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Advances in Engineering Materials, Structures and Systems:
Innovations, Mechanics and Applications – Zingoni (Ed.)
© 2019 Taylor & Francis Group, London, ISBN 978-1-138-38696-9
Design of thermally deformable laminates using machine learning
A. Abdel-Rahman
MIT, Cambridge, USA
M. Kosicki
Foster+Partners, London, UK
P. Michalatos
Autodesk, Boston, USA
M. Tsigkari
Foster+Partners, London, UK
ABSTRACT: Recent advances in material science and manufacturing have enabled designers to create objects
which respond to changing environmental conditions by controlled deformation, without external mechanical
or electrical actuation. The design of such smart materials has mostly been done through trial and error due to
their complex nonlinear behavior. This paper will present how this problem is addressed by introducing a novel
inverse design workflow. In this, a desired structural deformation is used as an input to a machine learned model
which subsequently outputs the required geometric and material properties that will produce said deformation
when exposed to an external stimulus. This workflow uses a Generative Adversarial Neural Network (GANN)
trained on pairs of input cut-out patterns of laminate layers and their nonlinear Finite Element Analysis (FEA)
simulation results. The method offers a significant performance speed-up while maintaining acceptable levels
of accuracy, especially at the early design stage. This methodology could be further extended to the design of
any nonlinear mechanical deformation.
1 INTRODUCTION
1.1 Motivation
The ability to manufacture components which can
change their shape in response to external environ-
mental conditions, is a desire shared across many
disciplines ranging from aerospace, medicine, elec-
tronics, soft robotics (Majidi 2014) (Wang et al. 2017)
to architecture and the building industry (Addington &
Schodek, 2005) (Szokolay 2008).
In architecture, a facade is a part of a building which
exchanges the most energy with the external envi-
ronment. Contemporary buildings, especially those
with fully glazed envelopes, must continuously adapt
to ever-changing external conditions to protect their
interior spaces. This raises the need for precise con-
trol of lighting, humidity and solar radiation, with the
facade being most often used as an interface. This issue
has been traditionally mitigated by static or dynamic
shading systems. Such facade components rely primar-
ily on mechanical hinges, sensors, multiple actuation
devices and controls. Today most adaptive facades,
such as the shading system designed by Jean Nouvel
for the south façade of the Arab World Institute in Paris
(1987) or Al Bahr’s modular screen in Abu Dhabi by
Aedas (2012), are still based on mechanical, usually
electrically-driven systems (Kolarevic and Malkawi
2005).
Achieving similar performance should be made
possible without the need of mechanically actuated
systems, but rather dynamic materials which can react
like living organisms. One such example is elec-
trochromic glass, which controls its transparency (and
therefore solar gains), by passing electrical current
through a layer of coating (Carmody et al. 2004).
One of the pioneering examples of a passive and
autonomous skin system was developed by Decker and
Yeadon (2010) in their homeostatic facade. They used
dielectric elastomer attached to silver electrodes on
both sides of the façade and wrapped over a flexible
polymer core. The silver reflects and diffuses light,
while distributing an electrical charge across the elas-
tomer causing the flexible core to bend.This biological
approach to dynamic architectural systems remains
rare due to many technical challenges and significant
prototyping costs of highly customizable components.
Therefore, this research is a part of a bigger effort
to develop an integrated workflow for the design and
1016
fabrication of passively actuated, adaptive building
facade elements.
1.2 Passively actuated systems
One of the most successful approaches to the afore-
mentioned problem, relies on using self-folding
kirigami and origami structures or auxetic materi-
als (materials with a negative Poisson’s ratio) and
transforming various forms of energy into mechanical
actuation (Tolley et al. 2014) (Javid et al. 2015) (Shan
et al. 2015) (Liu and Bertoldi 2015) (Mousanezhad
et al. 2015) (Liu et al. 2016) (Connolly et al. 2016)
(Deng et al. 2017) (Rafsanjani and Bertoldi 2017)
(Boatti et al. 2017) (Deng et al. 2017). This origami-
inspired approach, as shown by Peraza-Hernandez
et al. (2014), is challenging when it comes to rapid
and precise fabrication of highly complex 3D struc-
tures. Most of the currently used folding logic could
be divided into two groups: hinge type and bending
type. In the hinge type approach, the folds are clearly
restricted to structurally pre-determined hinge loca-
tions. The bending category on the other hand, does
not rely on discrete hinge systems but is based on
direct sheet bending triggered by actuation of an active
material. This type of actuation allows much greater
foldability than using hinges. This occurs because,
unless mechanically restricted, the fold can arise at
any place and direction to which the actuating force
is applied. Bending systems can be manufactured as
single or multi-layer laminates containing various dis-
tributions and cut out patterns of active and passive
material. The laminates are predominantly manufac-
tured as 2D structures, so they could be quickly and
accurately fabricated using either lithographic tech-
niques (Zhang et al. 2015, Maune et al. 2010) or
additive multi-material 3D printing (Khoo et al. 2015).
