Stress and strain analysis using Autodesk Inventor software in soil-cement brick

The computational analysis of materials is fundamental for a better understanding of their physical and mechanical properties, achieving more results in a shorter time. It is a cheaper, non-destructive, practical way, and easily adaptable to various types of models and physical influences. This study has the objective of ascertaining the stress and strain analysis in soil-cement brick through the Autodesk Inventor Professional software, which uses the finite element method. Three models of brick were made: two holes, monoblock, and groove, which are the most commonly used shapes. To the two holes model, the maximum first principal stress observed was 1.464x10 MPa and the third principal stress was 5.4x10 MPa, presenting an insignificant strain of 1.037x10 mm. In the monoblock model, the maximum first principal stress was 4.606x10 MPa, and the third principal stress was 1.19x10 MPa, presenting a strain of 1.611x10 mm. The groove model presented the maximum first principal stress at 3.263x10 MPa and for the third principal stress was 9.1x10 MPa, respectively, presenting a strain of 3.344x10 mm. It can also be observed that the models have stress concentrating regions in the sharp edges and notches of the part. Among the three models studied, the one that presented the most favorable stress-strain conditions was the two-hole model. Since it has a larger contact area, the load applied to it was better distributed, presenting higher resistance than the other models with a smaller contact area.


Introduction
Soil-cement brick is a more sustainable alternative than the common brick. It consists of soil, cement, and water, without the burning process, in which large quantities of wood or fuel oil are consumed (Ferraz & Segantini, 2004), so there are no cutting trees for burning and emission of toxic gases into the atmosphere (Valadão, et al., 2017).
Its structure provides a fitting system, which greatly reduces the use of mortar and reduces the construction time (Jordan & Freitas, 2018), and its two internal holes make it possible to embed the hydraulic and electric networks, avoiding future breaks in the construction site (Motta, 2014), reducing costs and solid waste disposal.
Besides the ecological advantages, it also presents economic attractiveness since there is a reduction in water and energy consumption (Motta, 2014), which makes it a more accessible material. Thus, it is an alternative to supply a housing shortage (Motta, 2014), since the demand for housing is a frequent problem in developing countries due to the high cost of production (Milani, 2005).
The finite element method is an approximate numerical method widely applied in engineering, which consists of dividing a continuous domain into small elements that have finite dimensions, "finite elements" (De Souza, 2003;Melo, et al, 2017;Bento & Ferrus Filho, 2018), while maintaining the properties of the original domain (Lotti, 2006). This makes complex problems simpler and enables more accurate results. The Inventor software uses this method through the application of meshes in the model, either bidimensional or three-dimensional, so it can be used to perform stress and strain analysis of soil-cement brick.

Methodology
The method applied in the work was scientific research of the experimental type (Cervo, et al., 2007), whose central problem was to identify the use of simulation as an alternative to identify the stresses and strains in various models of soil-cement brick. The hypotheses studied were to use the experimental reference parameters and to assign conditions of use of the brick as a one-story building wall.
Autodesk Inventor has a database with the properties of several materials and appearance suggestions that can be assigned to the model. As ceramic materials present only the silicon nitride and concrete in the database. The dimensions adopted for the bricks models were those supplied by the Verde Equipamentos company (Table 1). Thus, the physical and mechanical properties of soil-cement brick had to be added to the software, considering a survey in the literature for approximate compositions of 10 -15% of cement in brick, as shown in Table 2. For the soil-cement brick modeling, and the performance of the stress analysis, it was used Autodesk Inventor Professional software. Figure 1 shows the two-holes model, an example of a hollow brick.    Source: Authors.
In Figure 1 it is possible to see the soil-cement brick model simulated in the Autodesk Inventor program, which, due to the program's functions, is very similar aesthetically to the real model. On the right of the image is the model in the finite element method standards with the mesh parameter.
Autodesk Inventor uses the finite element method to calculate the distribution of forces applied to the model, which consists of the formation of several polygons that restrict the area to be studied, reducing error and bringing the calculations closer to actual results. These formed polygons are called "mesh parameters", which define the average and minimum size of the elements, leveling factor, and maximum turning angle. The parameters used in the mesh configuration were 0.099 for the average size of the elements, 0.200 for the minimum size of the elements, 1.500 for the leveling factor, 60.00 for the maximum turning angle, and the creation of curved mesh elements.
The soil-cement brick with 2 holes is normally used in walls, with the purpose of sealing, that is, without a load-bearing function. In this way, the load that usually bears is only the weight of the bricks stacked on it. For the dimensioning of the force applied to the brick, the load estimated in the stacking ( ) was used considering the first brick of a standard construction row bearing the weight of the other bricks above it and is indicated in Equation A. The side of force application was the loading surface shown in Figure 2 and left the side and bottom surfaces fixed, as shown in Figure 3.   Source: Authors.
In Figure 3 it is observed that the fixed faces of the brick are the sides and bottom, so the software determines that there are contacts in these areas. Thus, these regions will present a higher compressive load in the stress analysis.
The soil-cement brick is used in the production of non-bearing insulating walls, and the two-hole and monoblock models are used in stacking in an intercalated manner, which stabilizes the structure, avoiding the action of high shear stresses that could affect the integrity of the wall. And the groove model is used for the passage of ducts and pipes, avoiding unnecessary breakage of parts; this can also be used in the making of beams.
According to Hibbeler (2015), the principal stresses represent the maximum normal stress and the minimum normal stress at the point, and Equation B is used to determine it. This result gives the maximum or minimum normal stress in the plane acting at a point, 1 ≥ 2 depending on the chosen signal. This set of particular values is called principal stress in the plane, and the corresponding planes that they act are called principal stress planes, as shown in Figure 4. Source: Hibbeler (2015). Figure 4 illustrates the stress plane, where the stresses applied perpendicular to the surface represent the tensile stresses in the material, and the stresses parallel to the surface represent the shear stresses in the material. These stresses occur in the material when a compressive stress is applied, which can be observed in the first and third principal stresses.

