Exploratory study on geodesic domes under blast loads

Abstract

This article studies the feasibility of using geodesic domes as expeditionary protective structures, since they are fast-assembly lightweight structures and are able to withstand very heavy loads due to their specific geometry. A 6-m standard International Orginization for Standardization container is used as a benchmark structure for the study, which is developed using the nonlinear explicit code LS-DYNA. The blast simulations were performed with the Load Blast Enhanced option, using the phenomenological Johnson–Cook constitutive model to reproduce the behaviour of steel subjected to a large range of strain rates. The performance assessment of the protective structures under blast loading was based on the evaluation of the associated safety zones inside the protective shelter as well as on the characterization of the potential structural damage. With the additional insights provided by this article, it is possible to identify some of the competitive advantages shown by this type of structures which will hopefully foster new advances in the field.

Keywords

Protective structures geodesic dome blast loads LS-DYNA safety zone structural damage

Introduction

Expeditionary protective structures are becoming increasingly important as a safeguard against accidental loads and terrorist attacks, mainly in international operations taking place in unstable regions of the world. In these type of scenarios, it is mandatory to set camps for the troops, requiring the long-distance transportation and deployment of large amounts of protective equipment. The weight and volume of the system are thus critical parameters. To minimize the vulnerability of the personnel during the establishment of these new camps, the assembly of the shelters must be performed within the shortest period of time possible. The use of traditional shelter systems, like the International Orginization for Standardization (ISO) containers (Børvik et al., 2008a, 2008b), is therefore limited, and the design of alternative solutions relying on fast-assembly lightweight protective systems (Krauthammer, 2008) becomes a key issue.

Another potentially interesting type of structures are the geodesic domes. They are known to withstand very heavy loads due to their specific geometry, which allows to distribute the structural stress throughout the whole structure (Nie et al., 2014; Sahu and Gupta, 2015; Wang and Huang, 2013). Research on this specific geometry goes back to 1954 when the U.S. Marine Corps started experiments with helicopter-deliverable geodesic domes, where a 9-m wood and plastic geodesic dome was lifted and carried by helicopter at 90 km/h without any damage (Lane, 1954). The tests also included assembly practices in which untrained Marines were able to assemble a 9-m dome in 135 min and a durability test in which an anchored dome successfully withstood a day-long 190 km/h propeller blast from two 3000 horsepower engines of an anchored airplane without damage.

Inspired by these tests, this article explores the feasibility of using geodesic dome structures as a cost-effective and lightweight protection concept against blast loads. The performance of a geodesic dome, when resisting surface bursts associated with different terrorism threat levels, is analysed and compared with a conventional protective system based on a 6-m standard ISO container, having external dimensions of about 6 × 2.5 × 2.5 m³.

The intensity of a blast load can be quantified as a function of two, equally important, parameters: the TNT-equivalent weight of the charge and the standoff distance between the blast source and the target. The detonation of an explosive causes pressure disturbances in the surrounding air which develop into blast waves led by an incident shock wave. When hitting the target, the incident wave rebounds with greater amplitude as a reflected wave. This reflected pressure becomes the applied blast load (Baker et al., 1983; Kinney and Graham, 1985). A typical pressure profile is presented in Figure 1. For a given point in space, it is possible to define $t_{A}$ , as the arrival time of the shock wave. At this moment, the pressure almost instantaneously increases above the ambient pressure $P_{0}$ to a peak pressure $P_{s o}$ and then decays to the ambient pressure during $t_{d}$ . This positive phase is followed by a negative phase, characterized by a reverse air flow with a minimum pressure $P_{s o}^{-}$ and a duration of $t_{d}^{-}$ , generally longer than the positive phase. However, when analysing the blast effect on structures, the negative phase is often ignored as, being more weaker and gradual than the positive phase, induces a less-significant structural response (Bulson, 1997). When the incident wave strikes the structure, it is reflected and amplified to a maximum peak reflected pressure $P_{r}$ . The duration of the positive and negative phases remain unchanged.

Figure 1.

Incident and reflected pressure profiles for blast.

Geodesic domes

Structural engineers have always shown a keen interest for systems that enable them to cover large spans with minimal interference from internal supports. Dome structures are capable of encompassing maximum volume with minimum surface area and hence are one of the structural forms used since the earliest times. The original design of geodesic domes was based on the sphere division of an icosahedron, like the one represented in Figure 2(a), although octahedron and dodecahedron symmetry systems eventually became increasingly popular (Fuller and Applewhite, 1975).