Boatti et al. (2017) demonstrated that by combining
physical experiments and digital simulations, a wide
range of origami metamaterials with varying ther-
mal expansion coefficients could be designed. The
widespread approach to designing 3D morphologies
for such systems is by creating a digital prototype of
a 2D predecessor, with a predefined geometry and/or
a pattern of cuts. Then external forces are applied by
running a non-linear Finite Element Analysis (FEA)
simulation while observing the resulting deforma-
tion. Given the complex nature of the simulation, the
process requires a sophisticated and highly-accurate
simulation software. The FEA simulations are pre-
dominately used one way, from a 2D prototype to a 3D
buckled model. Therefore, designing a geometry and
material distribution for a 2D predecessor becomes a
core problem, which has not been well addressed due
to its computational complexity deriving by the size of
its design space. Xue et al. (2017) tackled it with topol-
ogy optimization solved with a Genetic Algorithm.
This approach, however successful, required a lot of
processing time and did not give real-time feedback
and design flexibility which are crucial at early design
stages. The current methods are time-consuming and
difficult to apply, especially when a specific final 3D
complex shape is desired. As previously shown, 3D
deployable structures are mostly designed by trial and
error and no systematic real-time tool exists that could
produce an initial multilayer material cut-out pattern
for a desired 3D complex shape. Current methods are
also not suitable for the early design stage when many
topologically different design alternatives should be
taken into consideration and where fast feedback is
much more valuable than accuracy.
Therefore, implementing a system capable of pre-
dicting a material distribution with a controllable level
of accuracy, for a given 3D morphology could be of a
great benefit to the design process. Recent advance-
ments in the fields of Machine Learning (ML) and
cognitive computing (Jordan and Mitchell 2015) pro-
vide us with effective methods of building predictive
models purely based on data. In the context of design-
ing a 3D morphology the FEA simulations could
be providers of well-structured and organized data
repositories. Ramprasad et al. (2017) point out that
learning from such data repositories in the context of
material science can lead to recognition of previously
unknown correlations between properties or qualita-
tive and quantitative rules. These can be culminated
in surrogate models which could then be used to pre-
dict material properties orders of magnitude faster and
cheaper and with reduced human effort. The accuracy
of such models is adaptive, meaning that as more data
accumulates, their power increases. To take advan-
tage of machine learning the data must be structured
as input-output pairs. In the context of the discussed
problem the input is a desired 3D morphology and
the output is a 2D material cutout pattern which can
produce said 3D morphology under a given stimulus.
2 METHODOLOGY
In this section a system capable of generating rapid
predictions of 2D cutout patterns from a given 3D
deformation was proposed and tested. The predic-
tions were generated by a generative adversarial neural
network (GANN) trained on a data generated by a non-
linear FEA simulation of flat laminates exposed to heat
buckle. The laminates were modelled as consisting of
layers differing in thermal expansion coeff icients.Two
geometrical models were created and evaluated. The
first focused on 1D deformation of long laminated
strips and the second, on a square-shaped laminate
exhibiting shell-like behavior. Both models targeted
self-folding behavior by using a three-layer laminate
structure with two active layers and one passive layer.
In such arrangements the passive layer generates neg-
ligible mechanical work compared to the active layers
when exposed to external thermal stress. When such
thermal stress is applied, the active layer is forced to
deform, usually axially, while the passive layer is not.
This difference in expansion or contraction between
the two layers generates localized bending of laminates
(Peraza-Hernandez et al. 2014).
