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Citation: Sangiorgio, V.; Parisi, F.;

Fieni, F.; Parisi, N. The New

Boundaries of 3D-Printed Clay Bricks

Design: Printability of Complex

Internal Geometries. Sustainability

2022,14, 598. https://doi.org/

10.3390/su14020598

Academic Editor:

Sayanthan Ramakrishnan

Received: 25 November 2021

Accepted: 2 January 2022

Published: 6 January 2022

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4.0/).

sustainability

Article

The New Boundaries of 3D-Printed Clay Bricks Design:

Printability of Complex Internal Geometries

Valentino Sangiorgio 1,2,3,4,* , Fabio Parisi 1,5, Francesco Fieni 6and Nicola Parisi 6

1ICITECH—Instituto de Ciencia y Tecnología del Hormigón, Universitat Politècnica de València,

46022 Valencia, Spain

2DICATECh—Department of Civil, Environmental, Land, Building Engineering and Chemistry,

Polytechnic University of Bari, 70125 Bari, Italy

3CONSTRUCT-LESE—Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal

4FCI—Facultad de Ciencias e Ingeniería, Pontiﬁcia Universidad Católica del Perú(PUCP), 15088 Lima, Peru

5DEI—Department of Electrical Engineering and Information Technology, Polytechnic University of Bari,

70125 Bari, Italy; fabio.parisi@poliba.it

6DICAR—Department of Civil Engineering Sciences and Architecture, Polytechnic University of Bari,

70125 Bari, Italy; francesco.ﬁeni@poliba.it (F.F.); nicola.parisi@poliba.it (N.P.)

*Correspondence: valentino.sangiorgio@poliba.it

Abstract:

The building construction sector is undergoing one of the most profound transformations

towards the digital transition of production. In recent decades, the advent of a novel technology for

the 3D printing of clay opened up new sustainable possibilities in construction. Some architectural

applications of 3D-printed clay bricks with simple internal conﬁgurations are being developed around

the world. On the other hand, the full potential of 3D-printed bricks for building production is still

unknown. Scientiﬁc studies about the design and printability of 3D-printed bricks exploiting complex

internal geometries are completely missing in the related literature. This paper explores the new

boundaries of 3D-printed clay bricks realized with a sustainable extrusion-based 3D clay printing

process by proposing a novel conception, design, and analysis. In particular, the proposed method-

ological approach includes: (i) conception and design; (ii) parametric modeling; (iii) simulation of

printability; and (iv) prototyping. The new design and conception aim to fully exploit the potential

of 3D printing to realize complex internal geometry in a 3D-printed brick. To this aim, the research

investigates the printability of internal conﬁguration generated by using geometries with well-known

remarkable mechanical properties, such as periodic minimal surfaces. In conclusion, the results are

validated by a wide prototyping campaign.

Keywords:

clay 3D printing; sustainable constructions; clay bricks; bricks design; building envelope;

additive manufacturing; printability simulation; periodic minimal surfaces

1. Introduction

The 21st century represents the beginning of the digital transition in the building

production sector. Among the enabling technologies of the fourth industrial revolution,

additive manufacturing is one of the most promising tools to renovate the construction

process with a sustainable perspective [1,2].

Nowadays, 3D printing can be considered a consolidated technology and several 3D-

printed buildings are being developed worldwide [

3

,

4

]. Most of the current applications

and companies’ interests are focused on full 3D-printed buildings. On the other hand, recent

researchers demonstrate the potential of this technology applied for small components

prefabrication [3,5,6].

In the last decade, the area of 3D printing prefabrication has grown with the advent of

a new sustainable technology for 3D printing of clay. The applications of this technique in

the construction sector has attracted interest of both companies and the academic world,

Sustainability 2022,14, 598. https://doi.org/10.3390/su14020598 https://www.mdpi.com/journal/sustainability

Sustainability 2022,14, 598 2 of 15

speciﬁcally in the architecture sector [

7

]. A signiﬁcant research group working on large

blocks realization is the Institute for Advanced Architecture (IAAC). Indeed, IAAC is one of

the ﬁrst research center that investigated the use of raw earth for construction by employing

massive technological systems destined for the architectural engineering through the

projects Digital Adobe and Terra Performa [

8

,

9

]. Other recent impactful applications of

clay 3D printing (prefabrication of small components) can be classiﬁed into three groups:

(1) bricks for non-structural walls and division; (2) building components for sunshades and

cladding; (3) non-structural brick vaults.

(1)

Bricks for non-structural walls and division have been studied by investigating the

external brick geometric freedom to achieve multifunctional behaviors [10].

(2)

Building sunshades and cladding realized in ceramic 3D printing have been investi-

gated in the University of California Berkeley in a broad range of different architec-

tural applications to explore materials like clay in a more technological and creative

way [11].

(3) Non-structural brick vaults to be used as shading systems have been developed in the

University of Minho by Carvalho et al. [12,13].

Beyond the freedom in the external shape, there are few studies regarding the re-

alization of 3D-printed clay components with different internal conﬁgurations. Some

preliminary investigations focused on the mechanical [

14

] and energy properties [

15

] of

3D-printed bricks by considering different internal simple geometries [

16

,

17

]. These studies

demonstrate the potential of both mechanical and energy performances and beneﬁt in

sustainability of these new 3D-printed bricks. More in detail, Peters et al. [

15

] argue that, in

3D-printed bricks, the performance is “promising because of the ability to embed different

shapes and sizes of air pockets in the wall”. On the other hand, such studies designed,

printed, and tested regular internal conﬁguration only (internal walls that do not vary their

section along the vertical axis) without investigating complex shapes with difﬁcult print-

ability. Indeed, exhaustive studies exploring the design of complex internal conﬁgurations

and consequent limits in printability is still missing in the related literature [5].

This paper proposes a novel conception, design, and prototyping of 3D-printed clay

bricks for building construction to be realized with extrusion-based 3D clay printing. The

sustainability of the clay 3D printing technology is widely recognized and evidenced in

the review of [

5

]. Consequently, the current work presents an important advance in both

knowledge and practice for the application of the sustainable production of 3D-printed

clay bricks.

