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Rotational multimaterial printing of filaments with subvoxel control


Helical structures are ubiquitous in nature and impart unique mechanical properties and multifunctionality1. So far, synthetic architectures that mimic these natural systems have been fabricated by winding, twisting and braiding of individual filaments1,2,3,4,5,6,7, microfluidics8,9, self-shaping1,10,11,12,13 and printing methods14,15,16,17. However, those fabrication methods are unable to simultaneously create and pattern multimaterial, helically architected filaments with subvoxel control in arbitrary two-dimensional (2D) and three-dimensional (3D) motifs from a broad range of materials. Towards this goal, both multimaterial18,19,20,21,22,23 and rotational24 3D printing of architected filaments have recently been reported; however, the integration of these two capabilities has yet to be realized. Here we report a rotational multimaterial 3D printing (RM-3DP) platform that enables subvoxel control over the local orientation of azimuthally heterogeneous architected filaments. By continuously rotating a multimaterial nozzle with a controlled ratio of angular-to-translational velocity, we have created helical filaments with programmable helix angle, layer thickness and interfacial area between several materials within a given cylindrical voxel. Using this integrated method, we have fabricated functional artificial muscles composed of helical dielectric elastomer actuators with high fidelity and individually addressable conductive helical channels embedded within a dielectric elastomer matrix. We have also fabricated hierarchical lattices comprising architected helical struts containing stiff springs within a compliant matrix. Our additive-manufacturing platform opens new avenues to generating multifunctional architected matter in bioinspired motifs.

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Fig. 1: Rotational multimaterial 3D printing of architected filaments with programmable subvoxel control.
Fig. 2: Patterning geometric complexity across scales.
Fig. 3: HDEA filaments.
Fig. 4: Springy filaments and lattices.

Data availability

The main data supporting the findings of this study are available within the paper and its Supplementary Information. Other datasets generated or analysed during the current study are available from the corresponding author on request. Source data are provided with this paper.


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We gratefully acknowledge support from the National Science Foundation under the Materials Research Science and Engineering Centers (DMR-2011754), National Science Foundation Designing Materials to Revolutionize and Engineer our Future (DMREF-15-33985), the Vannevar Bush Faculty Fellowship Program, sponsored by the Basic Research Office for the Assistant Secretary of Defense for Research and Engineering through the Office of Naval Research grant N00014-21-1-2958, and the GETTYLAB. We thank L. K. Sanders for assistance with photography and videography, J. W. Williams for assistance with the Python image analysis pipeline and E. Hajiesmaili, N. Colella, M. Kollosche, S. G. M. Uzel, A. Kotikian, R. D. Weeks, D. Kokkinis, D. Barber, E. Davidson, D. Foresti and E. Guzman for experimental assistance and helpful discussions.

Author information

Authors and Affiliations



N.M.L., J.M., A.C., Z.S.D. and J.A.L. designed the research. N.M.L., J.M., A.C. and Z.S.D. performed the research. N.M.L., J.M., A.C., Z.S.D. and D.R.C. analysed the data. N.M.L., J.M., A.C., Z.S.D., D.R.C. and J.A.L. prepared the manuscript.

Corresponding author

Correspondence to Jennifer A. Lewis.

Ethics declarations

Competing interests

A US patent has been filed by Harvard University on this research. J.A.L. serves on Advisory Boards for Autodesk, Azul 3D, and Desktop Health (a subsidiary of Desktop Metal, Inc.).

Peer review

Peer review information

Nature thanks Brittany Newell and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Shell–fan-core nozzle used for RM-3DP of PDMS inks.

ae, Nozzle for RM-3DP in the prototypical printing configuration (θP = 90°, θD = 0°). a, Top view of 3D model of entire nozzle showing four Luer lock fittings for connecting to syringes and square mounting component for coupling to centring stage. b, Side view of 3D model of entire nozzle. c, Section view of 3D model of entire nozzle from same viewing direction as b, with section taken along the dashed line in a. d, Dimensions of nozzle tip overlaid on 3D model of nozzle tip. ID, inner diameter; OD, outer diameter. e, Ideal filament cross-section dimensions for Q* = 1 assume extruded inks extend to half of the wall thickness, dividing the fans from the fan-core and shell. These dimensions were used to calibrate volumetric flow rates before printing. fh, Various views of 3D model of long shell–fan-core nozzle for RM-3DP in the angled printing configuration (θP < 90°, θD = 0°). Nozzle-tip dimensions and estimated filament cross-section dimensions are identical to those of the shorter nozzle illustrated in ae. f, 3D model of tip geometry. g, Top view of 3D model of entire nozzle. h, Section view of 3D model of entire nozzle, with section taken along the dashed line in g.

