grouping materials and processes for the designer: an ......materials and design 23 2002 1Ž. 10...

Ž .Materials and Design 23 2002 1�10

Grouping materials and processes for the designer:an application of cluster analysis

K.W. Johnson�, P.M. Langdon, M.F. Ashby

Engineering Design Centre, Engineering Department, Trumpington Street, Cambridge Uni�ersity, Cambridge CB2 1PZ, UK

Received 22 January 2001; accepted 9 April 2001

Abstract

In this paper, an analytical tool � cluster analysis � that is commonly used in biology, archaeology, linguistics and psychologyis applied to materials and design. Here, we use it to cluster materials and the processes that shape them, using their attributes asindicators of relationship. The chosen attributes are important to design and designers. The resulting clusters, and theclassifications that can be developed from them, depend on the selected attributes and � to some extent � on the method ofclustering. Alternative classifications for design that are focused on the technical or aesthetic attributes of materials and thematerials and shapes allowed by processes are explored. � 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Materials; Product design; Aesthetics

1. Introduction

Classification is the first step in bringing order intoany scientific endeavour. The founders of biology,zoology and geology were those who created a classifi-cation system. Classification orders the confusion ofdiversity, segregating an initially disordered variety intogroups. These groups can be further subdivided andcharacterised by seeking significant similarities withineach. The success of the great classification systemsrelies on the judgement of what are relevant attributes

Žand of what is ‘significantly similar’ and what is not theclassification of the animal kingdom and that of the

� Corresponding author. Tel.: �44-1223-332635; fax: �44-1223-332662.

Ž .E-mail address: [email protected] K.W. Johnson .

elements in the Periodic table are examples of success-.ful systems . Not all classifications survive � genetic

mapping is, even now, reconstructing the classificationsof biology and zoology. However, this in no way dimin-ishes the importance of the original classification; it isthe stepping stone to a higher level.

Classification has a key role in design. Design in-volves choice, and choice from enormous banks of dataand ideas. Among these is the choice of materials andprocesses. Effective classification allows the creation ofan intuitive grouping and indexing system that can beeasily interpreted. Grouping involves a judgement ofrelative similarity, across all attributes, for each ele-ment in that group. Indexing involves the assignment ordevelopment of a list of relevant attributes, and iscentral for both information retrieval and selection.However, to be efficient, the way the indexing is carriedout must be adapted to the subject under scrutiny andthe purpose of the search.

0261-3069�02�$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.Ž .PII: S 0 2 6 1 - 3 0 6 9 0 1 0 0 0 3 5 - 8

( )K.W. Johnson et al. � Materials and Design 23 2002 1�102

The scientific study of materials � materials science� seeks to understand the fundamental origins ofmaterial properties, and, ultimately, to manipulatethem. It has had remarkable success in doing both. Theorigins of many material properties derive directly fromthe atomic and electronic structure of the material:among these are density, modulus, thermal and electri-cal conductivity, optical transparency and more. Theseare now well understood, and can, within the limitsimposed by the laws of physics, be manipulated. Others� among them, strength, ability to be shaped andbrittleness � are well characterised, but less well un-derstood in a fundamental sense, though even that iscoming.

This science has, naturally, developed a classificationsystem to suit its purposes. It is shown, partly ex-panded, in Fig. 1a. The classifications of Kingdom,Family, Class, Subclass, Member may seem a bit grand,but there is sense in it; in Fig. 1a, this allows a classifi-cation based, at the first level, on the nature of theatoms of the material and the of the bonding between

Ž .them e.g. ‘metal’ , at the second level on the chemi-Ž .cally differences within that family e.g. ‘aluminium’ ,

and at subsequent levels, the details of composition.The sub-classes ‘1000’, ‘2000’, etc. are groups ofaluminium alloys with similar, but not identical, compo-sition and characteristics. The ‘6000’ series is one ofthese; and ‘6061’ is one of its members. The classifica-tion ends here. Each figure has been extended to listsome of the technical attributes of individual materials;density, price, modulus, various measures of strength,of thermal behaviour, of electrical characteristics, ofoptical properties and more.