In particular, the new design realized with a parametric modeling aim to fully exploit

the potential of 3D printing by proposing complex internal geometries in the 3D-printed

bricks. The proposed approach allows overcoming the existing limit of simple internal

geometries experienced in the related literature. Indeed, the external shape is generated

according to the classical bricks (rectangular parallelepiped), while the internal geometries

are developed starting from the well-known periodic minimal surfaces (surface that locally

minimizes its area) [

18

,

19

]. Such geometries are chosen for their well-known ability to

provide effective mechanical properties and energy absorption capability [

20

,

21

]. The

research identiﬁes the most effective internal shape of the bricks to be printed by considering

six different typologies of minimal surfaces and three different conﬁgurations of internal

cells with a total of 18 parametric models.

Finite element method simulations are developed by connecting directly the paramet-

ric model with Abaqus software to investigate the printability of such geometries with clay

material. In addition, numerous printing tests are carried out to validate the simulations

and investigate the best printing conﬁguration to reach an effective realization of the bricks.

In conclusion, the research provides useful guidelines to avoid the principal printing

error found and classiﬁed during the proposed investigation.

Sustainability 2022,14, 598 3 of 15

The novelties of the presented research are three-fold:

•

A novel methodological approach based on four phases is proposed to combine

concept design, parametric modeling, ﬁnite element method analysis, and prototyping;

•

A novel conceptual design of a complex brick to be realized with 3D printing and

exploiting ‘minimal surfaces’ is proposed;

•

The principal printing errors of clay bricks with complex internal configuration are

discussed and useful guidelines are proposed to suggest how to avoid these drawbacks.

The rest of the paper is structured as follows. Section 2proposes the methodological

approach. Section 3shows the results of the novel conceptual design, simulations, and pro-

totyping. Section 4discusses the results and presents suitable guidelines and suggestions

for technicians. Finally, Section 5draws the conclusions.

2. Methodology

The proposed research is developed in four phases: (i) conception and design; (ii) para-

metric modeling; (iii) simulation and printability; (iv) prototyping. Figure 1shows

a ﬂowchart of the four phases of the methodology (in the top left part) and the novel

conceptual design and prototyping of the 3D-printed clay brick (in the bottom).

Sustainability 2022, 14, x FOR PEER REVIEW 3 of 16

The novelties of the presented research are three-fold:

• A novel methodological approach based on four phases is proposed to combine con-

cept design, parametric modeling, finite element method analysis, and prototyping;

• A novel conceptual design of a complex brick to be realized with 3D printing and

exploiting ‘minimal surfaces’ is proposed;

• The principal printing errors of clay bricks with complex internal configuration are

discussed and useful guidelines are proposed to suggest how to avoid these draw-

backs.

The rest of the paper is structured as follows. Section 2 proposes the methodological

approach. Section 3 shows the results of the novel conceptual design, simulations, and

prototyping. Section 4 discusses the results and presents suitable guidelines and sugges-

tions for technicians. Finally, Section 5 draws the conclusions.

2. Methodology

The proposed research is developed in four phases: (i) conception and design; (ii)

parametric modeling; (iii) simulation and printability; (iv) prototyping. Figure 1 shows a

flowchart of the four phases of the methodology (in the top left part) and the novel con-

ceptual design and prototyping of the 3D-printed clay brick (in the bottom).

In particular, (i) in the first phase, the concept design investigates how to include

minimal surfaces in the design of a clay brick realized with 3D printing.

(ii) Successively, the parametric models of the new clay bricks of are generated by

exploiting algorithms-aided design [22].

(iii) In the third phase, an advanced printing simulation is developed in order to iden-

tify the best minimal surfaces configuration and other geometrical parameters suitable for

designing and printing the new bricks. The simulations are obtained by linking the bricks

parametric model with the Abaqus simulation software [23].

(iv) In the final phase, the best printable bricks configurations are selected for effec-

tive prototyping.

Figure 1. Flowchart of the four phases of the proposed methodology.

Figure 1. Flowchart of the four phases of the proposed methodology.

In particular, (i) in the ﬁrst phase, the concept design investigates how to include

minimal surfaces in the design of a clay brick realized with 3D printing.

(ii) Successively, the parametric models of the new clay bricks of are generated by

exploiting algorithms-aided design [22].

(iii) In the third phase, an advanced printing simulation is developed in order to

identify the best minimal surfaces conﬁguration and other geometrical parameters suitable

for designing and printing the new bricks. The simulations are obtained by linking the

bricks parametric model with the Abaqus simulation software [23].

(iv) In the ﬁnal phase, the best printable bricks conﬁgurations are selected for effec-

tive prototyping.

Sustainability 2022,14, 598 4 of 15

2.1. Novel Conception and Design

The conception of the new printable bricks starts from two ideas:

(a)

The observation of the traditional and widespread brick external shapes and related

regulatory in order to respect the external dimension and the internal wall thickness

(rectangle parallelepiped);

(b)

The use of minimal surfaces to generate the internal conﬁguration of the bricks.

Typically for structural bricks, the length, width, and height can be consistently varied

within the range 15–50 cm, 12–30 cm, and 15–25 cm respectively. The thickness of the

internal walls is considered to be at a minimum 0.8 cm. In addition, the minimum thickness

of the external walls (external shell) is 1 cm with a tolerance of the 10% to consider the

typical imprecision of the production [24,25].

Starting from the above boundaries, the novel conceptual design of 3D printable bricks

investigates how to use minimal surfaces to realize the internal geometry of the bricks. In

particular, periodic minimal surfaces are used in this work because previous research has

demonstrated the advantages of such shapes for 3D printing, including high mechanical

properties, low pressure drop, and elastic-plastic damage [20,26,27].

2.2. Parametric Modeling of Minimal Surfaces and Periodic Minimal Surfaces

In the second phase of the methodology, the parametric models of the new printable

bricks are modeled with the Grasshopper visual programming language (a visual script-

ing and environment that runs within the Rhinoceros 3D computer-aided design). The

parametric modeling of the brick is achieved in three steps: (i) Generation of the external

shell, (ii) generation of the periodic minimal surfaces, (iii) internal shape and ﬁnalization of

the brick.

