# Suiker's equations prevent 3-D-printed walls from collapsing or falling over

##### February 14th, 2018
3D-printed materials commonly are soft and flexible during printing, leaving printed walls susceptible to collapse or falling over. Akke Suiker, professor in Applied Mechanics at Eindhoven University of Technology, had a Eureka moment and saw the solution to this structural problem. He developed a model with which engineers can now easily determine the dimensions and printing speeds for which printed wall structures remain stable. His formulae are so elementary that they can become commonplace in the fast growing field of 3D printing.

Conventional concrete deposited in formwork typically is allowed to harden over period of several weeks. But 3D-printed concrete is not. With no supporting formwork, it almost immediately has to bear the weight of the subsequent layers of concrete that are printed on top of it. Everybody can feel the tension rising in their body as the structure gets higher. Is it already stiff and strong enough to add yet another layer on top? It is one of the most important issues in the new field of 3D printing.

This issue was not part of the package of tasks of Professor Akke Suiker, who regularly saw the king-sized concrete printer of his university in action on the way to his office. But on a Saturday morning last March he woke up with an exciting idea how to solve the problem, already jotting down the first mathematical equations on paper during breakfast. In the six months that follow Suiker is completely occupied by the problem, working feverishly on the details. The results are published this week in the International Journal of Mechanical Sciences.

Using his equations, Suiker is able to calculate how quickly he can lay down printing layers, given the material curing characteristics and wall dimensions - of course without the structure collapsing. But he can also calculate how to make the structure with as little material as possible, and what the influence of structural irregularities is. Or what happens when he makes a wall slightly thicker or increases the material curing rate, or uses a completely different material. Or if the wall has a tendency just to fall over or also pulls the connecting structure with it. In the latter case, the consequential damage that occurs clearly is considerably greater. In fact, there are about 15 to 20 factors that one has to take into account, but because Suiker has conveniently scaled his equations, he was ultimately left with just five dimensionless parameters. Hence the problem is tackled with a very elegant and insightful model.

When asked whether his results will be important for the field of 3D printing, Suiker is without doubt. "They should be. The insights provided by the model create essential basic knowledge for everyone who prints 3D structures. For structural designers, engineering firms but also, for example, for companies that print thin-walled plastic prostheses of small dimensions, because that is where my equations also apply." The first interest is already there: he has been invited by Cambridge University to give a seminar lecture about his work.

Suiker validated his model with results of tests done with the 3D concrete printer at Eindhoven University of Technology, carried out by PhD student Rob Wolfs. He developed a computer model at the same time as Suiker, with which he can also calculate the structural behavior during the printing process, but based on the finite-element method (2. It is great for both researchers that the results from their independently developed models confirm each other.

Wolfs' model is different in terms of application. It works well for a detailed analysis of complex problems under specific printing conditions, but due to the purely numerical character and the requested computing time it is not so suitable for identifying the most important effects of the printing process, and for mapping out overall trends.

A.S.J. Suiker, Mechanical performance of wall structures in 3D printing processes: Theory, design tools and experiments, International Journal of Mechanical Sciences (2018). DOI: 10.1016/j.ijmecsci.2018.01.010

R.J.M. Wolfs et al. Early age mechanical behaviour of 3D printed concrete: Numerical modelling and experimental testing, Cement and Concrete Research (2018). DOI: 10.1016/j.cemconres.2018.02.001

Provided by Eindhoven University of Technology

This Phys.org Science News Wire page contains a press release issued by an organization mentioned above and is provided to you “as is” with little or no review from Phys.Org staff.

## More news stories

#### New technologies enable better-than-ever details on genetically modified plants

Salk researchers have mapped the genomes and epigenomes of genetically modified plant lines with the highest resolution ever to reveal exactly what happens at a molecular level when a piece of foreign DNA is inserted. Their ...

#### Scientists ID another possible threat to orcas: pink salmon

Over the years, scientists have identified dams, pollution and vessel noise as causes of the troubling decline of the Pacific Northwest's resident killer whales. Now, they may have found a new and more surprising culprit: ...

#### Targeting 'hidden pocket' for treatment of stroke and seizure

The ideal drug is one that only affects the exact cells and neurons it is designed to treat, without unwanted side effects. This concept is especially important when treating the delicate and complex human brain. Now, scientists ...

#### Technology near for real-time TV political fact checks

A Duke University team expects to have a product available for election year that will allow television networks to offer real-time fact checks onscreen when a politician makes a questionable claim during a speech or debate.

#### Waves in Saturn's rings give precise measurement of planet's rotation rate

Saturn's distinctive rings were observed in unprecedented detail by NASA's Cassini spacecraft, and scientists have now used those observations to probe the interior of the giant planet and obtain the first precise determination ...

#### Researchers find cooling effect of aerosols in cumulus and MSC clouds twice as high as thought

An international team of researchers has found evidence that suggests the cooling effect of aerosols in cumulus and MSC clouds is twice as high as thought. In their paper published in the journal Science, the group describes ...

#### Making stars when the universe was half its age

The universe is about 13.8 billion years old, and its stars are arguably its most momentous handiwork. Astronomers studying the intricacies of star formation across cosmic time are trying to understand whether stars and the ...

#### Biologists discover deep-sea fish living where there is virtually no oxygen

Oxygen—it's a basic necessity for animal life. But marine biologists recently discovered large schools of fishes living in the dark depths of the Gulf of California where there is virtually no oxygen. Using an underwater ...

#### Researchers come face to face with huge great white shark

Two shark researchers who came face to face with what could be one of the largest great whites ever recorded are using their encounter as an opportunity to push for legislation that would protect sharks in Hawaii.

#### Classic double-slit experiment in a new light

An international research team led by physicists from the University of Cologne has implemented a new variant of the basic double-slit experiment using resonant inelastic X-ray scattering at the European Synchrotron ESRF ...