In a similar way, the processes used to shape, joinand finish materials have been studied with a view tocontrolling and optimising them. Books on manufactur-ing processes generally group them into classes thatrely on similarities in their underlying technology: pro-

Ž .cessing from the liquid state ‘casting’ ; from the vapourŽ . Žstate ‘deposition’ ; in the solid state ‘powder. Žmethods’ ; by plastic deformation ‘deformation meth-

.ods’ , etc. Fig. 1b shows such a classification, partlyexpanded to show the sub-classes and members of theclass ‘casting’.

The science-based classifications of Fig. 1a,b emergefrom an understanding of the way atoms bond to eachother to become solid, and how this solid is manipu-lated to give desired shapes. However, science is onething, design is another. Is the science-based classifica-tion helpful to the technical designer, or � moreinterestingly � to the industrial designer? Fig. 1c is a

Ž .classification of materials again, partly expanded as-sembled by a group of architects. It is quite differentfrom Fig. 1a, but to the audience of architects, it is

apparently more useful. Hence, we are faced with thequestions: what then are the best classifications andindexing materials and processes for designers? Domethods exist that might help in constructing them?

2. Method

� �Cluster analysis 1�3 is a way of developing a tax-onomy or classification for a number of objects. Thereare many types of cluster analysis. Such methods havebeen used to find groupings in biology, archaeology,

� �linguistics and psychology 1 . Here we apply them theclustering of materials and processes for design. Other

� �techniques for grouping, like factor analysis 4 and� �multi-dimensional scaling 5 may have applications

here as well, but have not been considered in thispaper. Cluster analysis can produce results that aresimilar to the methods currently used to cluster materi-als or processes � a hierarchical tree � so it is anatural starting point.

Cluster analysis is defined by the statement: given Nobjects, each characterised by p variables, derive aclassification scheme for grouping the objects into gclasses. The starting point is the definition of a set ofvalues for the p variables of the N objects. The value

Žof the jth variable for object I is X capitals for theIj.object, lower case subscript for the variable , as indi-

cated in Fig. 2a.The idea of seeking clusters in two dimensions

Ž .meaning two variables, p and p is easy to grasp �1 2Ž .just plot the two variables as if they were x, y co-

ordinates, as in Fig. 2b. Object I appears as the pointŽ .x�X y�X . Plots of this sort could be used toI1, I2create a hierarchy with members grouped into sub-

Ž . Ž .classes g1, g2 and g3 in Fig. 2b , classes g4 , andŽ .families g5 , based on their proximity on the plot.

� �Material property charts 6 are exactly such two-dimensional plots using pairs of material properties asthe variables. One is shown in Fig. 3: this is essentiallya cluster diagram using the values of two technicalattributes, Young’s modulus and density, for some 60‘objects’; here each ‘object’ is a material. Metals form acluster; polymers form a separated cluster, as do tech-nical ceramics, woods, and foams; the clusters overlapin some places but are separate in others. The cluster-ing extends down to the level of class: steels, forexample, form a cluster within metals as do nylonswithin polymers.

Cluster analysis goes further, identifying groups in pdimensions, where p can be much larger than two. Thisrequires a method of associating the N objects intogroups, or, if the clustering is hierarchical, into fami-

( )K.W. Johnson et al. � Materials and Design 23 2002 1�10 3

Ž .Fig. 1. a A classification of materials based on the scientific understanding of the nature of the atoms they contain and the nature of the bondsŽ . Ž .between these atoms. b A classification of processes based on the underlying principles of their operation. c A classification of materials

Ž .constructed by architects. ‘Known’ means well-established; ‘Unknown’ means known in engineering but not in architecture titanium ; ‘Emerging’Ž . Ž .means that their used in architecture is small but growing GFRP ; ‘Superseded’ mean no longer used thatch ; ‘Future’ means yet-to-be

developed.


Ž . Ž .Fig. 2. a N objects each characterised by p variables. b Two-dimensional clustering, of which materials property charts are an example.

lies, classes and sub-classes. When there is little or noprior knowledge, mathematical techniques are useful infinding clusters. Hierarchical clustering, the clustering

method we have chosen here, is based on a matrix thatŽ .describes the ‘distance’ between two objects Fig. 4a .

