 or J750 and an iPhone 6, you can make your own with these STL files, one for the rubber part and one for the clear part.
Other variations and additional possibilities would be made possible with the new Stratasys J750, the first true full color printer that can also mix clear and solid as well as hard and soft materials. The J750 was just released and highlighted on our recent road show. Visit our blog article on the Scottsdale show to learn more about this incredible printer.
Additional information about PADT and our wide range of 3D Printing offerings here.