Optimization of Dynamic Mechanical Properties of Knitted Barrier Meshes

2.1 Analysis of structural properties of the designed models of barrier meshes

For 20 designed variants of 1.5 × 1.5 m barrier mesh models, the following parameters were determined: mesh weight and volume, threads surface area, and cover factor. The calculations are presented in Table 1.

The results analysis shows that the above-mentioned parameters strictly depend on the a-jour geometry of the mesh. The weight of the model is an important parameter that should be taken into account to reduce material consumption in the future production of this type of technical meshes. Another important parameter is the cover factor that by an even distribution of threads in the mesh arms determines the distribution of stresses and deformations in the surface and volume of the mesh.

The data presented in Table 1 show that

1. the heaviest model is the four-axial eight-thread mesh with square a-jour structure with a weight of 12.50 kg and a volume of 8.62 dm³. The next one is the mesh with diamond-shaped a-jour geometry with a mass of 10.47 kg and a volume of 7.22 dm³. The third heaviest model is the mesh with regular hexagonal a-jour structure of “inverted honeycomb” with two axes, whose mass is 10.21 kg and volume equals 7.04 dm³. The next one is the mesh with regular hexagonal a-jour geometry in the shape of a “honeycomb” with two axes, whose mass is 9.58 kg and volume is 6.60 dm³. Similar meshes with large mass and not less than 9 kg are

2. the mesh with irregular hexagonal a-jour structure with two axes Ms = 9.37 kg, the one with irregular hexagonal a-jour geometry with oblique axes 2 Ms = 10.06 kg, and the mesh whose a-jour structure is a four-axial six-thread square 3 Ms = 9.32 kg.

3. the smallest mass was observed for models such as the mesh with regular hexagonal a-jour structure of inverted honeycomb whose mass equaled 4.20 kg and the volume reached 2.89 dm³, the biaxial four-thread mesh with square a-jour geometry whose weight was 4.26 kg and volume 2.94 dm³, and the model with regular hexagonal a-jour structure in the form of a “honeycomb” with a mass of 4.51 kg and a volume of 3.11 dm³.

It can be concluded that structural parameters of the meshes, including their mass, largely depend on the geometry of the a-jour structure. The mesh mass, volume, thread surface area, and cover factor are correlated and the relationships between these parameters are proportional. This means that the mass of the mesh can be described by a first-degree (linear) equation as a function of volume, threads surface area, or cover factor.

All the above-mentioned structural parameters affect the final mechanical properties of barrier meshes.

3.1 Analysis of simulation results of the model object collisions with barrier meshes

Dynamic crash tests were carried out for 20 variants of barrier meshes and one reference variant “a plate.” A ball made of steel with a diameter ϕ = 40 cm hit the mesh models at a speed of 110 km/h (30.55 m/s) with energy E_k = 70.93 kJ. The calculation results for each variant are maps showing the distribution of reduced stresses and absolute deformations, as well as charts presenting the analyzed parameters as a function of time. Sample result of numerical simulation of the mechanical properties of a four-axial six-thread mesh with square a-jour structure 3 is shown in Figures 7 and 8.

Figure 7

Stress distribution resulting from the four-axial six-string mesh model with openwork mesh in the shape of a square: (a) reduced stress distribution at maximum ball load and (b) maximum mesh deflection on a reduced scale.

Figure 8

Distribution of deformations arising in a four-axial six-string mesh model with a square-shaped openwork mesh: (a) absolute deformation distribution at maximum ball load on a reduced scale and (b) maximum mesh deflection on a full scale.

3.2 Quantitative analysis of the mechanical properties of the meshes

In the first stage of the analysis, absolute deformations of the meshes were compared by presenting them on two charts. Figure 9 shows the deformation characteristics changing over time, starting from the moment of impact Δu = f(t), and the second bar graph (Figure 10) compares the values of maximum deformations Δu_max for the analyzed mesh geometries.

Figure 9

Absolute deformations observed in 20 mesh models with different a-jour structures.

Figure 10

Maximum deformations observed in 20 mesh models with different a-jour structures.