Figure 2.

General definition of the geodesic dome: (a) icosahedron, (b) class I subdivision, (c) V2 geodesic frequency and (d) geodesic dome.

By exploding an icosahedron onto the surface of a sphere one obtains 20 equilateral spherical triangles, as illustrated in Figure 2(a). In order to limit the length of the frames in the geodesic network and control their excessive slenderness ratios as the diameter of the dome increases, the equilateral triangles are divided into a number of subdivisions. According to Kitrick (1990), a class I subdivision was used in this work, with the dividing lines parallel to the edges of the primary frame network, as shown in Figure 2(b). A V2 subdivision was implemented, meaning that the edges of the original geodesic network were divided into two triangles, as shown in Figure 2(c). CADRE Geo 7 geodesic design application was used to design the geodesic dome shown in Figure 2(d).

The radius of the geodesic dome was defined by equalizing the volume of the half sphere to that of the benchmark ISO container, yielding the dome illustrated in Figure 3, having a radius of 2.60 m.

Figure 3.

Size definition of the geodesic dome: similar volume.

The construction of the dome results from the assembly of hubs, struts and steel panels for cladding. The struts of the dome were defined as steel circular hollow sections (CHSs) with an outside diameter of 50 mm and a thickness of 2.5 mm, amounting to 30 type A struts, with a length of 1.42 m, and 35 type B struts, with a length of 1.61 m. In addition, six five-way hubs, 10 six-way hubs and 10 four-way hubs, around the base of the dome, were used (Figure 4(a)).

Figure 4.

Strut assembly: (a) geodesic dome and (b) ISO container.

A simplified outer geometry was used for the ISO container in combination with the strut system illustrated in Figure 4(b). This system resorts to the same steel CHSs as the geodesic dome. Finally, both the structures were covered by steel panels with a thickness of 2 mm, yielding a total weight of 1376.80 kg, for the ISO container and 993.57 kg, for the dome (this amounts to a 30% material optimization for the dome).

Finite-element modelling

Finite-element setup

The three-dimensional (3D) finite-element (FE) models were analysed using the nonlinear explicit code LS-DYNA, which takes into account both material and geometric nonlinearity. The models comprised fully integrated beam (ELFORM 1), shell (ELFORM 16) elements with 6 degrees of freedom per node, automatically generated by the LS-DYNA AutoMesh tool, and solid (ELFORM 11) multi-material Arbitrary Lagrangian Eulerian (ALE) solid elements. The FE models of the geodesic dome and of the ISO container are showed in Figure 5.

Figure 5.

FE models: (a) geodesic dome (black), air (grey) and (b) 6-m standard ISO container (black), air (grey).

A sensitivity analysis of the Lagrangian elements yielded stable results for a FE mesh with 0.1-m size elements and an integration time-step of $10^{- 6} s$ , values that were considered in all the computations reported in this article.

The interaction between the Lagrangian elements (structure) and the air (fluid) is achieved with a penalty-based method that applies a penalty force to the fluid and the structure when a penetration is detected. According to Hallquist (2006), two or three coupling points should be present per ALE element to achieve a good coupling between the fluid and the structure. Taking into account that two coupling points were considered on each Lagrangian element, the ALE mesh size should be comparable to that of the structure. Consequently, cubic elements with a size of 0.1 m were used to mesh the considered volume of air.

Material modelling

The numerical simulation of the steel shell behaviour was done using the popular phenomenological Johnson–Cook constitutive model (Johnson and Cook, 1983, 1985). This model is able to reproduce the main phenomena exhibited by metals subjected to impact and penetration, namely the strain hardening, the strain rate effects and the thermal softening.