In the following, every step is described in detail by mentioning the speciﬁc compo-

nents (in italics) to be dragged onto the Grasshopper canvas.

(i) The generation of the external shell starts from the deﬁnition of a rectangle par-

allelepiped by using the components rectangle,extrusion, and cap holes (by respecting the

length, width, and height constraint deﬁned in Section 2.1). By employing the component

centre box and solid difference, the thickness of the external wall is completed. More in detail,

these last two components operate a Boolean difference between the ﬁrst parallelepiped

and another one with the centre in common, i.e., the same height but reduced width and

length on the basis of the desired thickness.

(ii) In parallel, periodic minimal surfaces are generated through the visual script from

their implicit mathematical equations [

28

,

29

]. The functions are plotted with a domain

of negative and positive

π

exploiting the following grasshopper components: construct

domain,range,cross reference,evaluate, and iso surface of the plugin “millipede” (https://

wewanttolearn.wordpress.com/tag/millipede/ (accessed on 15 February 2021)).

(iii) Once the single periodic minimal surface (single geometry) is generated, it is pos-

sible to create a box array including the obtained geometry to create the internal shape of the

bricks. The vertices in contact of every geometry are joined with the component join meshes

and weld of the “weavebird” plugin [

30

] and the thickness (respecting constraint deﬁned in

Section 2.1) can be created with the components offset mesh of the “pufferﬁsh” plugin.

Once the number of internal cells is deﬁned and geometries have been adequately

scaled (in order to perfectly ﬁt the external shape) with the additional components (division

and domain box connected to the box array), the internal geometry can be joined and ﬁnalized

by using the component mesh join. To the sake of brevity, Figure 2shows the visual script

to generate the external shape of the brick, while Supplementary Figure S1 shows the

whole script.

Sustainability 2022,14, 598 5 of 15

Sustainability 2022, 14, x FOR PEER REVIEW 5 of 16

Figure 2. Extract of the visual scripting to generate the external shell of the bricks.

The complete parametric model (Supplementary Figure S1) can quickly change pa-

rameters of the brick—such as dimensions, external shape thickness, and internal geome-

try (changing the mathematical equations and consequently the minimal surface). In par-

ticular, for what concerns the internal geometry, the number of repetitions of the mini-

mum surfaces inside the bricks can be modified in the parametrical model by considering

the number of cells of the box array components.

2.3. Simulations and Printability

The third phase of the methodology is devoted to performing a finite element mod-

eling (FEM) analysis of the printability of the internal cells of the bricks. Such analyses are

aimed to identify the most effective minimum surfaces and the number of repetitions of

the geometry within the brick. The approach is based on an effective plug-in named

VoxelPrint for Grasshopper [23] that can be used to construct simulation files, designed

specifically for 3D printing applications for viscous material, such as concrete. Such plugin

exploits voxelization of the designed three-dimensional shapes into a set of identical finite

elements and it produces ready-to-use input files for simulation in Abaqus. The approach

has been initially developed for concrete printing. On the other hand, in this work, the

material parameters (that can be included in the tool) are modified and adapted to simu-

late clay extrusion instead of concrete. The visual scripting is reported in Figure 3 and the

used components are listed in the following: BerpToVoxel, Material, PrintSetting, VoxelPre-

view, and VoxelToAbaqus.

Note that in order to use VoxelPrint an additional part of the graphical script is needed

to convert the brick geometry in an input file in the form of a B-rep (a solid represented as

a collection of connected surface elements, which define the boundary between interior

and exterior points) [31]. Supplementary Figure S1 shows the whole script.

Figure 3. Visual scripting to create the input files for simulation in Abaqus.

Figure 2. Extract of the visual scripting to generate the external shell of the bricks.

The complete parametric model (Supplementary Figure S1) can quickly change pa-

rameters of the brick—such as dimensions, external shape thickness, and internal geometry

(changing the mathematical equations and consequently the minimal surface). In particular,

for what concerns the internal geometry, the number of repetitions of the minimum surfaces

inside the bricks can be modiﬁed in the parametrical model by considering the number of

cells of the box array components.

2.3. Simulations and Printability

The third phase of the methodology is devoted to performing a ﬁnite element modeling

(FEM) analysis of the printability of the internal cells of the bricks. Such analyses are aimed

to identify the most effective minimum surfaces and the number of repetitions of the

geometry within the brick. The approach is based on an effective plug-in named VoxelPrint

for Grasshopper [

23

] that can be used to construct simulation ﬁles, designed speciﬁcally

for 3D printing applications for viscous material, such as concrete. Such plugin exploits

voxelization of the designed three-dimensional shapes into a set of identical ﬁnite elements

and it produces ready-to-use input ﬁles for simulation in Abaqus. The approach has been

initially developed for concrete printing. On the other hand, in this work, the material

parameters (that can be included in the tool) are modiﬁed and adapted to simulate clay

extrusion instead of concrete. The visual scripting is reported in Figure 3and the used

components are listed in the following: BerpToVoxel,Material,PrintSetting,VoxelPreview,

and VoxelToAbaqus.

Sustainability 2022, 14, x FOR PEER REVIEW 5 of 16

Figure 2. Extract of the visual scripting to generate the external shell of the bricks.

The complete parametric model (Supplementary Figure S1) can quickly change pa-

rameters of the brick—such as dimensions, external shape thickness, and internal geome-

try (changing the mathematical equations and consequently the minimal surface). In par-

ticular, for what concerns the internal geometry, the number of repetitions of the mini-

mum surfaces inside the bricks can be modified in the parametrical model by considering

the number of cells of the box array components.

2.3. Simulations and Printability

The third phase of the methodology is devoted to performing a finite element mod-

eling (FEM) analysis of the printability of the internal cells of the bricks. Such analyses are

aimed to identify the most effective minimum surfaces and the number of repetitions of

the geometry within the brick. The approach is based on an effective plug-in named

VoxelPrint for Grasshopper [23] that can be used to construct simulation files, designed

specifically for 3D printing applications for viscous material, such as concrete. Such plugin

exploits voxelization of the designed three-dimensional shapes into a set of identical finite

elements and it produces ready-to-use input files for simulation in Abaqus. The approach

has been initially developed for concrete printing. On the other hand, in this work, the

material parameters (that can be included in the tool) are modified and adapted to simu-

late clay extrusion instead of concrete. The visual scripting is reported in Figure 3 and the

used components are listed in the following: BerpToVoxel, Material, PrintSetting, VoxelPre-

view, and VoxelToAbaqus.