The graphs show that the geometry and structural parameters of the mesh have a significant influence on its deformations, as well as on the maximum value of absolute deformation, in relation to the characteristics of deflection changes over time. Most susceptible to deformation is the variants with dodecagonal a-jour structure Δu = 23.32 cm, and the mesh with circular a-jour geometry 1 (classic side connection of spherical rings) with deflection Δu = 23.63 cm. Models that are less susceptible to deformations are the four-axial six-thread mesh with square a-jour structure 3: Δu = 14.95 cm and the mesh with circular a-jour geometry with a system of two additional vertical and horizontal thread reinforcements: Δu = 15.87 cm. Figure 9 shows the phenomenon of bouncing the ball against the mesh surface (deflections with positive deformation values), which is not a positive characteristic in case of impact absorbing barriers. In case of mesh deformability, it is difficult to clearly define the quantitative optimization criterion. Depending on the energy absorption function for objects of the assumed mass, the barrier mesh with appropriate level of boundary deformability should be designed. Another important factor is programming the braking time, i.e., negative acceleration values that are important for determining the overload on the human body at the moment a motor vehicle crashes against a barrier.

Comparative analysis of reduced stresses is illustrated by two graphs: a linear (Figure 11) and a bar one (Figure 12), on which the horizontal red line stands for boundary stress at the level Δб = 5.5 GPa.

Figure 11

Reduced stresses observed in 20 models of barrier meshes with different a-jour structures.

This analysis helps to select the optimum mesh—the one that is least dynamically loaded with tensile (breaking) forces. With the help of the graph (Figure 12), it is possible to select the meshes whose construction elements are loaded with stress of no more than 5.5 GPa, according to the criterion of minimum loading values.

Figure 12

Reduced stresses observed in 20 models of barrier meshes with different a-jour structures, together with boundary value of reduced stresses Δб > 5.5 GPa.

Five structural variants of meshes meet this boundary criterion. The best model is the variant with a-jour geometry of interlacing circles. Other variants that should be taken into account are the meshes with irregular and regular hexagonal a-jour structure in the form of a “honeycomb,” the mesh with connected circles, and the mesh with square four-axial eight-thread a-jour geometry. Quantitative analysis of the mesh characteristics presented in Table 2 summarizes the extreme values of deformations and stresses recorded in the meshes, and the table rows are arranged from the largest to the smallest deformations.

From simple relationship describing the strength of viscoelastic bodies in mechanics, it can be concluded that for the same material properties of the body subjected to stretching, the internal stresses within the body should increase together with the increase in forced deformations.

However, for the analyzed mesh models, this rule is not met. An important factor determining the final deformation–stress relationship is the geometry of the mesh structure and the resulting structural parameters. FEM numerical modeling of the mechanical characteristics of barrier meshes in the context of optimizing their structure and properties is a tool that can be used to select the most favorable variants, from the point of view of the assumed deformations and minimum dynamic forces in the stretched elements.

3.3 Optimization analysis of the mechanical properties of barrier meshes

Subsection 3.2 proves that both the geometry of the mesh and its basic structural parameters are of vital importance in assessing the mechanical properties of the mesh. Table 1 presents the selected structural parameters, and one of the most important is mass per unit area. Its values range from 2.65 to 12.05 kg.

The mesh with the smallest mass, built of classically connected circular loops, demonstrates the largest deformation Δu = 23.23 cm and significantly high stress equal to Δб = 7.2 GPa, while for the mesh with the largest mass per unit area, i.e., the one with four-axial eight-thread square a-jour structure the deflection is the smallest and equals Δu = 14.93 cm. For this variant, the average reduced stress of Δб = 6.15 GPa is recorded. Referring to this fact, it can be concluded that when the mass of the mesh increases, its susceptibility to deformation and reduced stresses decrease. The reduced stresses depend on the complexity of the stretching, bending, and shearing processes. It can be assumed that massive objects with low porosity are more resistant to non-dilatational deformations.