Extended Data Fig. 2 Effects of printing configuration and printing parameters on PDMS filament and subvoxel geometry.

PDMS filaments were extruded from shell–fan-core nozzles presented in Fig. 1b and Extended Data Fig. 1. Scale bar: 5 mm.

Extended Data Fig. 3 Rheological properties of printable inks.

Log–log plots of the apparent viscosity as a function of shear rate (a,c,e) and the shear moduli as a function of shear stress (b,d,f) for the uncured PDMS ink (a,b), the uncured dielectric elastomer and conductive carbon inks for HDEA filaments (c,d) and the uncured soft acrylic and stiff acrylic inks for springy filaments and lattices (e,f).

Source data

Extended Data Fig. 4 Materials and nozzle geometry for springy filaments and lattices.

ac, Tensile testing of cured soft, stiff and mixed acrylic base materials. a, Stress–strain curves for N = 17 tensile tests for cured soft acrylic (Young’s modulus = 0.52 ± 0.03 MPa; mean ± s.d.), used as both the dielectric elastomer ink in the HDEAs and as the soft structural ink in the springy filaments. b, Stress–strain curves for N = 9 tensile tests for cured stiff acrylic (Young’s modulus = 2,700 ± 200 MPa; mean ± s.d.). c, Stress–strain curves for N = 11 tensile tests for a fully mixed combination of the stiff and soft acrylic base materials in a 50:50 volume ratio (Young’s modulus = 220 ± 20 MPa; mean ± s.d.). d,e, Fan-core geometry used in RM-3DP of springy filaments and lattices. d, Dimensions of nozzle tip overlaid on 3D model of nozzle tip. e, Ideal filament cross-section dimensions for Q* = 1 assume extruded inks extend to half of the wall thickness, dividing the fans from the fan-core. These dimensions were used to calibrate volumetric flow rates before printing.

Source data

Extended Data Fig. 5 Material properties and nozzle geometry for HDEA filaments.

a,b, Dielectric constant of crosslinked dielectric elastomer ink. a, Static dielectric constant measurements. A Randles CPE model was found to fit the data better than a resistor in series with a parallel resistor and capacitor (R-(RC)). b, Dynamic dielectric constant for two specimens. For each specimen, capacitance measurements were performed three times. The plotted data points represent the average dielectric constant computed from the three measurements. For the tested capacitance, low-frequency measurements are expected to be of low accuracy owing to device signal noise. c, Conductivity measurement of carbon-black-based conductive electrode ink. Plot of total resistance, RT, versus gap height, g, using an AC signal frequency of 1 kHz. Linear regression of RT versus g gives a slope, ρ/Ap, of 260,000 ohm m−1 with a standard error of 54,000 ohm m−1, in which ρ is the resistivity of the ink and Ap is the area of the parallel plate. Thus, the resistivity of the ink ρ = 130 ± 30 ohm·m (mean ± standard error) and the conductivity, σ = 1/ρ, is 8 × 10−3 ± 2 × 10−3 S m−1 (mean ± standard error). d,e, Shell–fan-core geometry for RM-3DP of HDEAs. d, Dimensions of nozzle tip overlaid on 3D model of nozzle tip. e, Ideal filament cross-section dimensions for Q* = 1 assume extruded inks extend to half of the wall thickness, dividing the fans from the fan-core and shell. These dimensions were used to calibrate volumetric flow rates before printing, to compute dielectric layer thicknesses and to create filament geometries for finite element analysis simulations.

Source data

Extended Data Fig. 6 HDEAs fabricated with printhead at an angle and deposition surface oriented horizontally.

a, Photograph of HDEA filament deposition with UV curing on the fly. The filament being printed in the photograph has ω* = 5. The top, near and far sides of the filament are labelled for reference for the following images. b, Microscope images showing the top, under, near and far sides of a filament with ω* = 5, showing the warping of the helical architecture. The angle of the helical features on the outer surface on the far side (about 81°) is notably higher than that on the near side (about 68°). Also note that the filament surface on the top side is slightly bumpy, whereas the surface on the underside is relatively smooth. Scale bar: 1 mm. c, Photograph of actuation of an HDEA with ω* = 5, showing the filament at 0 kV and 9 kV applied voltages. The filament contracts slightly in the axial direction, twists in the direction that tightens the helix and bends towards the far and top sides. Scale bar: 5 mm.

