A Design Oriented Workflow to Prototype Functionally Graded Designs based on Solid Finite Element Analysis

Abstract

Multi-material additive manufacturing processes enable the fabrication of 3D objects composed of varying material properties at microscopic scale (Doubrovski et al. [7]). Selective material deposition offers opportunities to design and fabricate objects with heterogonous properties potentially exhibiting superior functional performance characteristics compared to objects comprised of homogenous material distributions (Wu, et al. [23]). Despite the availability of 3D printing hardware capable of producing such objects, access to this new technology is encumbered by the way in which the current modelling and simulation tools represent, exchange, and process information required for multi- material additive manufacturing. We present a computation-based approach for fabricating Functionally Graded Designs (FGD) based on solid Finite Element (FE) analysis results using Multi- Material Voxel Printing technology.

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Proceedings of the IASS Annual Symposium 2016
“Spatial Structures in the 21st Century”
26–30 September, 2016, Tokyo, Japan
K. Kawaguchi, M. Ohsaki, T. Takeuchi (eds.)
Copyright © 2016 by S. Kaijima, Z.Xuereb, M.L.Dunn
Published by the International Association for Shell and Spatial Structures (IASS) with permission.
A Design Oriented Workflow to Prototype Functionally Graded
Designs based on Solid Finite Element Analysis
Sawako KAIJIMA
1
, Zack XUEREB
1
, Martin L. DUNN
1
1
*Singapore University of Technology and Design, 487372, Singapore
sawakokaijima@sutd.edu.sg
Abstract
Multi-material additive manufacturing processes enable the fabrication of 3D objects composed of
varying material properties at microscopic scale (Doubrovski et al. [7]). Selective material deposition
offers opportunities to design and fabricate objects with heterogeneous properties potentially
exhibiting superior functional performance characteristics compared to objects comprised of
homogeneous material distributions (Wu, et al. [23]). Despite the availability of 3D printing hardware
capable of producing such objects, access to this new technology is encumbered by the way in which
the current modelling and simulation tools represent, exchange, and process information required for
multi-material additive manufacturing. We present a computation-based approach for fabricating
Functionally Graded Designs (FGD) based on solid Finite Element (FE) analysis results using Multi-
Material Voxel Printing technology.
Keywords: Multi-material 3D printing, Functionally Graded Design, Volumetric Data
1. Introduction
While the majority of commercially available Additive Manufacturing (AM) printers today deploy a
single material over an object’s volume, recent products such as the OBJET Connex [17] and the
Multi-Fab (Sitthi-Amorn et al. [21]) are capable of mixing and depositing multiple materials at a
microscopic scale. Multi-Material Additive Manufacturing (MMAM) enables the fabrication of three-
dimensional objects with geometries of arbitrary complexity comprised of a wide variety of typically
polymer composites. MMAM technologies enables the design and production of complex 3D artifacts
with heterogeneous material properties such as mechanical, thermal, chemical and optical (e.g. Sitthi-
Amorn et al. [21], Vidimˇc et al. [22]) which gives rise to the notion of Functionally Graded Materials
(FGM) (e.g. Sitthi-Amorn et al. [21], Mahamood et al. [15]). In this paper, we present a workflow for
creating Functionally Graded Designs (FGD) building up on the FGM design approach. Instead of
computationally optimizing the material distribution of an object against a particular functional
criterion, for example, mechanical behaviour, our approach introduces a direct material modelling
process which enables the design of material information in conjunction with functional criteria.
Despite the hardware availability, fabrication of FGD is not a trivial task. This is primarily due to the
access to this new technology being limited by the way in which current modelling and simulation
tools represent, exchange, and process information (Jackson et al. [9]). Our research investigates a
computational FGD workflow that overcomes some of those limitation, an overview thereof is
concisely captured in the figure below (Fig. 1). The document is organized into the following sections:
(a) An overview of current MMAM and relevant computational data structures; (b) Presentation of the
details of our design-to-fabrication process; and (c) Indicative case studies and preliminary results.

Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
2
Figure 1: An overview of our computational FGD workflow
2. Multi-material Additive Manufacturing workflow
The information workflow in AM is comprised of three consecutive phases including (a) geometric
modelling, (b) machine code generation, and (c) digital fabrication. Solid geometries are created in
CAD modelling software, exported as water-tight polygonal STL meshes, imported to vendor-specific
AM software, contoured and converted into machine instructions, and finally transmitted to hardware
for printing. In the case of MMAM, an additional task of volumetric material design specification is
required. It involves the generation of separate water-tight polygonal meshes per material domain and
assignment of material properties through the particular vendor-specific AM software. The software
subsequently contours all mesh geometries into successive layers assuming homogeneous material
distribution per contour (Vidimče et al. [22], Gao et al. [8], Chen and Wang [4]). While this approach
retains compatibility with conventional AM workflows it is certainly not sustainable for the design
with continuously varying material compositions over a substantial volume at a high-resolution. For
example, approximately 1,286,500 water tight meshes are required in order to print a cube of 5cm at
the maximum material resolution using the OBJET 3D printer. As such both geometric modelling and
post-processing are encumbered by the arguably substantial volume of information transactions. An
alternative raster-based, as opposed to vector-based mode, namely Voxel Printing (VP) is supported
by the OBJET 3D printers. Geometry along with its material information is directly transmitted to
hardware as a sequence of raster layers (Doubrovski et al. [7]) similar to volume data sets commonly
used in medical imaging and in computer graphics rendering. Each pixel holds positional and material
information in relationship to the printer’s work envelope and dimensional characteristics of its
smallest material droplet. This rasterization approach is exactly the same employed by conventional
2D printers.
3. Representation of Heterogeneous Object
To generate VP information, it is essential to couple geometry along its material information. This
requires computationally the definition of volumetric data structures such as voxels, rectangular boxes
arrayed in orthogonal 3D grid arrangements, named after being the equivalent of volume pixels, or any
arbitrary space filling compact polyhedral data structure (Wu et al. [23]). While voxel-based models
are common in MMAM due to their efficient translation into 2D raster layers, polyhedral models are
more prevalent in modeling solid FE Analysis.
3.1. voxel structure:
Voxel modeling is a volumetric geometry description approach typically implemented as arrays of
uniform 3D cells where each voxel is literally a small cubic element in 3-space associated with
additional non-geometric information such as material composition (Gao et al. [8], Kou and Tan [13]).
The structure is regarded as a computationally efficient representation for volume data manipulation

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Spatial Structures in the 21st Century
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because of its simple structure and implicit topology (Kaufman et al. [12], Chandru et al.[3]). Voxel
modelling allows for data processing with algorithms similar to those use for image processing such as
blurring, distorting, and mapping. Key drawbacks of modelling using voxels include its requirement
for very large memory footprints and geometric artefacts such as aliasing . Concise summaries of the
advantages and disadvantages of voxel-based modelling have been extensively discussed by Kaufman
et al. [12] and Kou and Tan [13].
3.2. polyhedral mesh-based structure
Solid Finite Element (FE) models commonly employ unstructured grids made of polyhedral, typically
tetrahedra and/or hexahedra, with no implicit connectivity among one another. One of the advantages
of this data structure compared to the voxel-based data structure is its capability to represent geometric
boundaries accurately. In addition, as the cells do not require uniformity of size, the structure is able to
tune data resolution according to geometric features and engineering considerations. However, mesh
generation from solid boundary representation models required in pre-processing as well as for post-
processing data manipulation with such structure can be time consuming due to the inherent
irregularity of the geometric information.
4. Heterogeneous Material Modelling based on FEM
Heterogeneous material information can be directly modelled obtained from empirical measurements
of real-world objects or extracted from computer simulation results. Methods for heterogeneous object
modelling have been studied extensively in the past two decades and a comprehensive review is given
by Kou and Tan [13]. Recent years have seen a growing interest in heterogeneous material modelling
for MMAM based on FEM analysis results. Chiu and Yu [5] proposed a method that assigns local
material properties based on a FE Analysis, Bickel et al. [2], Xu et al. [24] obtains material
distribution for desired deformation behaviour with FE simulation and optimization, and Schumacher
et al. [20] proposed a method for analysing and optimizing object elasticity by pre-analysing periodic
tiles along with specific material composition and interpolation functions. Though these research aim
to achieve a one-to-one mapping of a specific functional criterion to the material, in our research, we
assume another step between FE analysis and AM printing. The additional step is to directly design
material distribution in negotiation with the structural information extracted from the FE analysis.
5. Computational workflow
Our computational workflow transforms solid FE analysis result to fabricate FGD using multi-material
VP, supported by the OBJET Connex 3D printer. The machine uses PolyJet Matrix Technology where
materials are dispensed from designated micro-scale inkjet printing nozzles at approximately 600dpi
equivalent to a physical voxel size of 40um by 80um by 30 um. The primary materials, excluding the
support material, are the Vero and Tango-series where Vero-series materials are thermoset polymers
and come in multiple colours, while Tango-series materials are elastomers and they are only available
in black and semi-clear. By combining those two very different types of materials the printer offers the
capability of producing objects with varying elasticity. And as such, it is possible to design and
prototype structurally graded design solutions. Our method uses Rhinoceros [19] as CAD modelling
platform, ABAQUS [1] for FE analysis, a software tool we developed for material modelling based on
FE results, and Monolith [16] for rasterization.
5.1 Case Study: The Classic Cantilever Beam
As an initial reference study, we document the theoretically well-understood case of a cantilever beam
structure to illustrate the characteristics of the workflow. In this particular instance, the Von Mises
stress gradient determines the distribution of the thermoset polymer (Vero Magenta) and elastomer
(Tango Plus) materials. Principle stress lines are also printed using the same thermoset material (Vero
Magenta) which is analogous to fibre reinforcement (Fig 2).

Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
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Figure 2: a photo of a FGD prototype of a cantilever beam
totally fixed at the left corner with load at the right top side of the beam.
Initially, we modelled the boundary representation (B-Rep) of a rectilinear box using the CAD
software. Subsequently, we performed standard pre-processing operations for FE analysis such as
assignment of material properties, loading and boundary conditions as well as discretization of the
solid into polyhedral elements. The FE analysis calculation produced results consisting of response
values calculated at vertices/nodes and cells/elements. Typically, for post-processing purposes, cell
results are extrapolated and stored at vertices. This information per vertex becomes the input for the
material design step. Each vertex contain positional information as well as any FE result information
such as {x, y, z, s11, s22, s33, s12, s13, s23, vm } where s11 to s33 denotes normal stress tensor
values, s12 to s23 denotes shear stress tensor values and vm denotes the Von Mises stress value.
To move towards 3D volume printing we perform voxelization for the FE results, where we convert
the polyhedral mesh structured data into voxels. This requires the computation of the integrals over the
intersection volumes between cubical voxel cells and the input polyhedral. Voxelization of polyhedral
models was first proposed by Kaufman and Shimony [11] and there are multiple known algorithms for
efficient and accurate voxelization (Powell and Abel [18]).
As outlined earlier our process incorporates a material design process in reflection of the FE results.
From a computational design perspective, it is important to select an appropriate voxel resolution for
this process. The resolution must be high enough to capture important FE information critical for the
interpretation of the results and design while retaining the memory use low enough for interactive
material modelling. As such the native printer voxel resolution of 600dpi is too high for the material
design process. On the other hand, the design may require refined geometric features that mandate for
full print resolution. We thus implemented and combined two different information representations:
(a) A voxel modelling sub-system for perceptually amorphous material design and (b) An analytical
geometry modelling subsystem to support entities such as curves and solids for more discrete material
assignment.
Figure 3: Screen captures of the custom tool where dots colour coded by normalized von miese stress are placed
at the centre of each voxel. Left: voxelization at a low-resolution Right: voxelization at a higher resolution

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5.1.1 Voxel Sub-System
Perceptually amorphous material distribution employs primarily the Von Mises stress information
contained per voxel as {x, y, z, vm, nvm}, where nvm denotes the normalized Von Mises stress into
the unit range. With this data attributes, we can interpolate material composition such as nvm of 0.0
maps onto 100% elastomer material, 1.0 maps onto 100% thermoset material while nvm = 0.5
represents a ratio or 1:1. When the Von Mises data distribution is too skewed or noisy we use
statistical methods to equalize the data. An interesting opportunity for visualizing spatially distributed
properties is by using volumetric texture mapping methods used in computer graphics to apply per
voxel patterns, use of mathematical functions for filtering, overlay of information onto the existing
normalized Von Mises distribution and/or using external non-structural attributes associated with
voxels.
Figure 4: Examples of possible material designs by interpreting the FE results using Monolith. Left: iso-surface
extracted from the nvm field, Right: periodic pattern mapping to nvm field
Subsequent to the material distribution design, we generate raster bitmap information required for
printing. As the bitmap corresponds directly to physical material and location in the printer’s work
envelope, pixel density must correspond to the printer’s resolution. Each pixel value is computed by
trilinear interpolation of the voxel material values. The printer’s layer thickness is 30um so the voxel
model is contoured by this dimension to create bitmaps per layer. One pixel corresponds to physical
dimensions of 40um by 80um. The printer requires one monochrome mask per material per layer
where white specifies presence while black the absence of material. Therefore, the total number of
bitmap files generated equals to the number of material types times the number of layers.
5.1.2 Geometry Sub-System
However, as we operate on medium to low voxel resolution for material design, the boundary of the
geometry is not accurately represented; a problem known as aliasing in computer graphics which
presents itself as stepped edges along the boundaries of shapes. This may not be apparent in the case
of the axis-aligned rectilinear volumes it becomes problematic especially when the global geometry
contains complex boundaries (Fig 5).

