Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 420

The DOI matches its Crossref record; 23 of the 23 references it cites were found in a registry or an index.

Shape-shifting structured lattices via multimaterial 4D printing

Open access
Boley, J. William, van Rees, Wim M., Lissandrello, Charles, Horenstein, Mark N., Truby, Ryan L., Kotikian, Arda, Lewis, Jennifer A., Mahadevan, L.·2019·Proceedings of the National Academy of Sciences

Abstract

Shape-morphing structured materials have the ability to transform a range of applications. However, their design and fabrication remain challenging due to the difficulty of controlling the underlying metric tensor in space and time. Here, we exploit a combination of multiple materials, geometry, and 4-dimensional (4D) printing to create structured heterogeneous lattices that overcome this problem. Our printable inks are composed of elastomeric matrices with tunable cross-link density and anisotropic filler that enable precise control of their elastic modulus ( E ) and coefficient of thermal expansion ( α ) . The inks are printed in the form of lattices with curved bilayer ribs whose geometry is individually programmed to achieve local control over the metric tensor. For independent control of extrinsic curvature, we created multiplexed bilayer ribs composed of 4 materials, which enables us to encode a wide range of 3-dimensional (3D) shape changes in response to temperature. As exemplars, we designed and printed planar lattices that morph into frequency-shifting antennae and a human face, demonstrating functionality and geometric complexity, respectively. Our inverse geometric design and multimaterial 4D printing method can be readily extended to other stimuli-responsive materials and different 2-dimensional (2D) and 3D cell designs to create scalable, reversible, shape-shifting structures with unprecedented complexity.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1073/pnas.1908806116

Cites

23 of 23 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 23 references

Cited by

See all 420

Metadata

Authors
Boley, J. W., van Rees, W. M., Lissandrello, C., Horenstein, M. N., Truby, R. L., Kotikian, A., Lewis, J. A., & Mahadevan, L.
Venue
Proceedings of the National Academy of Sciences
Published
2019-10-02
Volume
116
Issue
42
Pages
20856-20862
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
OpenAlex
W2978155273
Cited by
420
References
23
FWCI
25.96
Type
journal article
Language
en
Open access
green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Shape-shifting structured lattices via multimaterial 4D printing. https://app.cochat.ai/papers/10.1073/pnas.1908806116
The paper
Boley, J. W., van Rees, W. M., Lissandrello, C., Horenstein, M. N., Truby, R. L., Kotikian, A., Lewis, J. A., & Mahadevan, L. (2019). Shape-shifting structured lattices via multimaterial 4D printing. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.1908806116

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.