Extended Data Fig. 7 Actuation of HDEAs printed in the vertical configuration (θP = 90°, θD = 90°).

Photographs of side views and bottom views of several HDEAs before actuation (0 kV) and during actuation (>0 kV), showing filament twisting and axial extension (ω* = 1) or contraction (ω* = 5, 10 and 15). Examples of both bare filaments (a) and speckled filaments (b) (for twist and axial strain measurements) are shown. Scale bars in a and b: 5 mm. In c, magnified views of the filaments in a are provided. Scale bar: 1 mm.

Extended Data Fig. 8 Tensile measurements on springy filaments.

ak, Stress–strain curves for springy filaments with ω* ranging from 0 to 5 (N = 5 for all). l, Failure strain of springy filaments as a function of ω*.

Source data

Extended Data Fig. 9 Springy 3D lattices.

ad, Photographs of springy lattices composed of filaments with ω* = 0 (a), ω* = 0.75 (b), ω* = 3 (c) and a gradient in ω* ranging from 0 to 3 in the 0° direction and ω* = 0 in the 90° direction (d). Scale bar: 10 mm. e, Image of one of the cut faces of a springy lattice with a gradient in ω* in the 0° direction. The spanning of the filaments across gaps in the woodpile lattice results in slightly wavy, rather than straight, filaments within the structure. The wavy nature of the filaments is expected to influence the mechanical properties of the lattices. Scale bar: 4 mm.

Extended Data Fig. 10 Tensile measurements on 3D lattices.

ac, Stress–strain curves for springy lattices composed of filaments with ω* = 0 (N = 2) (a), lattices composed of only stiff acrylic filaments (N = 3) (b) and lattices composed of only soft acrylic filaments (N = 3) (c). d, Moduli of springy lattices as a function of ω* (N = 2 for each ω*). Solid grey lines are the moduli of the springy lattices with a gradient in ω* in the 0° direction (N = 2), solid blue lines are the moduli of the lattices composed of pure stiff acrylic filaments (N = 3) and solid black lines are the moduli of the lattices composed of pure soft acrylic filaments (N = 3).

Source data

Supplementary information

Supplementary Information

This file contains Supplementary Information on rotational multimaterial 3D printing, mechanical measurements, HDEA filament actuation, analytical modelling of HDEAs and finite element simulations of HDEAs. This file also contains Supplementary Figures 1–9.

Supplementary Video 1

RM-3DP of a multimaterial PDMS filament using a vertically oriented printhead (θP = 90°) in which ink deposition occurs in the horizontal plane (θD = 0°).

Supplementary Video 2

RM-3DP of a multimaterial PDMS filament with an angularly oriented printhead (θP = 25°) in which ink deposition occurs in the horizontal plane (θD = 0°).

Supplementary Video 3

RM-3DP of 1D filaments with gradients in ω*, switching in ω* and alternating chirality.

Supplementary Video 4

RM-3DP of 2D square spirals with 90° printhead rotation at each corner to ensure blue ink remains on the outside of the trace.

Supplementary Video 5

RM-3DP of 3D helical patterns with: (i) no nozzle rotation, (ii) nozzle rotation at ω* = 2 and (iii) one nozzle rotation per printhead revolution.

Supplementary Video 6

RM-3DP of HDEAs with ω* = 1, 5, 10 and 15 using the vertical printing (θP = 90°, θD = 90°) configuration with UV curing on the fly.

Supplementary Video 7

Fabrication and actuation of HDEA printed with θP = 15°, θD = 0° and ω* = 5.

Supplementary Video 8

Actuation of several HDEAs printed in the vertical configuration. Sine wave voltage applied at 0.1 Hz to maximum voltage indicated.

Supplementary Video 9

RM-3DP of springy 1D filaments with UV curing on the fly.

Supplementary Video 10

Tensile test of springy 1D filament with ω* = 3 and 3D lattices with ω* = 0.75, ω* = 3 and a gradient in ω*.

Source data

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Larson, N.M., Mueller, J., Chortos, A. et al. Rotational multimaterial printing of filaments with subvoxel control. Nature 613, 682–688 (2023).

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