Note that in order to use VoxelPrint an additional part of the graphical script is needed

to convert the brick geometry in an input file in the form of a B-rep (a solid represented as

a collection of connected surface elements, which define the boundary between interior

and exterior points) [31]. Supplementary Figure S1 shows the whole script.

Figure 3. Visual scripting to create the input files for simulation in Abaqus.

Figure 3. Visual scripting to create the input ﬁles for simulation in Abaqus.

Note that in order to use VoxelPrint an additional part of the graphical script is needed

to convert the brick geometry in an input ﬁle in the form of a B-rep (a solid represented as

a collection of connected surface elements, which deﬁne the boundary between interior

and exterior points) [31]. Supplementary Figure S1 shows the whole script.

Sustainability 2022,14, 598 6 of 15

Once imported in Abaqus, the ﬁle (generated as the output of the VoxelPrint plugin)

already contains all the conﬁgurations to run a non-linear static analysis, useful to evaluate

large displacements on the basis of the considered printing material. Another important

parameter to be set is the “number_of_Steps” used for the deﬁnition of the number of

progressive steps of the analysis. Every step represents a portion of the 3D printing process

into which the simulation is divided to evaluate the displacements. In this way, the software

is able to rebuild and simulate the whole printing process.

2.4. Prototyping

The prototyping phase has two purposes: (i) validate the results and the printability

information achieved from the simulations; (ii) investigates some additional errors related

to the limits of the technology in order to create useful guidelines for researchers and

practitioners on how to avoid such speciﬁc printing errors.

3. Results

The proposed methodology is applied to investigate the limits of the novel design

of 3D-printed bricks including different internal possible conﬁguration inside a deﬁned

external shell. This section presents the results in three subsections according to the

proposed methodology.

Firstly, a set of 18 bricks are modeled by exploiting the novel conceptual design

(respecting the traditional and widespread brick external shapes) and the parametric

modeling by varying the minimal surfaces and the number of internal cells of the brick.

Secondly, the results of the FEM analysis performed by ABAQUS software are pre-

sented and the best printable conﬁgurations are selected (among the 18 bricks modeled).

Thirdly, the results of the wide prototyping campaign are showed, and the validation

of the simulations is discussed. The prototyping involves a total of 18 printings.

3.1. Novel Conceptual Design Results

The generation of the 3D models of the bricks precisely follows the proposed three

steps of the parametric modeling (Section 2.2): (i) generation of the external shell; (ii) gener-

ation of the periodic minimal surfaces; (iii) internal shape and ﬁnalization of the brick.

In the ﬁrst step, the parametric modeling starts from the deﬁnition of the external shell

of the brick respecting the traditional external shapes (rectangular parallelepiped). The

current research investigates small brick of 15

×

12.5

×

9 cm since this dimension can be

effectively doubled or tripled to achieve standard brick and block sizes in construction (e.g.,

walls of 30 or 45 cm of width).

In the second step, the minimal surfaces can be generated to create the internal geome-

try of the brick with walls thickness of about 0.8 cm. In particular, six minimal surfaces

are investigated by considering some of the most used surfaces in digital manufactur-

ing [

32

–

34

]: Gyroid [

28

], Shwarz Primitive [

28

], Shoen’s Batwing [

35

], Battista-Costa [

36

,

37

],

Diamond [29], Sherk tower [38].

In the third step, by exploiting the last part of the visual scripting, it is possible to

combine multiple cells through the box array, assign thickness and automatically scale the

internal geometry to perfectly join the external shell.

Figure 4shows the single cell of minimal surfaces and the combination of many cells

in a box array 2

×

2. More in detail, in the upper part, the ﬁgure displays the single cell of

the minimal surface generated by using the proposed visual scripting. In the bottom part

of the image, an example of the combination of multiple cells is showed (in this simpliﬁed

illustration, a 2 ×2 box array is considered).

Sustainability 2022,14, 598 7 of 15

Sustainability 2022, 14, x FOR PEER REVIEW 7 of 16

Figure 4. Single cell of minimal surfaces and combination of many cells in a box array 2 × 2.

Once the parametric model is completed with the necessary information, it is possible

to quickly change the internal configuration of the brick by using different minimal sur-

faces and box arrays setting.

As previously mentioned, in this work, 18 printable bricks models are generated by

considering all the combinations of six different minimal surfaces and three different set-

ting of box arrays including the configurations 2.5 × 3, 4 × 5, and 5 × 5.

Figure 5 shows an example of how different configurations of the 3D bricks models

can be investigated by varying minimal surfaces and box arrays.

Figure 5. Different configurations of the 3D bricks: three different box arrays for the Shwarz P and

Gyroid minimal surfaces.

3.2. Simulation Results

With the aim of achieving a complete understanding of the internal brick’s geometry

printability, a series of FEM analyses of bonding is undertaken by using SIMULIA

ABAQUS software. In particular, the printability of the cells is investigated by considering

Figure 4. Single cell of minimal surfaces and combination of many cells in a box array 2 ×2.

Once the parametric model is completed with the necessary information, it is possible

to quickly change the internal conﬁguration of the brick by using different minimal surfaces

and box arrays setting.

As previously mentioned, in this work, 18 printable bricks models are generated by

considering all the combinations of six different minimal surfaces and three different setting

of box arrays including the conﬁgurations 2.5 ×3, 4 ×5, and 5 ×5.

Figure 5shows an example of how different conﬁgurations of the 3D bricks models

can be investigated by varying minimal surfaces and box arrays.

Sustainability 2022, 14, x FOR PEER REVIEW 7 of 16

Figure 4. Single cell of minimal surfaces and combination of many cells in a box array 2 × 2.

Once the parametric model is completed with the necessary information, it is possible

to quickly change the internal configuration of the brick by using different minimal sur-

faces and box arrays setting.