There is more than one way of measuring ‘distance’.

Fig. 3. A chart of modulus and density for materials, showing the clustering of metals, polymers, ceramics, foams, woods, etc.


Ž . Ž .Fig. 4. a An example of a distance matrix for five objects. The diagonal components are all zero. b An example tree, or dendrogram, is shownon the left. The same tree, segmented to show a way of classifying the kingdom into families, classes, sub-classes and members, is shown at theright. The dashed lines showing divisions in the tree are not standard, they are a matter of interpretation and can be done in more than one way.

We have chosen a Euclidean distance measure becauseit is intuitive and recommended for quantitative data ofthe sort used here.1 The Euclidean distance betweenobject I and object J for variable j�1 is defined by:

1�22Ž . Ž .d � X �X 1� 4I J I1 J 1

where the powers are introduced to make all distancespositive. This generalises to:

1�2k�p2Ž . Ž .d � X �X 2ÝI J Ik J k½ 5

k�1

as a measure of distance incorporating informationfrom all p variables. The use of this Euclidean distancerequires caution. First, if all p variables have the same

1 Other distance measures such as percentage, Chi-squared andgamma are possible but are not chosen here, they are relevant forother types of data � for example, percentage is better for categori-cal data.

range, the definition weights them all equally; but ifsome variables have a large range and others a smallone, the distances d are heavily weighted towards theI J

large-range variables. This problem is overcome bynormalising the data such that all are dimensionless

Ž .and have the same range 0�1 . Second, if the distribu-tion of the data across the range of each variable isevenly spaced, each is weighted equally; but if, for agiven variable, it is skewed to either end, that variableis weighted differently from the others. We have over-come this problem in dealing with material propertiesby using the logarithm of the value, not the value itselfŽ .as is done in Fig. 3 .

Clusters are found by linking the nearest objects.The simplest method for linking a number of objects ina tree structure first identifies the pair of objects that isseparated by the smallest distance; this pair is thenaggregated and replaced by a single object, assigning itdistances that are the smallest values from the originalpair: if we suppose that the smallest distance is d12then objects 1 and 2 are aggregated and assigned

Ž .distances �min d , d . The next-nearest groupings1 J 2 J

are then formed, and so on. This method is known as


Ž . Ž .Fig. 5. a Material cluster tree by technical attributes . The families introduced in Fig. 1a are distinguished by colour: ceramics � pink; metalsŽ .� light red; composites � dark red; foams � dark blue; polymers � light blue; elastomers � orange; natural materials � green. b Material

Ž .cluster tree by aesthetic attributes .


Table 1Materials and material attributes selected for clustering

Materials Materials, continued Technical properties Aesthetic properties

ABS Natural rubber Density Base colourAcrylic Oak Ductility Integral colourAlumina Palm Fracture toughness Refractive indexAlumina foam Polycarbonate Hardness TransparentAluminium Polychloroprene Tensile strength TranslucentAluminium foam Polyester Thermal conductivity Coefficient of reflectionAluminium�silicon carbide Polyester�glass fibre Thermal diffusivity OpaqueAsh Polyethylene Young’s modulus WarmthBamboo Polyethylene foam ReflectiveBeryllium Polypropylene SoftnessCarbon steel PolystyreneCork Polystyrene foamDiamond PVC foamEpoxy PVCEpoxy�carbon fibre PlywoodEVA Silicon carbideGlass ceramic SiliconeInvar Soda-limeMagnesium Stainless steelMelamine Titanium

the single linkage method.2 The results � regardlessof the method � can be arranged as a tree or dendro-gram as shown on the left of Fig. 4b. Classificationsemerge by segmenting the tree at progressively largerinter-member distances, as shown on the right of Fig.4b. The positioning of these classification boundaries ofFig. 4b requires some individual interpretation. It islike looking at the night sky through a telescope withvariable power: at high power, the individual stars areresolved, but as the power is reduced, their non-ran-dom distribution causes them to appear to cluster andeach cluster appears as one star. The details of thisdepend on the precise setting of the magnification, but

Žif the population of stars has a natural clustering and.is not randomly distributed , the resulting hierarchy is

Žinsensitive to resolution. The materials tree shown.previously in Fig. 1a is an example of a hierarchical

scheme for expressing the natural clustering of materi-als based, as explained earlier, on the understanding ofatomic type and bonding. In an effort to evaluate theapplicability of cluster analysis to materials andprocesses we choose to cluster 40 materials and 49

� �processes using the SYSTAT software package 7 and� �data from the Cambridge Engineering Selector 8 .

