Packaging for the post-Amazon world: Case Study Part IV – PatternFox DesignKit

By Katie Mencke | September 27, 2019 |

This is our fourth and final installment of a case study developed to highlight PatternFox’s Biologically Inspired Design (BID) methodology while pursuing the design question:

What can nature teach us about designing transport packaging for a decentralized delivery system?

If you are new to this blog series, or need a refresher, you can find all our past case studies blogs on our website. In Part I we introduced our PatternFox ProblemKit used to understand the context in which the problem exists (Step 1) and identify particularly challenging aspects of the problem (Step 2). In Part II we completed the PatternFox ProblemKit by abstracting the problem into universal functions (Step 3) and defining the ideal solution in terms of function, operating environment, and other limitations affecting the current system (Step 4). In Part III, we combed the breadth of biological research (Step 5) and tested the possible biological solutions against our ideal (Step 6).

This final installment describes how PatternFox examines the potential applicability of a biological system against our ideal solution and then builds a research plan to systematically break down any remaining barriers to prototyping.

Figure 1. PatternFox process for biologically-inspired problem solving and implementation

PatternFox DesignKit Step 7: How do we evaluate the potential of a biological system before getting into the lab?

Before investing in the process of designing the final product based on biological strategies, it’s a good idea to examine the biological system’s theoretical engineering performance. PatternFox does this by conducting a quantitative analysis of the most promising solutions in order to estimate the performance of an idealized design based on the biological system. This allows us to make a preliminary comparison against existing performance and determine whether the potential gains outweigh the time and money required for making a prototype.

In Part III we identified engineering principles derived from the turtle shell, alligator skin, toucan beak and woodpecker skull as having a higher probability of being transferable to packaging design than those from the other biological systems investigated during this case study.

Can foam structures based on the toucan beak beat corrugated performance?

These systems share several design patterns, but the one pattern that is common to all of them is Pattern 4: Energy absorption via foam-like structures. We decided to use the toucan beak as the basis of our inspiration; scientific papers on toucan beak provide good information on the performance characteristics, which allows comparisons to product requirements.

Seki et al. describes the toucan beak as a “sandwich” system of inner foam wrapped in a thin keratin ‘shell’.[1] This also a good analogy for the standard shipping box wall as a “sandwich” of linerboard and corrugated medium.

Figure 2. Sandwich structures of corrugated box wall and toucan beak wall.

A typical box requirement in the US is 32 ECT (edge crush test); that is, the box must be able to withstand $32\, lb_f$ of compression per lineal inch along the box edge without failing. This measure ensures that each box will be able to withstand the weight of evenly sized and stacked boxes. Assuming a box wall thickness of $\frac{3}{16}\, in$ (roughly corresponding to a C-flute), the crushing stress (compression pressure at which the box fails) would be:

$32\, \frac{lb}{in} \div \frac{3}{16}\, in \approx 170\, \frac{lb}{in^2} \: \left( or \, psi \right)\;\;[1]$

Seki et al. recorded the compressive strength of the foam portion of the toucan beak around $25\, psi$ . That’s not a very impressive number compared to the current box. However, the foam structure does not function in isolation, as is true for most biological structures. The compressive strength of the beak as a system (foam-plus-keratin wrapper) was recorded above $3300\, psi$ .[2] That’s supporting the weight of a Volkswagen Beetle, per square inch. How?The combined system provides compressive strength by balancing toughness and flexural rigidity for the specific geometry of the beak.

Keratin is, itself, a very tough material. However, it is very flexible and deforms before failure. The cancellous bone-like foam is just the opposite; it is very brittle (the opposite of tough), but it is not very flexible and provides the keratin layers with thickness and scaffolding to increase flexural rigidity of the system. We see this same strategy repeated in the alligator’s osteoderm and the turtle shell; sandwich structure combining a tough outer layer and a thick, low-density layer to maximize defense against impact and puncture without adding too much weight.