As previously mentioned, in this work, 18 printable bricks models are generated by

considering all the combinations of six different minimal surfaces and three different set-

ting of box arrays including the configurations 2.5 × 3, 4 × 5, and 5 × 5.

Figure 5 shows an example of how different configurations of the 3D bricks models

can be investigated by varying minimal surfaces and box arrays.

Figure 5. Different configurations of the 3D bricks: three different box arrays for the Shwarz P and

Gyroid minimal surfaces.

3.2. Simulation Results

With the aim of achieving a complete understanding of the internal brick’s geometry

printability, a series of FEM analyses of bonding is undertaken by using SIMULIA

ABAQUS software. In particular, the printability of the cells is investigated by considering

Figure 5.

Different conﬁgurations of the 3D bricks: three different box arrays for the Shwarz P and

Gyroid minimal surfaces.

3.2. Simulation Results

With the aim of achieving a complete understanding of the internal brick’s geometry

printability, a series of FEM analyses of bonding is undertaken by using SIMULIA ABAQUS

software. In particular, the printability of the cells is investigated by considering the

Sustainability 2022,14, 598 8 of 15

minimum surface typology and the number of repetitions of the geometry. Consequently, in

the ABAQUS software, 18 simulations are considered including three different dimensions

for every one of the six different minimum surfaces. Such analysis allows to perfectly

simulate the 3D printing setting including both the layer dimension, the thickness of the

extrusion, printing speed and the characteristic of the material.

In particular, the following characteristics are set in the simulation according to the

selected 3D printer and material deﬁned for the prototyping. Note that the used setting

is deﬁned considering the current common features of printers on the market, e.g., Delta

Wasp 40100 for clay. Both material and printing characteristics are deﬁned in VoxelPrint

and reported automatically in Abaqus by the imported model ﬁle. The material simulation

parameters are speciﬁed in Figure 3, according to the supplier speciﬁcations and the related

literature [

39

]. The simulation is also performed consistently with the real machine printing

process: a layer thickness of 1 mm printed by a nozzle of 2 mm diameter and a printing

speed of 30 mm/s.

In addition, some boundary conditions are set in order to consider a simulation

consistent with the whole geometry while analyzing an isolated cell of the different minimal

surfaces. For the continuity of the geometries, in each simulated cell, the orthogonal

displacements of the cell cutting plane are not allowed.

The outcome of the simulation for every cell can be interpreted with three possible

outputs: cell collapse,partial cell collapse, and perfectly printable model.

In particular, the cell collapse refers to an irreversible collapse that generates a necessary

stop of the 3D printing (the collapse is so severe that it does not lead to the positioning of

another layer of material).

The partial cell collapse means that a part of the model suffers a slight collapse during

the extrusion, but 3D printing can theoretically continue. In addition, such criticality affects

the ﬁnal printed geometry that cannot be exactly the same of the designed 3D model.

In the perfectly printable model, there are no collapses and no signiﬁcant

local deformations.

Figure 6shows three examples of the FEM results, one for every possible output.

More in detail, the upper part the Figure 6shows the cell collapse corresponding to the

Shwarz P minimal surface in the conﬁguration of a 2.5

×

3 box array. The central part of

the ﬁgure shows the partial collapse of a Sherk tower minimal surface in the conﬁguration

of

a 2.5 ×3

box array. The bottom part of the ﬁgure shows the effective printable model of

aSherk tower minimal surface in the conﬁguration of a 4 ×5 box array.

In Figure 6, the nodal displacements are highlighted in a chromatic magnitude scale.

In the cell collapse, high deformations (~7 mm) are diffused along the last layer where the

collapse occurs with highest values in the most overhanging portions (~11 mm).

Also in the partial cell collapse, high values of deformations (~9 mm) are detected. On

the contrary, in this case, the large displacements are focused in a very small portion of the

central part of the cell, while the rest of the geometry remains with very low deformations

(~0.07 mm).

The perfectly printable simulation is conﬁrmed by the deformation values of the last

layers (less than 1 mm) about one order of magnitude smaller than the cases of cell collapse

and partial collapse.

In total, the analysis shows that 12 of the cells of the designed 18 bricks could be

effectively printed and one of suffers a partial internal collapse.

Table 1summarizes the printability results of the internal geometries of the 18 designed

blocks obtained with the FEM analysis.

Sustainability 2022,14, 598 9 of 15

Sustainability 2022, 14, x FOR PEER REVIEW 9 of 16

Figure 6. Three examples of the FEM analysis results: collapse, partial cell collapse, and perfectly print-

able.

In Figure 6, the nodal displacements are highlighted in a chromatic magnitude scale.

In the cell collapse, high deformations (~7 mm) are diffused along the last layer where the

collapse occurs with highest values in the most overhanging portions (~11 mm).

Also in the partial cell collapse, high values of deformations (~9 mm) are detected. On

the contrary, in this case, the large displacements are focused in a very small portion of

the central part of the cell, while the rest of the geometry remains with very low defor-

mations (~0.07 mm).

The perfectly printable simulation is confirmed by the deformation values of the last

layers (less than 1 mm) about one order of magnitude smaller than the cases of cell collapse

and partial collapse.

In total, the analysis shows that 12 of the cells of the designed 18 bricks could be

effectively printed and one of suffers a partial internal collapse.

Table 1 summarizes the printability results of the internal geometries of the 18 de-

signed blocks obtained with the FEM analysis.

Figure 6.

Three examples of the FEM analysis results: collapse,partial cell collapse, and perfectly printable.

Table 1. Output of FEM analyses in term of printability of the 18 investigated geometries.

Simulation Results Printability

Minimal Surface Box Array 2.5 ×3 Box Array 4 ×5 Box Array 5 ×6

Gyroid •Printable •Printable •Printable

Shwarz P •Geometry collapse •Printable •Printable

Batwing •Geometry collapse •Geometry collapse •Geometry collapse

Battista-Costa •Geometry collapse •Printable •Printable

Diamond •Printable •Printable •Printable

Sherk tower •Partial collapse •Printable •Printable

•

Green colour corresponds to “Printable”;

•

Yellow colour corresponds to “Partial collapse”;

•

Red colour

corresponds to “Geometry collapse”.