3. Results

Fig. 5a shows the resulting cluster for these 40 mate-

2 Other linkage methods exist, such as complete, average andWard’s; these methods were tested and did not produce significantlydifferent results here, but could be relevant in other studies.

rials grouped on eight thermal and mechanical proper-Ž .ties Table 1 central to technical design. Ceramics

group to form a family; so too do foams, metals,natural materials and polymers; and within polymers,thermoplastics and elastomers form distinct classes.3

The analysis has led to groupings that, in most ways,resemble those of Fig. 1a, and suggests that usefulclassifications might result by repeating the same analy-sis first with different variables and then with differentobjects.

Looking more closely at the clustering, some materi-als fall outside their accepted science-based groupings,for reasons that can be understood. Aluminium foamsstand on their own as materials with properties quitedifferent from anything else, though if electrical con-ductivity were included among the technical attributes,a link with metals would have been more evident.Epoxy�carbon fibre composites are more similar � interms of the eight properties � to metals than they areto other polymer composites. Alumina foam behavesmore like a polymer or natural material than theceramic from which it is made. Cork, a natural mate-rial, by grouping on physical attributes, behaves morelike an elastomer or a polymer foam when grouped ontechnical attributes. There is more to be gained byexpanding the list of materials, but even this ex-ploratory analysis suggests how a designer might beable to use such an analysis to suggest materials thatare similar to each other: perhaps magnesium could be

3 These families are distinguished in each figure by colour.


Ž . Ž . Ž . Ž .Fig. 6. a Shaping process cluster tree by possible material combinations . b Shaping process cluster tree by possible shape categories .


Table 2Processes and shapes used in clustering

Processes Shapes

3D printing Micro-blanking Axisymmetric prismatic, plain hollowBMC moulding Polymer casting Axisymmetric prismatic, plain steppedCalendering Polymer extrusion Axisymmetric prismatic, stepped hollowCentrifugal casting Powder extrusion Axisymmetric prismatic, stepped solidCentrifugal moulding Powder injection moulding Dished axisymmetric, deepCeramic extrusion Press forming Dished axisymmetric, re-entrantCold closed die forging Pultrusion Dished axisymmetric, shallowCold shape rolling Reaction injection moulding Dished non-axisymmetric, deepCompression moulding Roll forming Dished non-axisymmetric, re-entrantContinuous laminating Rotational moulding Dished non-axisymmetric, shallowDeep drawing RTM Flat sheet, cut-outsDie pressing and sintering Shape drawing Flat sheet, no cut-outsExtrusion blow moulding Slip casting Hollow 3D, complex parallel featuresFilament winding SMC moulding Hollow 3D, complex transverse featuresGravity die casting Spinning Hollow 3D, simple parallel featuresGreen sand casting Stamping Hollow 3D, simple transverse featuresHand lay-up Stereolithography Non-axisymmetric prismatic, plain hollowHIPing Superplastic forming Non-axisymmetric prismatic, plain steppedHot closed die forging Swaging Non-axisymmetric prismatic, stepped hollowHot extrusion Tape casting Non-axisymmetric prismatic, stepped solidHot open die forging Thermoforming Solid 3D, simple transverse featuresHot shape rolling TP injection moulding Solid 3D, complex parallel featuresInjection blow moulding TS injection moulding Solid 3D, complex transverse featuresInvestment casting Wire drawing Solid 3D, simple parallel featuresLaminated object

substituted for aluminium, epoxy for acrylic, cork forpolyethylene foam.