The constitutive relation equation (1) or the hardening rule, expresses the effective stress $σ_{e f f}$ as a function of plastic strain, strain rate and temperature (Hallquist, 2006)

σ_{e f f} = [A + B {({\bar{ε}}^{p})}^{n}] (1 + C \ln {\dot{ε}}^{*}) [1 - {(T^{*})}^{m}]

(1)

where A, B, C, m and n are model constants, ${\bar{ε}}^{p}$ is the effective plastic strain, ${\dot{ε}}^{*} = {\dot{ε}}^{p} / {\dot{ε}}_{0}$ is the effective plastic strain rate when the reference strain rate ${\dot{ε}}_{0} = 1 s^{- 1}$ and $T^{*} = (T - T_{r}) / (T_{m} - T_{r})$ , with T, $T_{r}$ and $T_{m}$ being the working, room and melting temperature, respectively.

The Johnson–Cook model includes a fracture criteria based on cumulative damage, in which the failure strain is sensitive to stress triaxiality, temperature, strain rate and strain path. The model assumes that damage accumulates in the material element during plastic straining, defining a damage variable D between 0 and 1. Failure is assumed to occur when D reaches unity

D = \sum \frac{Δ {\bar{ε}}^{p}}{ε^{f}}

(2)

In definition (2), the summation is performed over all increments of deformation, $Δ ε^{p}$ is an increment of the equivalent plastic strain, and $ε^{f}$ is the equivalent plastic strain at failure that depends on stress triaxiality, strain rate and temperature and can be expressed as

ε^{f} = [D_{1} + D_{2} e^{D_{3} σ^{*}}] (1 + D_{4} \ln ({\dot{ε}}^{*})) (1 + D_{5} T^{*})

(3)

where $D_{1}$ to $D_{5}$ are material constants, and $σ^{*}$ is the ratio of pressure p divided by the effective stress $σ_{e f f}$ .

A simplified version of the Johnson–Cook material model, which neglects the thermal effects, was used to model the steel behaviour on the beam elements.

The air, considered a perfect gas, was modelled with a null material model in combination with a simplified linear polynomial equation-of-state (EOS), presented in equation (4), where the pressure P is defined as a function of the internal energy of air E, the ratio of current density to reference density $ρ / ρ_{0}$ and the ratio of specific heats γ.

P = (γ - 1) \frac{ρ}{ρ_{0}} E

(4)

The complete set of parameters that define the Johnson–Cook and simplified Johnson–Cook material models (MAT015 and MAT098 in LS-DYNA), as used in this article, are given in Table 1. In addition, Table 2 illustrates the utilized parameters to completely define the null material model (MAT009) and the linear polynomial EOS (EOS001).

Table 1.

Parameters for the Johnson–Cook material model.

Parameters	Units	Value
Density	${kg / m}^{3}$	7860
Young modulus	GPa	210
Shear modulus	GPa	80
Poisson ratio	−	0.3
Strain hardening constant, A	GPa	0.849
Strain hardening coefficient, B	GPa	1.340
Strain rate coefficient, C	−	0.03
Strain hardening exponent, n	−	0.092
Thermal softening exponent, m	−	0.870
Melting temperature, $T_{m}$	K	1800
Room temperature, $T_{r}$	K	293
Reference strain rate, ${\dot{ε}}_{0}$	$s^{- 1}$	1.0
Specific heat	J/(kg K)	450
Failure parameter, $D_{1}$	−	0.015
Failure parameter, $D_{2}$	−	1.0
Failure parameter, $D_{3}$	−	0.15
Failure parameter, $D_{4}$	−	0.0015
Failure parameter, $D_{5}$	−	0.0

Table 2.

Parameters for the null material model and linear polynomial EOS.

Parameters	Units	Value
Density	${kg / m}^{3}$	1.204
Ratio of specific heats, γ	−	1.4
Initial internal energy per unit reference volume, $E_{0}$	${J / m}^{3}$	$2.533 \times 10^{5}$
Initial relative volume, $V_{0}$	−	1.0

Lagrangian model validation

The blast simulation was performed in LS-DYNA using the Load Blast Enhanced (LBE) option, in which empirical pressure loads are applied directly to the surfaces of a Lagrangian structure. These pressures, drawn upon a database of experimental pressure histories due to conventional explosions, provide a simplified and proven analysis approach over more computationally expensive methods (Randers-Pehrson and Bannister, 1997). The validation of the model was performed using a benchmark example obtained from Sahu and Gupta (2015), in which the blast response of different-shaped domes is addressed, including the analysis of a circular dome. The circular dome is rigidly fixed at the base and a TNT equivalent of 0.15 kg is blasted inside, at the centre, at mid height of dome. Figure 6(a) and (b) show the simulated Lagrangian FE model of the dome and the obtained blast-off response at t = 2 ms, respectively.