The use of Machine Learning (ML) aimed at pre-
dicting a 2D cutout pattern by providing a target
1017
Figure 1. Proposed Workflow. From user-def ined deforma-
tion through a trained neural network to a predicted material
cutout pattern.
deformation. More broadly the task was to map an
input data into corresponding output data, which
is known in ML literature as supervised learning
(Bishop. 2008). Over the past years many algo-
rithms capable of doing supervised learning have
been developed, including linear regression, support
vector machines, decision trees and deep neural net-
works. Deep Neural Networks (DNN) have the most
widespread use due to their optimal performance over
other techniques. One of the most effective solutions
using a variation of DNN is pix2pix, a Conditional
Adversarial Neural Network (GANN) developed by
Isola et al. (2016). The network proved to be effective
in a variety of image related tasks e.g. synthesiz-
ing photos from label maps, reconstructing objects
form edges or colorizing images without the need
of hand-tuning the network’s architecture or tweaking
its parameters. The research presented in this paper
adapted a Tensorflow (Abadi 2016) implementation
of the pix2pix network trained on pairs of images
(Figure 1).
Training data for the neural network was produced
by two parametric models capable of generating varia-
tions of each type of analyzed geometry. It was devel-
oped in Rhinoceros (Robert McNeel & Associates)
CAD environment using its parametric modelling plat-
form Grasshopper. Each parametric model described
a design space of material distribution for a given type
of laminate. The design space was then automatically
sampled to build a training set for the machine learn-
ing algorithm. The detailed description of each model
is provided in the next section. The ML algorithm
required inputs as set of images with a constant num-
ber of pixels. Therefore, a quad mesh, with a constant
number of faces, was used to model each laminate. The
faces were mapped to pixels and the material proper-
ties of each face were encoded in grayscale as follows:
the passive layer being white, the active upper layer
black and the active bottom layer grey (Figure 2).
After running the FEM simulation, the resulting 3D
deformation of each sample was also encoded as a
displacement map; an image with the same resolution
as the matching input image. For the displacement
map, the full RGB spectrum was used to maximize
discrete displacement states stored for each sample.
This approach ensured a clear data structure where
each material distribution image corresponded to a
displacement image.
All samples were evaluated using Autodesk
Explicit, a nonlinear FEA solver to simulate
responses of the geometries under thermal stresses.
Figure 2. Laminated pieces bitmap representation.
A distributed computing system was used to speed-
up the simulations. The simulations were parallelized
using bespoke software and distributed over 400
CPUs using Foster+Partners on-premise computing
infrastructure.
3 RESULTS AND DISCUSSION
3.1 Introduction
In this section, detailed information of the two mod-
els will be presented to demonstrate the effectiveness
of using ML in the design of thermally actuated
geometries.
3.2 Model 1
The first is a simplified model of a family of longi-
tudinal laminate strips (20 cm by 6 cm) to study the
relative deformation in two dimensions. The strips
were meshed uniformly in low resolution (16 by 5
faces) and the left column of vertices was assumed
to have fixed nodes. To generate the training and test
sets, a total 600 random samples were generated. In
each sample, each column of mesh faces was randomly
assigned one of three material setting: passive mate-
rial, passive with an active top layer, passive with an
active bottom layer. These iterations were bulk simu-
lated using Autodesk’s Explicit Solver according to the
following settings. A uniform increase in temperature
(15 degrees ◦C) throughout 1.0 second was introduced
to actuate the membrane. To speed up the simulations,
and since the tests were not concluded against real
physical models, dummymaterial settings were used to
amplify the mechanical deformation. Both passive and
active materials had a Young’s modulus of 69 MPal,
Poisson ratio of 0.334, density of 2700kg/mm3and
thickness of 0.01 mm.The first material (active) had a
high expansion coefficient of 0.01 mm/◦C, and the sec-
ond material (passive) had a lowexpansion coeff icient:
0.00001 mm/◦C.
The next step was the translation of the input mod-
els and FEA findings into 2D images for them to be
trained using the proposed method. The meshes were
mapped into input grayscale bitmaps (256 by 256 px)
where grey, white and black expressed the different
material settings (Figure 3).