We have explored another way of clustering materi-Žals, based on their aesthetic properties Table 1, right

.hand column . Fig. 5b shows these results. Some impor-tant differences emerge. Glass ceramic now groupsclosely with alumina; one is a glass, the other is atechnical ceramic, but neither can be transparent.Epoxy�carbon fibre composites seem to be closely re-

Ž .lated to polychloroprene largely because of colour , arelationship that was not seen when the materials weregrouped on technical properties. Soda-lime glass, EVA,acrylic and epoxy group together partly because �although none are opaque � all can be transparent ortranslucent. Melamine stands on the outside of onecluster of polymers because this material is difficult tocolour lightly. The metals still group closely togetherbecause so many of their aesthetic properties, likereflectivity, are determined by the nature of the bond-ing of their atoms, which are closely related to thetechnical properties selected for clustering previously.The polymer foams still group together; these materialshave similar aesthetic properties � both visual andtactile.

To cluster processes, we have chosen a similar tech-nique. A process either can or cannot be used with agiven material: ABS, for example, can be injectionmoulded or extruded, but it cannot be spun or reactioninjection moulded. We can make similar statementsabout processes and shape. Rapid prototyping processes

Ž .like three-dimensional 3D printing can make almostany shape, but extrusion can only make prismaticshapes.

In Fig. 6a,b, we have clustered processes based onwhether they can be applied to a given material, usingthe 40 materials of Table 1 and the processes listed inTable 2, and based on the ability of a process toachieve a specific category of shape. By clusteringprocesses we allow designers to see the similaritiesbetween them. Using these trees as a visual guide, adesigner can judge whether possible materials or shapesare similar for individual processes. Micro-blankingand spinning can shape similar materials; thermo-forming and superplastic forming allow similar shapes.

4. Discussions

At its most basic level, grouping and indexing allowsthe quick retrieval of information; but the use of acreative system of classification can allow inspiration aswell � both are equally important to designers.Grouping materials and processes also allows a de-signer to assess the similarity of two materials orprocesses, stimulating innovation and suggesting substi-tutions. In addition, the hierarchical, tree-like organisa-tion expresses knowledge about the complex space ofthe designer’s mind in a concise manner. Some morechallenging questions enter at this point: if there is nomaterial available to match a specified set of attributes,


could the material and process groupings suggest inno-vative possibilities of combination? Could the introduc-tion of a new material or process, through this method,suggest similarities that would lead to innovativeproduct applications? Can we apply the same methodto product categories so that similarities and differ-ences can be highlighted for further investigation? Themethod of clustering has picked up some subtleties thatdifferentiate materials based on their inherent techni-cal or aesthetic attributes and that differentiateprocesses based on allowable materials or shapes. Tocontinue, a more detailed list of attributes is necessaryfor each � particularly for the aesthetics of materials.Further studies will consider the stability and reliability

Žof this analysis the ability of one set of data to yieldthe same results regardless of sample ordering or

.method ; the full validity of these results will be testedwith designers; and some of the questions stated abovewill be explored.

Acknowledgements

We gratefully acknowledge helpful inputs from Dr.

Hugh Shercliff and Professor Yves Brechet, and thefinancial support of the Royal Society of London and ofthe EPSRC through its grant to the Cambridge Engi-neering Design Centre.

References

� �1 Everitt B. Cluster analysis. London: Heinemann EducationalBooks Ltd, 1974.

� �2 Lance GN, Williams WT. A generalised sorting strategy forcomputer classifications. Nature 1966b;212:246.

� �3 Jardine N, Sibson R. The structure and construction of tax-onomic hierarchies. Math BioSc 1967;1:173.

� �4 Fisher RA. The use of multiple measurements in taxonomicŽ .problems. Ann Eugenics 1935;VII Pt. II :178�188.

� �5 Kruskal JB, Wish M. Multi-dimensional scaling. California:SAGE Publications, Inc, 1979.

� �6 Ashby MF. Material selection in mechanical design. Oxford:Butterworth Heinemann, 1999.

� �7 SYSTAT software program, Clecom Software Specialists,Birmingham, UK, www.clecom.co.uk.

� �8 Cambridge Engineering Selector software program, GrantaDesign, Cambridge, UK, www.grantadesign.com

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