Let’s take a look at the toughness of the toucan beak. Based on the stress-strain curves developed by Seki et al.^1,2, the toughness of the foam by itself is negligible:

For foam, this equates to:

$25\, psi \times 0.02\, \frac{in}{in} = 0.5\, in \cdot \frac{lb_f}{in^3}\;\;[2]$

For the sandwich structure, Seki’s experimental results indicated that the toughness of the sandwich system was more than the toughness of the independent components added together.

Foam + Shell (tested independently and added together):

$1523\, psi \times 0.07\, \frac{in}{in} = 1.07\, in \cdot \frac{lb_f}{in^3}\;\;[3]$

Foam + Shell (tested as a sandwich structure):

$1668\, psi \times 0.1\, \frac{in}{in} = 167\, in \cdot \frac{lb_f}{in^3}\;\;[4]$

The sandwich structure results in higher failure stress.

To compare with the current box, we can calculate the toughness using a typical ECT stress strain curve. From Roman Popil’s work at the Renewable Bioproducts Institute (The Georgia Institute of Technology), we see that a typical box has average stress of $~19\, \frac{lb}{in}$ before failure at $1.6\%$ strain[3].

$19\, \frac{lb_f}{in} \div \frac{3}{16}\, in \times 0.016\, \frac{in}{in} = 1.6\, in \cdot \frac{lb_f}{in^3}\;\;[5]$

The toughness of current boxes is more than 3 times greater than the foam component of the toucan beak (Equation [5] $1.6\, in \cdot \frac{lb_f}{in^3}$ vs Equation [2] $0.5\, in \cdot \frac{lb_f}{in^3}$ ). However, compared to the foam and shell of the toucan beak as a system, the current box underperforms by 2 orders of magnitude (Equation [5] $1.6\, in \cdot \frac{lb_f}{in^3}$ vs Equation [4] $167\, in \cdot \frac{lb_f}{in^3}$ ). There are more factors at play here than just materials, for example system shape and configuration. ECT tests are performed under specific conditions for comparability, so our comparison isn’t exactly apples to apples. Nonetheless, 2 orders of magnitude difference is a difference worth exploring.

Why does the toucan beak have much higher toughness? We believe this is due to the superior toughness of keratin over linerboard. Keratin is one of the toughest biological materials known. Beak keratin (β-keratin) is a protein that consists of helically twisted β-sheets of long proteins that assemble into filaments. Extensive twisting and hydrogen bonding support large deformation (strain) prior to damaging the covalent bonds of the component protein chains. Might we be able to transfer these properties to form tougher linerboard?

Moving on to another important aspect of performance, flexural rigidity of a sandwich structure is determined by the thickness of the “sandwich” and the stiffness of the outer layer material.

Flexural rigidity for sandwich structures can be calculated as follows:

$\frac{Flexural Rigidity}{w} \approx \frac{{E_s}{t_s}^3}{6} + \frac{{E_f}{t_f}^3}{12} + \frac{{E_s}{t_s}{\left( t_s + t_f \right)}^2}{2}\;\;[6]$

$w=$ width

$E=$ modulus of elasticity

$t=$ thickness

$s$ denotes properties of “shell” outer layer

$f$ denotes properties of “foam” inner layer

To achieve a “toucan-beak sandwich” with the same mass as a C-Flute single wall corrugated board, we’ve estimated that the thickness of the keratin would be $0.00625 in$ and the thickness of the foam portion would be $0.155 in$ . (Calculated with data from [1,[4],[5]].) The resulting flexural rigidity could be calculated as:

$\frac{Flexural Rigidity}{w} \approx \frac{{(205,000)}{(0.00625)}^3}{6} + \frac{{(810)}{(0.155)}^3}{12} + \frac{{(205,000)}{(0.00625)}{\left( 0.00625 + 0.155 \right)}^2}{2}$