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Spatial Structures in the 21st Century
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Figure 5: An element with a hole in the middle where voxel stepping effect can be observed with the voxel data
structure. Left: FE polyhedral data structure, Right: voxel data structure
To resolve aliasing we utilize geometric information that is best at representing discrete shapes such as
B-Reps and spline curves. We scan convert those to extract intersection geometry per layer as well as
to operate on the layer bitmaps at printer resolution to achieve smooth anti-aliased boundaries. For the
principle stress flow lines physical thickness is assigned as a radius around the intersection points with
the contour planes (Fig. 6). Figure 7 shows printed prototypes where the left image shows the case
printed with homogeneous material composed of 20% thermoset and 80% elastomer, and the right side
shows the case designed using our FGD workflow. Though in this instance, we miss the analysis-
optimization cycle to reflect the principle stress streamlines to adapt to the new material distribution,
reduction in stress concentration around the support can be observed from the simple prototypes.
Figure 6: Monochromatic bitmaps for printing with two types of materials. Top: a layer for thermoset material,
Bottom: the same layer for elastomer material
Figure 7: Left: a physical prototype printed in homogeneous material composed of
20% thermoset, 80% elastomer material, Right: a physical FGD prototype designed with our workflow

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Spatial Structures in the 21st Century
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5.2 Case 2: Interlocking Joint
The process is applied to a more complex case of the Basara Joint, a topologically interlocking joinery
found in traditional Japanese timber structure which is part of our broader research investigation
(Kaijima et al. 31). The figure below illustrates a process comprised of (a) Solid FE Contact Analysis,
(b) Material Design, (c) Segmentation and Rasterization and (d) Rapid Prototyping.
Figure 8: computational workflow with the interlocking joint example
In the case of interlocking joineries, it is difficult to understand the complex stress distributions within
the solids. Typically, in order to understand the inner workings of the solid geometry, we use two
dimensional sectional visualisations and/or rely on numerical values to understand the phenomena.
Both approaches are useful yet pose difficulties in communicating with the wider audience. Therefore,
the multi-material printing, in this case, is used for physical 3D visualization of complex stress
distributions inside the solids. The case uses coloured thermoset material for stress visualization inside
a clear thermoset material. The Material Design step in the case includes the use of statistical methods
to equalize the extremely skewed Von Mises values due to the stress concentrations around the sharp
edges of the joint geometry. In addition, the thickness and the density of principles stress streamlines
are decided based on visual qualities in considering optimal wood grain directions for the joinery. This
is assuming in the future we may be able to 3D print organic materials with varying mechanical
properties. Furthermore, the particular problem of assembly revealed a need for material design based
on surface friction and contact considerations which we are investigating at the moment.
5.3 Case Study: A Table Leg
The final case presented is from a furniture design, namely the analysis of a table’s leg, to illustrate
another aspect we consider useful in the voxelization of FE polyhedral mesh process. In many
instances, a component of interest is oriented in space and analysed concerning the overall structure
and connectivity (Fig. 9). However, it is inefficient to voxelize such component with respect to the
global coordinate system. This is because the volume domain for voxelization becomes large
increasing the memory consumption, while a large number of voxels may not hold any information.
The issue can be improved by finding the minimum bounding box of the component for voxelization.
The two cases shown in Figure 10 use approximately the same number of voxels. The resultant data
resolution illustrates the importance of the consideration in efficiently capturing the analysis data.

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Spatial Structures in the 21st Century
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Figure 9: Left: FE analysis of an assembled table leg, Right: a particular leg element for multi-material printing
Figure 10: Left: voxelization without adjusting the bounding box,
Right: voxelization with minimum bounding box
6. Conclusions
Multi-material additive manufacturing (MMAM) offers opportunities for one to design and prototype
objects with heterogeneous properties holding superior functional performance over objects made of
homogeneous materials. Although current MMAM technology, due to its material selection and scale,
is used for prototyping and not immediately deployable for buildings, developing a computational
framework for FGM and FGD could significantly impact the future architecture and structural design.
The paper presented a computational workflow to prototype FGD based on FE analysis. In order to
describe and control both geometry and heterogeneous material distribution, we use multiple data
structures suitable for each operation. The process required data exchange among four different
software tools, which highlights the need for new CAD systems to integrate material modelling
considerations. In addition, programmable interface to MMAM hardware would improve the
workflow efficiency.
Acknowledgements
The research is funded by the SUTD-MIT International Design Centre and the Digital Manufacturing
and Design Centre. In addition, this research was conducted on the Stratasys Connex3 through
Stratasys’ Voxel Print Research Program, which enhances the value of 3D printing as a powerful
platform for experimentation, discovery and innovation. For more information contact Stratasys
Education, Academic Research and Development Unit: academic.research@stratasys.com.
References
[1] ABAQUS, Version 6, Dassault Systèmes, France
[2] Bickel, Bernd, et al. "Design and fabrication of materials with desired deformation behavior."
ACM Transactions on Graphics (TOG) 29.4 (2010): 63.