3.3. 3D Printing Prototypes

The last phase consists of the realization of the prototypes of the 18 designed bricks.

The prototyping phase is designed to verify that the FEM analysis effectively simulate

the 3D printing of the bricks and to investigate other unpredictable printing errors. For

Sustainability 2022,14, 598 10 of 15

this purpose, the 18 bricks including six different minimal surfaces and three different

array conﬁgurations (box arrays 2.5

×

3, 4

×

5 and 5

×

5) are printed in the FabLab Poliba

laboratory of the Politecnico di Bari (Bari, Italy). In particular, the prototyping exploits the

slicing software Simplify3D and the 3D printer Delta Wasp 40100 for clay. The raw material

used for the printing is clay, a type of ﬁne-grained natural soil material. Table 2shows the

speciﬁc mix compositions of the used clay while the percentage of water is 20%. In addition,

the printing laboratory is a climate-controlled room with constant indoor microclimate.

The temperature is around 20 ◦C and the relative humidity is about 60%.

Table 2. Mix composition.

Composition SiO2Al2O3TiO2Fe2O3CaO MgO K2O Na2O CaCo3

3D printable clay 43.8% 15.3% 0.5% 4.1% 11.6% 1.8% 2.6% 1.5% 19.3%

SiO

2

(Silica); Al

2

O

3

(Aluminium oxide); TiO

2

(Titanium dioxide); Fe

2

O

3

(Ferric oxide); CaO (Calcium oxide);

MgO (Magnesium oxide); K2O (Potassium oxide); Na2O (Sodium oxide); CaCo3(Calcium carbonate).

The printing setting includes a layer thickness of 1 mm a nozzle size of 2 mm diameter

and printing speed about 30 mm/s (analogously to the print conﬁguration of the FEM

analysis). The results of the prototyping phase are perfectly consistent with the outputs

of the FEM analyses. To provide some examples, Figure 7shows the collapse,partial cell

collapse, and the brick perfectly printable in the conﬁguration of Shwarz P 2.5

×

3, Sherk tower

2.5 ×3, and Sherk tower 4×5 respectively (the same example of Figure 6).

Sustainability 2022, 14, x FOR PEER REVIEW 10 of 16

Table 1. Output of FEM analyses in term of printability of the 18 investigated geometries

Simulation Results Printability

Minimal Surface Box Array 2.5 × 3 Box Array 4 × 5 Box Array 5 × 6

Gyroid • Printable • Printable • Printable

Shwarz P • Geometry collapse • Printable • Printable

Batwing • Geometry collapse • Geometry collapse • Geometry collapse

Battista-Costa • Geometry collapse • Printable • Printable

Diamond • Printable • Printable • Printable

Sherk tower • Partial collapse • Printable • Printable

• Green colour corresponds to “Printable”; • Yellow colour corresponds to “Partial collapse”; •

Red colour corresponds to “Geometry collapse”.

3.3. 3D Printing Prototypes

The last phase consists of the realization of the prototypes of the 18 designed bricks.

The prototyping phase is designed to verify that the FEM analysis effectively simulate the

3D printing of the bricks and to investigate other unpredictable printing errors. For this

purpose, the 18 bricks including six different minimal surfaces and three different array

configurations (box arrays 2.5 × 3, 4 × 5 and 5 × 5) are printed in the FabLab Poliba labor-

atory of the Politecnico di Bari (Bari, Italy). In particular, the prototyping exploits the slic-

ing software Simplify3D and the 3D printer Delta Wasp 40100 for clay. The raw material

used for the printing is clay, a type of fine-grained natural soil material. Table 2 shows the

specific mix compositions of the used clay while the percentage of water is 20%. In addi-

tion, the printing laboratory is a climate-controlled room with constant indoor microcli-

mate. The temperature is around 20 °C and the relative humidity is about 60%

Table 2. Mix composition

Composition SiO

2

Al

2

O

3

TiO

2

Fe

2

O

3

CaO MgO K

2

O Na

2

O CaCo

3

3D printable clay 43.8% 15.3% 0.5% 4.1% 11.6% 1.8% 2.6% 1.5% 19.3%

SiO

2

(Silica); Al

2

O

3

(Aluminium oxide); TiO

2

(Titanium dioxide); Fe

2

O

3

(Ferric oxide); CaO (Cal-

cium oxide); MgO (Magnesium oxide); K

2

O (Potassium oxide); Na

2

O (Sodium oxide); CaCo

3

(Cal-

cium carbonate).

The printing setting includes a layer thickness of 1 mm a nozzle size of 2 mm diame-

ter and printing speed about 30 mm/s (analogously to the print configuration of the FEM

analysis). The results of the prototyping phase are perfectly consistent with the outputs of

the FEM analyses. To provide some examples, Figure 7 shows the collapse, partial cell col-

lapse, and the brick perfectly printable in the configuration of Shwarz P 2.5 × 3, Sherk tower

2.5 × 3, and Sherk tower 4 × 5 respectively (the same example of Figure 6).

Figure 7. Collapse (left), partial cell collapse (central photo), and the perfectly printable brick (right).

Figure 7. Collapse (left), partial cell collapse (central photo), and the perfectly printable brick (right).

More in detail, the geometries that collapse according to the FEM model effectively

collapse even in prototyping (in these cases the printing must be stopped). Even the partial

collapse of the Sherk tower 2.5

×

3 occurs as predicted by the FEM simulation. The other

bricks can be easily printed as foreseen by the FEM analysis with the only difference for the

Batista-costa and Gyroyd geometry in the conﬁguration array 5

×

6. Indeed, these geometries

have a complex texture and a very dense geometry (e.g., Gyroid has a very complex shape

and a void ratio of less than 20%) which causes critical printing issues. In particular, the

resolution of the 3D printer is not enough to create the small voids and the extruded

geometry loses its characteristic geometric features (extruded material starts to overlap

even when it should not). This last printing error is named hereafter ‘too dense error’.

Figure 8shows the 18 3D-printed bricks (with different internal geometries) and the

printing result in terms of too dense error,collapse,partial cell collapse, perfectly printable.