$\frac{Flexural Rigidity}{w} \approx 16.9\, lb_f \cdot in\;\;[7]$

Where $E_s \approx 200,000\, psi$ and $E_f \approx 810\, psi$

For comparison, we can approximate corrugated cardboard as a series of I-beams. In production, these corrugations are made across the sheet paperboard, perpendicular to the direction that the paper is being unrolled. We consider a corrugated sheet made from 2 out layers of 42lb liner, and a 26lb C-flute. C-fluting provides about $39\, \frac{flutes}{foot}$ , or one flute (I-beam) per $0.308\, in$ . For such an I-beam, using cross-direction data from [4]:

$\frac{Flexural Rigidity}{beam} \approx \frac{{E_{42}}{t_{42}}^3{w_{42}}}{6} + \frac{{E_{26}}{t_{26}}^3{w_{26}}}{12} + \frac{{E_{42}}{t_{42}}{\left( t_{42} + t_{26} \right)}^2{w_{42}}}{2}\;\;[8]$

$42$ denotes properties of the 42# linerboard

$26$ denotes properties of 26# fluting

$\frac{Flexural Rigidity}{beam} \approx \frac{{(363,000)}{(0.0114)}^3{(0.308)}}{6} + \frac{{(254,000)}{(0.156)}^3{(0.0118)}}{12} + \frac{{(363,000)}{(0.0114)}{\left( 0.0114 + 0.156 \right)}^2{(0.308)}}{2}]$

$\frac{Flexural Rigidity}{beam} \approx 18.8\, lb_f \cdot in^2\;\;[9]$

$\frac{Flexural Rigidity}{w} = \left( \frac{Flexural Rigidity}{beam} \right) \left( \frac{beam}{w_{beam}} \right) \approx 61.0\, lb_f \cdot in\;\;[10]$

Corrugated clearly performs better from this perspective. In order to meet the performance of corrugated cardboard, the toucan beak foam would have to be about $0.3]\, in$ thick, or 60% thicker than then is currently used. This doesn’t come as much surprise, considering we’ve separated the toucan beak from the context in which it functions and for which it is optimized; a cylindrical foam-filled shell optimized across many additional functions (like heat transfer), and not simply for stacking. A little bend in the beak is acceptable to the Toucan. So, while the Toucan beak is 100 times tougher, we will require extra bulk if we require the same kind of rigidity as is currently expected for packaging – a requirement important for stacking and packing in bulk.

The results from the toughness comparison are promising, but the beak is just not as rigid as the current box. So, to take this biological inspiration to the next steps, we want to know…

To what extent can we relax rigidity constraints for non-palletized shipping?

With shipping moving to this new, single-box mode, maybe rigidity isn’t as high a priority as it is for neatly palletized stacks.

What other trade-offs can we make, other than thickness, to provide rigidity without sacrificing toughness?

It is possible that there are additional material properties to adjust that could provide rigidity without sacrificing toughness.

How can we augment the design with additional features to maintain rigidity, without compromising toughness or adding bulk?

We have been assuming the box will remain as a traditional box with 6 faces. Perhaps there are other designs levers we can use to optimize packaging characteristics, such as shape.

Also consider, the Toucan beak is but one example of foam-based protective structures in nature. One recommendation from this analysis would be to identify and investigate other foam-based structures to identify the roles shape and configuration play in responding to variable stresses. We are also interested in other methods nature uses to deal with these stresses: for example, the alligator osteoderm, which uses both foam-based structures and a unique type of joint to differentiate its response under different load conditions.

How do plate-and-suture structures based on the alligator osteoderm compare to traditional corrugated box performance?

Encouraged by the potential gains in the Toucan beak, we also investigated another promising pattern: Pattern 7: Non-linear bending modulus. Alligator osteoderm and turtle carapace both use this strategy for flexible protection. These biological systems are not composed of monolithic homogenous materials. Instead, the they are composed in a series of plates connected with suture joints that are held together with flexible collagen. Each individual plate is bony and stiff, resisting deformation. However, the joints facilitate flexure; below the critical angle, adjacent plates can flex relative to one another according to the mechanical properties of the connective collagen. Above that angle, the plates press on one another and the joint stiffens, limiting the maximum flex and behaving more like a single plate.

