According to an April 12, 2017 news item on ScienceDaily, shapeshifting in response to environmental stimuli is the fourth dimension (I have a link to a posting about 4D printing with another fourth dimension),

A team of researchers from Georgia Institute of Technology and two other institutions has developed a new 3-D printing method to create objects that can permanently transform into a range of different shapes in response to heat.

The team, which included researchers from the Singapore University of Technology and Design (SUTD) and Xi’an Jiaotong University in China, created the objects by printing layers of shape memory polymers with each layer designed to respond differently when exposed to heat.

“This new approach significantly simplifies and increases the potential of 4-D printing by incorporating the mechanical programming post-processing step directly into the 3-D printing process,” said Jerry Qi, a professor in the George W. Woodruff School of Mechanical Engineering at Georgia Tech. “This allows high-resolution 3-D printed components to be designed by computer simulation, 3-D printed, and then directly and rapidly transformed into new permanent configurations by simply heating.”

The research was reported April 12 [2017] in the journal Science Advances, a publication of the American Association for the Advancement of Science. The work is funded by the U.S. Air Force Office of Scientific Research, the U.S. National Science Foundation and the Singapore National Research Foundation through the SUTD DManD Centre.

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An April 12, 2017 Singapore University of Technology and Design (SUTD) press release on EurekAlert provides more detail,

4D printing is an emerging technology that allows a 3D-printed component to transform its structure by exposing it to heat, light, humidity, or other environmental stimuli. This technology extends the shape creation process beyond 3D printing, resulting in additional design flexibility that can lead to new types of products which can adjust its functionality in response to the environment, in a pre-programmed manner. However, 4D printing generally involves complex and time-consuming post-processing steps to mechanically programme the component. Furthermore, the materials are often limited to soft polymers, which limit their applicability in structural scenarios.

A group of researchers from the SUTD, Georgia Institute of Technology, Xi’an Jiaotong University and Zhejiang University has introduced an approach that significantly simplifies and increases the potential of 4D printing by incorporating the mechanical programming post-processing step directly into the 3D printing process. This allows high-resolution 3D-printed components to be designed by computer simulation, 3D printed, and then directly and rapidly transformed into new permanent configurations by using heat. This approach can help save printing time and materials used by up to 90%, while completely eliminating the time-consuming mechanical programming process from the design and manufacturing workflow.

“Our approach involves printing composite materials where at room temperature one material is soft but can be programmed to contain internal stress, and the other material is stiff,” said Dr. Zhen Ding of SUTD. “We use computational simulations to design composite components where the stiff material has a shape and size that prevents the release of the programmed internal stress from the soft material after 3D printing. Upon heating, the stiff material softens and allows the soft material to release its stress. This results in a change – often dramatic – in the product shape.” This new shape is fixed when the product is cooled, with good mechanical stiffness. The research demonstrated many interesting shape changing parts, including a lattice that can expand by almost 8 times when heated.

This new shape becomes permanent and the composite material will not return to its original 3D-printed shape, upon further heating or cooling. “This is because of the shape memory effect,” said Prof. H. Jerry Qi of Georgia Tech. “In the two-material composite design, the stiff material exhibits shape memory, which helps lock the transformed shape into a permanent one. Additionally, the printed structure also exhibits the shape memory effect, i.e. it can then be programmed into further arbitrary shapes that can always be recovered to its new permanent shape, but not its 3D-printed shape.”

Said SUTD’s Prof. Martin Dunn, “The key advance of this work, is a 4D printing method that is dramatically simplified and allows the creation of high-resolution complex 3D reprogrammable products; it promises to enable myriad applications across biomedical devices, 3D electronics, and consumer products. It even opens the door to a new paradigm in product design, where components are designed from the onset to inhabit multiple configurations during service.”

Here’s a video,

Uploaded on Apr 17, 2017

A research team led by the Singapore University of Technology and Design’s (SUTD) Associate Provost of Research, Professor Martin Dunn, has come up with a new and simplified 4D printing method that uses a 3D printer to rapidly create 3D objects, which can permanently transform into a range of different shapes in response to heat.

Here’s a link to and a citation for the paper,

Direct 4D printing via active composite materials by Zhen Ding, Chao Yuan, Xirui Peng, Tiejun Wang, H. Jerry Qi, and Martin L. Dunn. Science Advances  12 Apr 2017: Vol. 3, no. 4, e1602890 DOI: 10.1126/sciadv.1602890

This paper is open access.

Here is a link to a post about another 4th dimension, time,

4D printing: a hydrogel orchid (Jan. 28, 2016)