# TU/e Professor Develops Equations to Keep 3D Printed Concrete Walls From Collapsing

3D printing with concrete.

Concrete 3D printing has made it possible for us to rapidly build all sorts of structures, from benches and bridges to houses and hotel villas. But the construction method is not without its faults. The concrete comes out flexible and soft during the process, which leaves the 3D printed walls at risk of falling over or collapsing in on themselves.

Concrete that is deposited in traditional formwork is normally able to harden over several weeks, while 3D printed concrete isn’t – it lacks supporting formwork, and so has to hold up under the weight of subsequent concrete layers almost immediately.

It can be tense for those onsite, hoping that the concrete is strong and stiff enough to add another layer without collapsing the work that’s already been done. But Akke Suiker, a professor in Applied Mechanics at Eindhoven University of Technology (TU/e), may have come up with a way to relieve this stress…and keep 3D printed concrete walls upright.

Suiker often passes the university’s giant concrete 3D printer while walking to his office, and suddenly woke up one day last spring with a solution to the structural problem. He got straight to work, writing out the first mathematical equations while eating breakfast, and hasn’t stopped ironing out the details since.

The concrete 3D printer at Eindhoven University of Technology. [Image: Rien Meulman]

All the hard work has finally paid off, and Suiker published his results in a paper, titled “Mechanical performance of wall structures in 3D printing processes: Theory, design tools and experiments,” in the International Journal of Mechanical Sciences this week. Additionally, the University of Cambridge has invited Suiker to present a seminar lecture about his work.

The abstract reads, “In the current contribution for the first time a mechanistic model is presented that can be used for analysing and optimising the mechanical performance of straight wall structures in 3D printing processes. The two failure mechanisms considered are elastic buckling and plastic collapse. The model incorporates the most relevant process parameters, which are the printing velocity, the curing characteristics of the printing material, the geometrical features of the printed object, the heterogeneous strength and stiffness properties, the presence of imperfections, and the non-uniform dead weight loading.”

Graphical abstract: Rectangular wall lay-out during failure under 3D printing. L-R: modeled buckling profile; experimental buckling profile. The critical buckling length from the model is 0.276 m (30 layers), and is close to the experimental value of 0.304 m (33 layers).

Suiker used his equations to develop a model that will determine how quickly 3D printed layers can be deposited on top of each other, taking into consideration wall dimensions and material curing characteristics, without the structure falling over or collapsing under its own weight.

Akke Suiker [Image: TU/e]

“They should be,” Suiker replied when asked if his results will be important to the 3D printing industry. “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 model is very versatile, and can also calculate what happens if a wall is made slightly thicker, or out of a material other than concrete, or the exact influence of structural irregularities. It can also determine how to make the structure with as little material as possible, what will happen if the material curing rate is increased, and even if the wall will have a tendency to fall over, and if so, if it will also pull the connecting structure down as well. In this last instance, the damage would obviously be far greater, giving engineers roughly 15 to 20 factors to consider.

But, thanks to Suiker, who scaled his equations, only five dimensionless parameters remain, which allows users to take on the problem with an insightful model. Engineers can use Suiker’s model to easily find the proper printing speeds and dimensions that will keep 3D printed wall structures standing, and his formulas are easy enough to complete that they, according to TU/e, could “become commonplace in the fast growing field of 3D printing.”

“Hence, the model can be applied to systematically explore the influence of individual printing process parameters on the mechanical performance of particular wall structures, which should lead to clear directions for the optimisation on printing time and material usage. The model may be further utilised as a validation tool for finite element models of wall structures printed under specific process conditions,” the abstract concludes.

Rectangular shapes printed on the TU/e 3D concrete printer. Suiker elaborated his equations for rectangular layouts like these. [Image: Rob Wolfs, TU/e]

In order to validate the model, Suiker needed to complete tests, using the university’s concrete 3D printer, on a free wall, a simply-supported wall, and a fully-clamped wall. PhD student Rob Wolfs, with TU/e’s Department of the Built Environment, carried out the tests, and even developed an additional computer model, which, unlike Suiker’s model, is based on the finite-element method and can be used to calculate structural behavior during 3D printing.

Additionally, Wolfs published his own paper in Cement and Concrete Research, titled “Early age mechanical behaviour of 3D printed concrete: Numerical modelling and experimental testing,” with co-authors F.P. Bos and T.A.M. Salet.

Wolfs’ model would not work as well as Suiker’s for mapping out overall trends and determining the most important effects of the concrete 3D printing process, due to its request computing time and completely numerical character. But, it is good for developing a detailed analysis of difficult problems that emerge under specific 3D printing conditions. Both researchers can be proud of their work, as the results from their separate models confirm each other.

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[Source: Eindhoven University of Technology]