As for the FEA results, the mesh deforma-
tion achieved after 1.0s was translated into output
grayscale bitmaps according to the following strategy:
a surface was first reconstructed from the deformed
1018
Figure 3. Translation of material settings and deformation
to bitmaps (model 1).
Figure 4. Mean curvature calculation.
Figure 5. Desired Deformation (white) vs Predicted
Defor-mation (blue) A) Samples Performing Poorly, B) Top
Perform-ing Samples.
vertices, and since the membranes are treated as lin-
ear strips and only the 2D deformation is of interest,
the mean curvature was calculated at the middle of the
strips in a number of points and mapped smoothly into
an output bitmap (from −1 to 1, to 0–255) (Figure 3-
4). The next step was to use the test set output images
(desired deformation) and the trained machine learn-
ing model to predict input cut out patterns. Lastly, to
evaluate the prediction, the predicted cut out patterns
were re-simulated using the FEA solver and compared
to initial desired deformations.
Figure 5 shows examples of the top performing
samples and some that had low performance using
the root mean squared error (RMSE). The ones that
had large desired deformation had higher error that
the flatter examples, however the predicted model was
able to capture the general curvature of the desired
deformation. The average root mean squared error for
all samples is 0.37 (Figure 5–6).
3.3 Model 2
Model 2 tested the applicability of the proposed
method for more complex doubly-curved deformed
Figure 6. Predicted vs Desired Mean Curvature for all the
points in all the samples for Model 1.
Figure 7. Probability Density Function for Root Mean
Squared Error for Model 1.
membranes. The meshes tested in this model were
much coarser (41 by 41) and supported at the center of
the mesh by a fixed point. To generate a family of ran-
dom complex cutout patterns, the interference of four
random set of wave functions was used to generate 300
3D surfaces (Equation 1).
Equation 1: x, y and z are the vertices positions, a =1,
u and v are lists of four random values from −1to0.
The surfaces generated were then intersected with
two planes with different heights to threshold and
generate the cutout patterns of the membrane with
the three materials settings (Figure 8). These surfaces
where consequently batch simulated using the FEA
solver with the same material, time and temperature
settings as the first model. The cutout patterns were
mapped into grayscale input images in the same pro-
cess as the first example. The simulation results were
however mapped into RGB bitmaps where the x,y,z
1019
Figure 8. The Random 3D Waves and their Mapping into
Cutout Patterns.
Figure 9. Simulation Results and Output Displacement
Images: the x,y,z displacement values were into rgb.
vertices displacements were mapped into rgb values
(Figure 9). The image pairs were then divided equally
into a training and a testing set. After the model was
trained, the cutout pattern from the testing set was sim-
ulated to evaluate the accuracyof the model. Figures 11
and 12 show that this model had a higher RMSE than
the first model as the required input deformation is
more complex. The average RMSE for all samples
was 0.42. However, Figure 10 shows that the predicted
model is visibly similar to the desired mesh and was
produced in a fraction of a second compared to run-
ning a standard FEM simulation. This means that the
method could be more suited to applications that do
not require high precision. To increase the accuracy
of the method, given a desired membrane deforma-
tion and after the cutout pattern is generated from the
ML model, another optimization step could be done
to reach the desired deformation with a lower RMSE.
4 CONCLUSIONS
This research proposed a new workflow for the design
of complex deployable three-dimensional structures
using machine learning and nonlinear FEA simulation.
Machine learning presents a unique opportunity in
Figure 10. Example of Predicted vs Desired Mesh Defor-
mation.
Figure 11. Predicted vs Desired Mean Curvature for all the
points in all the samples for Model 2.
Figure 12. Probability Density Function for Root Mean
Squared Error for Model 2.
terms of the ability to solve correlations that were
believed to be unsolvable using any other method. The
workflow also offers a distinctive advantage compared
to other evolutionary and optimization techniques
1020
since, once the model is trained, the output is instanta-
neous and within the acceptable level accuracy; one
can get real time results for a desired input. The
proposed workflow offers a fast and systematic way
for the design and exploration of thermally actuated
structures. In future research, this method will be
extended to model other actuation techniques, shapes,
systems (origami and kirigami), as well as any other
three-dimensional geometries.
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