Proceedings of the IASS Annual Symposium 2016
Spatial Structures in the 21st Century
9
[3] Chandru, Vijay, Swami Manohar, and C. Edmond Prakash. "Voxel-based modeling for layered
manufacturing." Computer Graphics and Applications, IEEE 15.6 (1995): 42-47.
[4] Chen, Yong, and Charlie CL Wang. "Regulating complex geometries using layered depth-normal
images for rapid prototyping and manufacturing." Rapid Prototyping Journal 19.4 (2013): 253-
268.
[5] Chiu, W. K., and K. M. Yu. "Direct digital manufacturing of three-dimensional functionally
graded material objects." Computer-Aided Design 40.12 (2008): 1080-1093.
[6] Cho, W., et al. "Methods for distributed design and fabrication of parts with local composition
control." Proceedings of the 2001 NSF Design and Manufacturing Grantees Conference. 2001.
[7] Doubrovski, E. L., et al. "Voxel-based fabrication through material property mapping: A design
method for bitmap printing." Computer-Aided Design 60 (2015): 3-13.Wu, X. L., et al.
"Synergetic strengthening by gradient structure." Materials Research Letters 2.4 (2014): 185-
191.
[8] Gao, Wei, et al. "The status, challenges, and future of additive manufacturing in engineering."
Computer-Aided Design 69 (2015): 65-89.
[9] Jackson, Todd R., et al. "Memory analysis of solid model representations for heterogeneous
objects." Journal of Computing and information Science in Engineering 2.1 (2002): 1-10.
[10] Kaijima S., Conti Z. X., and Dunn M. L. "Parametric Finite Element Contact Analysis for
Topologically Interlocking Joinery.", in Proceedings of the International Association for Shell
and Spatial Structures (IASS), 2015.
[11] Kaufman, Arie, and Eyal Shimony. "3D scan-conversion algorithms for voxel-based graphics."
Proceedings of the 1986 workshop on Interactive 3D graphics. ACM, 1987.
[12] Kaufman, Arie, Daniel Cohen, and Roni Yagel. "Volume graphics." Computer 26.7 (1993): 51-
64.
[13] Kou, X. Y., and S. T. Tan. "Heterogeneous object modeling: A review." Computer-Aided Design
39.4 (2007): 284-301.
[14] Laine, Samuli. "A topological approach to voxelization." Computer Graphics Forum. Vol. 32.
No. 4. Blackwell Publishing Ltd, 2013.
[15] Mahamood, Rasheedat M., et al. "Functionally graded material: an overview." Proceedings of the
World Congress on Engineering, WCE 2012, 2012.
[16] Monolith, Autodesk, USA, http://www.monolith.zone
[17] OBJET. Connex multi-material 3D printing system, Stratasys.
[18] Powell, Devon, and Tom Abel. "An exact general remeshing scheme applied to physically
conservative voxelization." Journal of Computational Physics 297 (2015): 340-356.
[19] Rhinoceros, Version 5.0, Robert McNeel & Associates, USA
[20] Schumacher, Christian, et al. "Microstructures to control elasticity in 3D printing." ACM
Transactions on Graphics (TOG) 34.4 (2015): 136.
[21] Sitthi-Amorn, Pitchaya, et al. "MultiFab: a machine vision assisted platform for multi-material
3D printing." ACM Transactions on Graphics (TOG) 34.4 (2015): 129.
[22] Vidimče, Kiril, et al. "Openfab: A programmable pipeline for multi-material fabrication." ACM
Transactions on Graphics (TOG) 32.4 (2013): 136.
[23] Wu, Xiaojun, Weijun Liu, and Tianran Wang. "Voxel-based model and its application in
advanced manufacturing." Fourth ionternational conference On Virtual Reality and Its
Applications in Industry. International Society for Optics and Photonics, 2004.
[24] Xu, Hongyi, et al. "Interactive material design using model reduction." ACM Transactions on
Graphics (TOG) 34.2 (2015): 18.