Figure 3. Diagram of alligator osteoderm suture joint

For the sake of computational tractability and the information available in the biological literature, we focused on analyzing one suture joint and how it would behave in isolation.

The plate material is assumed to be corrugated board with a thickness of $\frac{3}{16}\, in$ and a bending stiffness of $100\, lb_f \cdot in$ (easily achieved by C-flute corrugated board). The effective elastic modulus for the board is assumed to be $180,000\, psi$ with a yield stress of $1500\, psi$ , a reasonable value for linerboard⁴. The flexible joint material, likely an elastomer material, must have a notably lower elastic modulus to provide for greater energy storage at a given load: we choose $18,000\, psi$ (10% of the stiff modulus).

The bending behavior of a solid material versus two types of joints were calculated and compared using classical bending beam analysis. Each is assumed to be clamped near the edges with force distributed evenly across the beam as in Figure 4 below.

Figure 4. Schematic assumptions for bending analysis comparison between a solid material, a simple joint and a suture joint.

In bending beam analysis, mechanical behavior of the beam is dependent on the ratio of its length to its thickness, which in our case is dependent on the size of the single plate unit (osteoderm analog). To keep things simple and roughly in line with biology, we chose a ratio of $16:1$ which means a length ( $L_w$ ) of $3\, in$ using the $\frac{3}{16}\, in$ corrugated thickness. The implication of the results can be generalized to other ratios, and indeed this becomes a tunable parameter.

An optimized simple joint as calculated has the highest yield load and absorbs the highest amount of energy before failure. In this example, the optimized simple joint length should be $0.12\, in$ . On the other hand, the suture joint can be customized to behave anywhere along the spectrum of performance between the solid material and the simple joint. For example, with a flexible material length of $0.12\, in$ and a suture length of $0.21\, in$ , the results are somewhere in the middle.

It is possible that one can find an alternative combination of material properties for a simple joint that outperforms the suture joint in this context but practically, and for cost, material properties are limited. Thus, the suture joint, provides more tunable performance features than a simple joint even when constrained by the choice of materials. Note, this is a simple analysis in two dimensions with a single plate and two joints. An actual packaging system would encase a product in many tessellated plates, each connected to another along the edges, as with a turtle shell. The situation, therefore, warrants further consideration and analysis. The suture joint is more complex than the simple joint structure. Since competition tends to select for efficiency in biology; if the simpler structure were superior, why is it not selected by nature? The independent switch-like behavior of each joint, each joint changing from flexible to stiff as its load changes, creates very complex system behavior across a wide range of tunable parameters, and therefore precludes a general analytical evaluation. Investigation of the behavior of a networked system of many plates together is needed. To do so, we could extend the study and perform computer simulations/finite element analysis; a step too far at this early stage as the resources required involve additional investment. This is a typical outcome at this stage in bioinspired design: we’ve identified a promising system, we understand the tunable parameters, and now we have a specific set of research questions and a variety of methods we can deploy in order to understand if the system will provide benefit in our packaging context. This is what we need to move to Step 8.

PatternFox DesignKit Step 8: How do we get from inspiration to prototype?

We have some theoretical evidence that foam sandwich structures like the toucan beak, could increase the toughness of boxes, but not the bending stiffness. And while the osteoderm did not provide good results at the individual suture level, we still don’t know how the plates and sutures behave as a complex system. Our back of the envelop calculations suggest that either technology could work, but further progress requires modeling, research, and/or a physical prototype before determining whether full scale production is warranted.

Bridging the gap between the biology that inspires us and creating a protype to test the design is one of the most neglected steps in Biologically Inspired Design methodologies. Frequently, as we’ve seen here, the available biological literature describes a system that performs a function in a specific context but does not explain in sufficient detail how the components work together to perform the function. Although some biological systems have been researched more deeply than others, for example the human heart, such systems are the exception not the rule. Very rarely can a design lab apply information directly from available literature, particularly since the environments and constraints of biological systems will not match precisely those governing the technological application. In the absence of rich knowledge regarding the mechanisms underlying the biological function, what variables govern system performance, and how variation in the components affects performance, decisions at the prototyping stage may be arbitrary.