Results and Discussion
The value obtained using Equation A, considering a 3 m height wall, was 1663.15 N. It is referred to the estimated stacking load was assigned to the force parameter applied to the model on its upper side.
The first principal stress ( Figure 5 (a) for the two holes, (b) for the monoblock and (c) for groove brick) refers to the value of the stress that is normal to the plane where the shear stress is zero and helps to understand the yield strength, represented by the red color in the spectrum of the model. As for the third principal stress represented in Figure 6 (a) and (b) for the two holes, (c) and (d) for the monoblock, (e) and (f) for groove brick, it acts in the opposite way to the normal plane direction. It represents the maximum compressive stress, composing the lower limit of the color spectrum, in blue.
According to Callister Jr and Rethwisch (2012) stress amplification is not restricted only to microscopic flaws; it can also occur in macroscopic internal discontinuities, sharp edges, and notches. Thus it can be analyzed that reacting to the load applied, the brick has a concentration of stress in the edges of the side surfaces, in the notches on the bottom, and the bumps on top of the holes.
For the two holes brick was verified the strain of only 1.037x10 -3 mm (Figure 7 (a)) characteristic of ceramic materials, which are relatively rigid and resistant, present fragile behavior because ceramics fail after a strain of only approximately 0.1% (Callister Jr & Rethwisch, 2012). The percentage distant from the strain of 1.105x10 -3 mm given by the software. For the other two models the strain was also small (Figure 7 (b) and (c)), being in line with the characteristics of the material. Linear distributed loads produce a resulting force that passes through the area centroid (Buffoni, 2017). Thus a concentrated strain was observed in the central region of the brick, due to its load distribution. The results of the stress analysis, first and third maximum and minimum principal stress, and strain, obtained through the Inventor software can be seen in Table 3.

Conclusion
We can conclude that the soil-cement brick has many applications and is a commercial product of notable importance, thus, the studies that seek to improve its properties are important. And with the use of Autodesk Inventor, which is a very convenient software for computational analysis of the physical and mechanical effects of soil-cement brick. Since it is a more practical method of studies and without the need for large investments, it is possible to analyze the behavior of the forces acting on the model, adapting the parameters for the most diverse purposes.
Based on the results obtained, the models presented are more practical and ecological to use, and can be used in civil construction for making non-bearing insulation walls, with the facility of having a specific model for the arrangement of ducts and pipes, and also as a mold for beams.
Considering the graphic results of the stress, it can be concluded that the edges whose angle is near or equal to 90º, have a higher concentration of stress, becoming a region most susceptible to fracture. The results obtained for the model studied, being a fragile material, resulted in an insignificant strain between 1.037x10 -3 mm and 3.344x10 -3 mm. Such results demonstrate that the soil-cement brick in its different presentations can be used as a non-bearing sealing element, respecting the mandatory criteria of the standard.
For future work it is suggested to develop the experimental part of the models to compare the results obtained experimentally with those obtained through simulations. Another suggestion is to use the program for modeling other sizes and shapes of soil-cement bricks to improve understanding of the stresses in various models.