Sustainability 2022,14, 598 11 of 15

Sustainability 2022, 14, x FOR PEER REVIEW 11 of 16

More in detail, the geometries that collapse according to the FEM model effectively

collapse even in prototyping (in these cases the printing must be stopped). Even the partial

collapse of the Sherk tower 2.5 × 3 occurs as predicted by the FEM simulation. The other

bricks can be easily printed as foreseen by the FEM analysis with the only difference for

the Batista-costa and Gyroyd geometry in the configuration array 5 × 6. Indeed, these ge-

ometries have a complex texture and a very dense geometry (e.g., Gyroid has a very com-

plex shape and a void ratio of less than 20%) which causes critical printing issues. In par-

ticular, the resolution of the 3D printer is not enough to create the small voids and the

extruded geometry loses its characteristic geometric features (extruded material starts to

overlap even when it should not). This last printing error is named hereafter ‘too dense

error’.

Figure 8 shows the 18 3D-printed bricks (with different internal geometries) and the

printing result in terms of too dense error, collapse, partial cell collapse, perfectly printable.

Figure 8. Prototyping and 3D printing of the 18 bricks and specification of the results in terms of too

dense error, collapse, partial cell collapse, and perfectly printable.

4. Discussion and Guidelines

In recent years, few applications can be found in literature concerning the field of 3D-

printed clay bricks. On the other hand, some research institutes and companies (IAAC

and Wasp) are demonstrating the huge potential of clay 3D printing for sustainable con-

struction [8,9,40,41].

To this aim, this section discusses the characteristics and the differences of the pro-

posed bricks by comparing the proposed ideas and results with previous investigations

[5].

The most relevant research in the 3D printing of large walls and large blocks is per-

formed by Izard et al. [8] in the IAAC institute where cable-driven parallel robots were

applied. More in detail, the IAAC researchers investigated different aspects of 3D-printed

clay building components—including columns [40], bricks, and large blocks with various

types of openings [41]. The IAAC research demonstrated the potential of such technology

and stated the current limits of the application at the large scale. In addition, such inves-

tigation did not delve into complex internal geometries and printability limits since the

focus was directed towards the potential of large-scale applications.

Figure 8.

Prototyping and 3D printing of the 18 bricks and speciﬁcation of the results in terms of too

dense error,collapse,partial cell collapse, and perfectly printable.

4. Discussion and Guidelines

In recent years, few applications can be found in literature concerning the ﬁeld of

3D-printed clay bricks. On the other hand, some research institutes and companies (IAAC

and Wasp) are demonstrating the huge potential of clay 3D printing for sustainable con-

struction [8,9,40,41].

To this aim, this section discusses the characteristics and the differences of the proposed

bricks by comparing the proposed ideas and results with previous investigations [5].

The most relevant research in the 3D printing of large walls and large blocks is

performed by Izard et al. [

8

] in the IAAC institute where cable-driven parallel robots

were applied. More in detail, the IAAC researchers investigated different aspects of 3D-

printed clay building components—including columns [

40

], bricks, and large blocks with

various types of openings [

41

]. The IAAC research demonstrated the potential of such

technology and stated the current limits of the application at the large scale. In addition,

such investigation did not delve into complex internal geometries and printability limits

since the focus was directed towards the potential of large-scale applications.

On the contrary, the current proposal investigates small bricks which can be made with

commercial printers, such as the Delta Wasp 40100, for clay. In the ﬁeld of small 3D-printed

bricks, the ﬁrst research investigation has been conducted by Cruz et al. [

12

–

14

] in the

School of Architecture of the University of Minho (Guimarães, Portugal). This Portuguese

research contains the results of more than 3 years of research and provides the evidence

of the performance potential of the 3D-printed bricks, including the freedom to create

customized shapes.

Other investigations conﬁrmed the potential of both geometry and mass customization

in 3D-printed clay bricks for different applications [

42

,

43

] (artistic and architectural) and

multi objective performances [

15

,

44

] (e.g., structural and thermal). On the other hand, none

of these previous studies investigate the possibility and limitations of printing complex

geometries inside bricks [5].

In the current work, ﬁrstly a suitable methodology is deﬁned in order to design,

simulate (the 3D printing), and prototype novel complex clay bricks. Secondly, geometries

with well-known remarkable mechanical properties such as minimal surfaces and periodic

minimal surfaces are used to generate a parametric modeling with the novel complex

internal shapes of the bricks.

Sustainability 2022,14, 598 12 of 15

Six different minimal surfaces are investigated in three different internal conﬁgurations

(with a total of 18 bricks) in order to identify the most printable conﬁgurations.

In conclusion, the most promising geometry is the Diamond, printable in all the in-

vestigated conﬁgurations. Moreover, a good printability is also found in the Sherk Tower,

Swarts P, and Gyroyd since these geometries can be effectively printed in different internal

conﬁgurations of the bricks. Batwing is the most complex geometry and not suggested to

be effectively printed in a clay brick with the current technologies.

4.1. Guideline for the Design of the Novel Bricks (Avoid Printing Error)

Three different 3D printing errors have been identiﬁed in the attempt to print bricks

with complex internal geometries: cell collapse,partial cell collapse, and the too dense error.

The cell collapse conﬁgurations occur when internal geometry is increased too much in

size, the cells become large and consequently are difﬁcult to print due to the presence of

larger surfaces with horizontal tangents. The research points out that geometries such as

Diamond,Gyroid, and Sherk tower are less prone to this problem due to their geometry.

The partial cell collapse occurs exactly for the same reason of the cell collapse. On the

contrary, in this case, the cell suffers a deformation only and the printing can be continued

even if the result could be different form the designed 3D model. In this case, the limit of

the cell size has been reached. If the cell dimension is further enlarged, a collapse would

occur. Both partial cell collapse and collapse can be predicted and avoided with the proposed

FEM analysis.

The too dense error differs from the two previous ones because it cannot be predicted

in the FEM analysis. In addition, this error occurs when the geometry is too dense (the

number of arrays is too high and the void ratio decreases reaching the limit of the printing).

In this case, the tolerance and precision of the machine are not sufﬁcient to actually generate

the shape. The extruded material starts to overlap where it should not, and the result is

a fully deformed shape that is different from the original 3D model. This speciﬁc error

depends from the printed material and the precision of the 3D printer. Consequently, it

may or may not occur depending on the used technology.