We are often asked the question, why do some BID projects yield prototypes in six months while others fail to ever get there even over the course of years, often ending up as a good idea collecting dust on a shelf? PatternFox prevents design results from becoming yet another dusty volume on the shelf by assessing the ability to go from inspiration (or conceptual design) to prototype using two important tools: the Biological Readiness Level^TM (BRL), and a Request-for-Proposal (RFP). The PatternFox BRL assesses potential timeline, order of magnitude cost, and uncertainty with respect to current knowledge of the biological system in question. This provides decision makers with information for realistic planning. With our access to world-class researchers and experience in BID research, PatternFox is uniquely positioned to determine where a project would fall on the BRL scale and to identify critical data required to move the design forward.

Figure 5. PatternFox Biological Readiness Leve

Should a client decide to move forward, PatternFox will develop a request-for-proposal (RFP) that is specifically aimed at delivering a functional prototype that meets our client’s needs. The quantitative analysis is critical in exposing the key design levers and unknowns in the system, which become the backbone of the RFP. In this example, the RFP for alligator osteoderm would first include a rough computational model of a 3-dimensional plate-and-suture systems to determine if further development of the idea would be warranted. If the computational model returns promising results, the next step would be prototyping to see what we can learn from building a system and how to best transfer the application to packaging. We would also refine the computational model to identify optimal material and design parameters; prototyping and bench testing usually expose gaps in the model, which we can then be refined further. With our worldwide network of biologists and research facilities, in addition to building an actionable plan, PatternFox can connect the RFP with laboratories and scientists who are working on the cutting edge of advancements in manufacturing and biology, connecting clients with the resources needed to execute the plan. This is particularly important, since many research organizations provide deep domain expertise, but often lack the full range of expertise that might be needed to investigate the breadth of solutions that biology offers.

Summary: What did we learn from nature about transport packaging?

Although we may not have completely disrupted current packaging technology, we know quite a lot about nature’s protective packaging strategies:

Right-sizing the container
Changing the orientation of protective layers
Tailoring energy absorption and stiffness by using heterogenous materials
Staggering layers
Crosslinking fibers
Absorbing energy through tough joints with limited bending angles
Deforming to protect what’s inside (crumple zones)
Redirecting the force through a rod

More importantly, we learned that nature rarely relies on just one solution principle. What strategies have you tried?

We hope this is not the end of our involvement in packaging design, even if it is the end of our blog series on this topic. If you are part of a design organization, packaging or otherwise, and want to know more about what nature can us about your specific problem, connect with us using one of the links below!

[1] Seki, Y., et al. (2006). The toucan beak: Structure and mechanical response. Materials Science and Engineering: C, 26(2006) 1412 – 1420

[2] Seki, Y., Schneider, M., & Meyers, M. (2005). Structure and mechanical behavior of a toucan beak. Acta Materialia, 53(20), 5281–5296.

[3] Popil, R.E. Corrugated Board Strength: effects of the localized buckling of linerboard facings – modeling, management and control [Powerpoint slides]. Retrieved from http://www.rbi.gatech.edu/sites/default/files/documents/Guntersville%20Alabama%20presentation_for%20Valdosta%20students.pdf

[4] Carson, C. G., & Popil, R. E. (2008). Examining interrelationships between caliper, bending, and tensile stiffness of paper in testing validation. TAPPI Journal, 2008(December), 17–24.

[5] Biancolini, M. E., & Brutti, C. (2003). Numerical and experimental investigation of the strength of corrugated board packages. Packaging Technology and Science, 16(2), 47–60. http://doi.org/10.1002/pts.609

Posted in Process, Research

PatternFox DesignKit Step 7: How do we evaluate the potential of a biological system before getting into the lab?

PatternFox DesignKit Step 8: How do we get from inspiration to prototype?

Summary: What did we learn from nature about transport packaging?

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