Figure 6.

Lagrangian FE model used for validation: (a) circular dome and (b) blast-off (t = 2 ms).

The results obtained with the proposed Lagrangian model were compared with the results obtained by Sahu and Gupta (2015), showing a good correlation as it can be seen in the depiction of the resultant displacement at the top of the dome, shown in Figure 7.

Figure 7.

Resultant displacement at the top of the dome.

Blast simulation

The entire exterior face of both the geodesic dome and the container was selected to receive pressure resulting from the surface blast. The sequence of frames presented in Figure 8 illustrate the numerical estimates for the pressure evolution associated with a surface burst of a TNT charge of 500 kg at a standoff distance of 10 m, for the geodesic dome and the ISO container, respectively. Analysing the referred figure, one can verify that, due to the geometry of the geodesic dome, the reflected overpressure applied on the ‘front face’ reaches lower values than the ones observed on the ISO container. Furthermore, for the illustrated blast scenario, the pressure applied on the geodesic dome seems to have more uniform geometrical distribution, again, a result of the geometry of the dome. Therefore, a better behaviour is expected in terms of displacements when comparing with the displacements present on the ISO container.

Figure 8.

Pressure resulting from the surface burst of 500 kg TNT at 10 m: (a) t = 6.5 ms, (b) t = 10 ms and (c) t=15 ms.

Maximum deformation estimates

The corresponding maximum displacement is plotted in Figure 9, also for both structures. Through this figure, one can see that, in general, for the same blast scenario, the deformation estimates associated with the geodesic dome are lower than the corresponding deformations for the ISO container. This difference will be further scrutinized in the following sections.

Figure 9.

Maximum displacements (500 kg TNT at 10 m).

Vulnerability assessment of the geodesic dome to blast loading

The vulnerability assessment of the geodesic dome to blast loading was evaluated taking into account several possible loading scenarios, defined as a combination of the TNT-equivalent weight of the explosive charge and the standoff distance. Three TNT charge weights were considered, 50, 150 and 500 kg, that correspond, respectively, to an improvised explosive device (IED) in a small hand luggage, an automobile or a van (U.S. Department of Homeland Security, 2003), while the standoff distances varied from 5 to 50 m.

Two different approaches were used to substantiate the performance assessment of the dome under blast loading. The first one relied on the concept of a safety zone inside the protective shelter, defined according to the maximum and residual displacements obtained after a certain blast scenario. The second approach was based on the damage characterization of the shelter, based on the response of its structural components during a blast load.

Influence of the consideration of air inside the structures

A preliminary study was performed to verify the influence of the consideration of air, on the inner side of the protective structures and on their response. For this purpose, all blast scenarios were simulated, resorting to the FE models illustrated in Figure 5, both with the air volume and without it, and the resulting maximum displacement of the front surface $δ_{y}^{m a x}$ was compared.

Figure 10 presents the ratio of maximum displacement, when the air is considered, to maximum displacement determined resorting only to the Lagrangian elements. On average, the consideration of air inside the protective structures leads to a reduction of 8.5% and 8.7% for the ISO container and the geodesic dome, respectively. On the other hand, the largest reduction (22%) was verified when the ISO container is subjected to a surface burst of 50 kg at a distance of 5 m. Therefore, on the remainder of the study, the air will be considered.

Figure 10.

Influence of air on the maximum displacement of the front face.

Safety zone definition

The definition of a safety zone inside the protective shelter is based on the evaluation of the maximum displacements obtained during a given blast scenario. As an example, the maximum displacements shown by the mid-sections of the tested protective shelters after a blast loading of 500 kg TNT at 10 m are illustrated in Figure 11. Analysing the plots, one can clearly see that, for this blast scenario, a much wider safety zone can be defined inside the geodesic dome than in the ISO container. By plotting the maximum and residual displacements along the lengths of the mid-sections of the proposed protective shelters, one obtains the lines depicted in Figure 12 (50 kg TNT at 5, 10 and 15 m) and Figure 13 (500 kg TNT at 10, 30 and 50 m), respectively.

Figure 11.

Maximum displacements at mid-sections (500 kg TNT at 10 m): (a) mid-section of the geodesic dome and (b) mid-section of the ISO container.