4.2. Limits of the Technology and Future Direction

The presented research, and in particular the prototyping of the complex bricks,

pointed out three technological limits which need to be faced in the future in order to

ensure a sustainable and wide application of clay 3D printing in the construction sector.

The principal drawback found in the experimental phase concerns the printing time

of the bricks. Indeed, the average printing time is about 3 h. The complete overview of the

printing time of the proposed bricks is showed in Table 3. Consequently, the production of

bricks to realize a wall 3 ×4 m may require more than 400 printing hours.

Table 3. Printing time of the 18 bricks.

Minumal Surface Box Array 2.5 ×3 Box Array 4 ×5 Box Array 5 ×6

Gyroid •4 h 27 min •3 h 10 min •4 h 27 min

Shwarz P •Geometry collapse •2 h 40 min •3 h 35 min

Batwing •Geometry collapse •Geometry collapse •Geometry collapse

Battista-Costa •Geometry collapse •2 h 40 min •3 h 00 min

Diamond •3 h 20 min •1 h 40 min •3 h 20 min

Sherk tower •1 h 50 min •2 h 20 min •2 h 50 min

•

Green colour corresponds to “Printable”;

•

Yellow colour corresponds to “Partial collapse”;

•

Red colour

corresponds to “Geometry collapse”; •Black colour corresponds to “Too dense error”.

The second limit concerns the printing of some of the geometries that collapse without

a support [

45

]. In addition, recent studies have demonstrated how spatial 3D-printed

polymer elements can be used to efﬁciently reinforce 3D-printed geometries [

46

]. Such

intuition of Katzer and Szatkiewicz could be combined with the complex geometries

investigated in the current work to optimize efﬁciency of clay bricks.

Sustainability 2022,14, 598 13 of 15

The third important limits of current clay 3D printing concern the control of the extru-

sion of the material. The extrusion of the clay 3D printer is affected by small variations in

density of the clay and the mechanics of the printer extruder. These limits lead to insufﬁ-

cient precision in printing very dense geometries with a low void’s ratio (too dense error). In

this ﬁeld, it would be useful to improve the existing technology with an automatic extrusion

ﬂow control in order to increase the precision and avoid inaccuracies of the printing.

In addition, in the proposed research, the printing phase is not signiﬁcantly affected

by the indoor micro-climate since the height of the bricks is very small. On the contrary, in

larger printings [

40

,

41

] temperature and humidity can reduce or speed up the hardening of

the material. To this aim, a future development of the technology can improve the control

on the printing material. An automatic control could correct the extrusion ﬂow and the

percentage of water in the material preparation tank. Consequently, the extruded material

features can be adjusted in real time on the basis of external temperature and humidity to

optimize the printing.

In conclusion, it would be useful to increase the automation of processes, for example

by exploiting the production with 3D printing together with collaborative robots [

47

] to

reduce manpower and the consequent production times.

5. Conclusions

This paper explores, for the ﬁrst time, the possibility of realizing new 3D-printed

clay bricks for building construction with complex internal geometries based on minimal

surfaces. A novel methodological approach is proposed to design, test, and prototype these

new sustainable bricks including three main steps.

Firstly, the conception and design are established for respecting external dimensions

and internal wall thickness of classical structural bricks.

Secondly, a parametric modeling is developed to realize 3D-printed bricks and to gen-

erate the input ﬁles for a FEM simulation in Abaqus suitable for verifying the printability.

Thirdly, a wide prototyping campaign is performed to realize the prototypes of 3D-

printed clay bricks and validate the performed analysis.

In total, a set of 18 brick models are designed, the relative printing is simulated

with a FEM analysis and the effective 3D printings are realized. In conclusion, the most

promising conﬁguration is based on the minimal surface of Diamond, followed in the second

place by Sherk tower,Swarts P, and Gyroyd.

In comparison with previous research, the proposed work demonstrates the potential

of 3D printing in achieving 3D-printed bricks by exploiting different internal conﬁgurations

based on the minimal surfaces. In addition, the current research proposes a methodology

for designing and printing by using modern FEM analysis to simulate the printability. On

the contrary, previous experiences are mainly focused on the investigation of bricks for

architectural use only and without the complex internal geometry. Consequently, in the

previous works the simpliﬁed geometry did not require the FEM analyses proposed in the

current work to simulate the printability.

This research opens up new sustainable perspectives and possibilities to use 3D

printing for the realization of high-performance 3D-printed brick walls by reducing the

consumption of raw materials and optimizing the internal shape of the brick. On the

other hand, the research emphasizes the need for an improvement of the technology to be

competitive with traditional techniques from a realization time point of view.

Future research will investigate both the structural and thermal performances of the

achieved printable bricks conﬁgurations in order to identify most effective ones to realize

high-performance 3D-printed brick walls. Beyond this, another study will investigate the

possibility of modifying the external shell of the brick in order to enhance the combination

of brick 3D printing and the automatic construction of walls with collaborative robotic arms.

Sustainability 2022,14, 598 14 of 15

Supplementary Materials:

The following supporting information can be downloaded at: https:

//www.mdpi.com/article/10.3390/su14020598/s1, Supplementary Figure S1: The complete visual

scripting to generate the bricks.

Author Contributions:

Conceptualization, V.S.; Data curation, V.S. and F.F.; Formal analysis, V.S.

and F.P.; Funding acquisition, N.P.; Investigation, V.S.; Methodology, V.S.; Resources, V.S.; Software,

V.S., F.P. and F.F.; Supervision, V.S. and N.P.; Validation, V.S. and F.P.; Visualization, V.S. and F.F.;

Writing—original draft, V.S.; Writing—review and editing, V.S. and N.P. All authors have read and

agreed to the published version of the manuscript.

Funding: This research and APC was funded by “Fondi Casa delle Tecnologie Emergenti Matera”.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable.

Acknowledgments:

A special thanks is addressed to FabLab Bitonto for supporting the development

of the prototype in the laboratory “Fablab Poliba”.

Conﬂicts of Interest: The authors declare no conﬂict of interest.

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