Figure 12.

Maximum and residual displacements for the geodesic dome and corresponding effective volume reduction: (a) TNT = 50 kg and (b) TNT = 500 kg.

Figure 13.

Maximum and residual displacements for the ISO container and corresponding effective volume reduction: (a) TNT = 50 kg and (b) TNT = 500 kg.

Observing the graphs in Figure 12, one can see that the maximum deformation associated with the geodesic dome, for a TNT charge of 50 kg and a stand-off distance of 5 m, is approximately 0.33 m. This means that, to be safe, the personnel inside this protective shelter should keep inside a safety zone, defined as a 4.55 m diameter circular area centred in the middle of the dome, 0.33 m away from the walls of the structure, corresponding to a 33% effective volume reduction (EVR) of the dome. In the case of the ISO container, see Figure 13, this distance amounts to 0.7 m, leading to a very limited safety zone (67% EVR). As the stand-off distance increases, the safety zone also increases. For standoff distances of 10 and 15 m, the maximum displacements are almost null in the case of the geodesic dome (no significant EVR), whereas in the case of the ISO container are about 0.34 m (32% EVR) and 0.23 m (21% EVR), respectively.

For a TNT charge of 500 kg, the safety zone associated with the geodesic dome is limited to a 2.9-m diameter circular area centred in the middle of the dome (82% EVR). For this charge weight and the considered standoff distances, it is not possible to define a safe zone in the ISO container.

For all the above analysed cases, the corresponding EVR is indicated in Figures 12 and 13, for charges of 50 and 500 kg TNT, respectively.

An alternative way to visualize the safety zones is to use an adequate colour contour definition for the maximum displacements graph. By choosing a displacement threshold of 0.2 m to be associated with the definition of the safety zone, one can obtain a clear depiction of these areas as shown in Figures 14 and 15.

Figure 14.

Safety zone definition for 50 kg TNT at 5 m and 0.20 m displacement threshold: (a) geodesic dome and (b) ISO container.

Figure 15.

Safety zone definition for 500 kg TNT at 10 m and 0.25 m displacement threshold: (a) geodesic dome and (b) ISO container.

From these figures, one can see that, for the analysed blast scenarios, the safety zones associated with the geodesic dome are always much wider than the ones associated with the ISO container, providing a safer environment for the personnel inside these protective shelters.

Damage characterization

The design of expeditionary structures required to resist the air-blast associated with terrorist explosive threats, where the minimum standoff distances are not available, has to guarantee adequate levels of protection to its inhabitants, minimizing casualties (U.S. Department of Defense, 2008). The potential levels of protection are described qualitatively in Table 3 and are usually used to characterize the goals associated with each level of protection (LOP).

Table 3.

Levels of protection for expeditionary structures.

Level of protection	Potential structural damage
Below AT Standards	Severe damage. Frame collapse/massive destruction
Very Low	Heavy damage. Major portions of the structure will collapse
Low	Moderate damage. Damage will be unrepairable
Medium	Minor damage. Damage will be repairable
High	Minimal damage

The response of a given structure to a blast scenario and the associated LOP can be assessed by the damage levels shown by its structural components. Component damage can be assigned to one of the five regimes shown in Table 4 (U.S. Army Corps of Engineers Protective Design Center, 2008).

Table 4.

Component damage levels.

Component damage level	Description of component damage
Blowout	Component is overwhelmed by the blast load causing debris with significant velocities
Hazardous failure	Component has failed, and debris velocities range from insignificant to very significant
Heavy damage	Component has not failed, but it has significant permanent deflections causing it to be unrepairable
Moderate damage	Component has some permanent deflection. It is generally repairable, if necessary, although replacement may be more economical and aesthetic
Superficial damage	Component has no visible permanent damage

One can define certain response limit boundaries for these component damage levels (U.S. Army Corps of Engineers Protective Design Center, 2008). The relationship between the described damage levels and the response limit boundaries (B1, B2, B3 and B4) is given in Table 5.

Table 5.

Component damage levels relationship to response limits.

Component damage level	Relationship to response limits
Blowout	Response greater than B4
Hazardous failure	Response between B3 and B4
Heavy damage	Response between B2 and B3
Moderate damage	Response between B1 and B2
Superficial damage	Response is less than B1

The maximum rotation $(θ)$ of the structural components was evaluated for all the considered blast scenarios, for both of the protective shelters under consideration. According to U.S. Army Corps of Engineers Protective Design Center (2008), the response limits for hot rolled structural steel members are 1°, for B1 and 3° for B2 to B4. The rotation-stand-off curves for TNT charges of 50, 150 and 500 kg are presented in Figure 16. The curves were plotted using the obtained data with power regression functions, yielding coefficients of determination ${(R}^{2})$ close to the unit. The maximum rotation associated with heavy damage appears in the graphs as a yellow dashed line.

Figure 16.

Rotation–stand-off diagrams: (a) 50 kg TNT, (b) 150 kg TNT and (c) 500 kg TNT.

One can see that the rotations associated with the geodesic dome are always below their ISO container counterparts, meaning that for a given stand-off distance, the observed rotations were always lower in the dome.

Finally, by determining the stand-off distances associated with the specified rotation limits of 1° and 3°, one can draw the diagrams presented in Figures 17 and 18 through linear regression, which represent the charge weight–standoff diagrams, showing the potential structural damage for the dome and for the container, respectively.

Figure 17.

Charge weight–stand-off diagram showing the potential structural damage (dome).

Figure 18.

Charge weight–stand-off diagram showing the potential structural damage (container).

The diagrams show that the ISO container shows a higher potential for structural damage than the geodesic dome.

Pressure

During this numerical study, a set of tracers was placed on the inside of both protective structures to measure the observed pressure during the considered blast scenarios. The tracers were placed at the centre of the structures at heights of 0, 1 and 2 m above the ground. Figure 19 illustrates the pressure–impulse diagram for lung damage, where each of the curves represent combinations of pressure and impulse for which the survival probability takes the same value. Analysing the referred figure, one can verify that a maximum scaled overpressure of 0.54 was obtained for all considered load cases and, therefore, the lung injury threshold was not surpassed. However, when ISO container was subjected to the effects of a 500 kg surface burst at a distance of 10 m, a maximum scaled pressure of 2.2, in combination with a scaled impulse of 3.7 (considering an atmospheric pressure of 101.325 kPa and a human with 75 kg), was registered. Observing Figure 19, it is possible to verify that the referred combination of pressure and impulse exceeds the lung injury threshold. Apart from the referred blast scenario, all other combinations determined for the ISO container did not surpass a scaled overpressure of 0.57. Nonetheless, it is important to note that the registered values of scaled pressure on the inside of the ISO container are, on average, three times higher than their geodesic dome counterparts.

Figure 19.

Pressure–impulse diagram for lung damage.

Conclusion

This article addresses the performance of geodesic domes as protective expeditionary structures under blast loadings. It is shown that dome-inspired structures can excel in this type of applications. From the performed analysis, in which an ISO container was used as a benchmark structure, one can draw the following conclusions:

According to the obtained maximum and residual displacements shown by a protective shelter under a given blast scenario, appropriate safety zones inside the shelter were defined to minimize casualties. The corresponding EVRs were also computed. Under the tested blast scenarios, the geodesic dome always performed better than the ISO container, showing wider safety zones.

Rotation–stand-off curves were obtained with the discrete data from the blast numerical simulations using power regression functions. It was evident that the rotations associated with the geodesic dome were always smaller than their ISO container counterparts.

The rotation–stand-off curves were used to obtain the charge weight–stand-off diagrams for both structures showing the respective potential structural damage as a function of these two variables. It was clearly shown that the geodesic dome protective expeditionary structure shows minor potential for structural damage than the ISO container.

The scaled overpressures determined for the inner part of the ISO container were, on average, three times higher than the ones registered from the inside of the geodesic dome. In addition, none of the obtained combinations of pressure–impulse, computed with the geodesic dome FE model, exceeded the lung injury threshold. The same cannot be said about the ISO container, for which, the threshold was surpassed. Therefore, it is considered that the use of a geodesic dome as a protective expeditionary structure provides a safer environment for the personnel inside these protective shelters.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial contributions given for this research from the Portuguese funding institution FCT – Fundação para a Ciência e Tecnologia (grant no.: SFRH/BD/115599/2016).

ORCID iD

Filipe Amarante dos Santos

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