A more reliable parameter for assessing mechanical properties of the meshes is their relative characteristics: relative deformation Δu/M_mesh and relative stress Δб/M_mesh related to the unit mass of the mesh M_mesh. A question can be asked: “How does the unit mass of the mesh affect its susceptibility to deformation and determine its stresses?” In this case, the most important factor determining the mechanical properties of the mesh is its geometry. Bearing in mind the dependence of the mechanical parameters of the mesh on its weight, it is possible to change this parameter in the design process by, for example, changing the thickness of the mesh or the apparent density of the mesh material. Analysis of the mechanical properties of the meshes in terms of relative deformation and stresses is presented in Table 3.

The presented calculations show that the lowest stresses accompanied by low deformations have been recorded for three mesh variants: two models with square a-jour structure, one of them a four-axial six-thread variant, and the other an eight-thread structure with four axes, and the third mesh with a-jour geometry in the form of thickened diamonds. For these meshes, reduced stresses take the values from 0.43 to 0.66 GPa/kg and relative deformations from 1.02 to 1.6 cm/kg. Taking into account the criterion of the lowest possible values of relative stress, these variants are optimum, i.e., most favorable with regard to the expected strength of the produced meshes. The deformability criterion is labile, and it is difficult to clearly define it because the designed impact barriers demonstrate different deflections depending on the predefined impact energy absorption time. It should be emphasized that the conducted numerical experiment proved the thesis concerning a significant influence of the geometric structure of the mesh on its mechanical properties.

3.4 Analysis of surface distribution of deformations and stresses in barrier meshes

In subsection 3.3, the meshes were evaluated in the context of quantitative differences in deformation parameters and reduced stresses. This section aims to carry out a qualitative analysis concerning surface distribution of deformations and stress. This analysis is important because it presents the shape of isolines connecting points on the meshes with the same stress and deformation values, as well as growth and decrease gradients of these parameters. According to designer's assumptions, the ideal mesh should be characterized by even distribution of stresses and deformations, and in more realistic terms the best distribution means that the absolute gradients take the lowest possible values. The idealized model is impossible to obtain due to the differences in the shape and size of the mesh itself, the method of fixing it, the a-jour geometry, structural features, the method of connecting the a-jour structure into a knitted fabric, and many others. Moreover, it should be emphasized that the analyzed distribution of the mechanical characteristics of the meshes also depends on the input parameters, i.e., the shape of the solid or the complex characteristics of the object, e.g., a car hitting the barrier—its mass, speed, angle of impact, susceptibility to deformation, and other anisotropic mechanical properties of the striking object. In case of this study, a simplifying assumption was made that the striking object is a steel ball. The received results of stress and deformation distributions are presented in Tables 4 and 5. The colors of the lines and fields correspond to specific values of deformation and stresses. The presented results are typical for calculations made in the FEM environment, in this case using the Ansys program. The isolines representing stress and deformation distribution are arranged symmetrically toward two perpendicular symmetry axes. The results of deformation and stresses analysis are presented in the following two sections.

Table 4

Distribution of absolute directional deformations in mesh models with different a-jour structures

Table 5

Stress distribution in mesh models with different a-jour structures

3.4.2 Analysis of surface distribution of mesh stresses

Depending on the model, stress images take different shapes (Table 5).

The distribution of mesh stresses depends on the a-jour geometry. In addition, differences were observed in stress distribution maps immediately after the impact. Stress distribution can take the shape of a circle, a diamond, a “cross,” and a figure resembling the letter “X.” Impact simulations were also carried out for a cube with the external dimensions comparable with those of the ball, for one selected variant of a tetragonal mesh.

The diversity of the isoline shapes is illustrated in Table 6, comparing the effects appearing when the barrier mesh is hit by the ball and by the cube. More regular oval lines can be observed for the mesh hit with the ball. For the mesh hit with the cube, the lines take a “wavy” tetragonal shape.

Table 6

Deformation and stress distribution for a biaxial four-thread mesh model with square a-jour structure, hit with a ball and a cube

The presented qualitative analysis of stress and deformations distribution visually illustrates the dependence between the shapes of the propagating deformations and stresses, the diverse geometry of the barrier meshes, and the shape of the hitting object. For a thorough analysis of this phenomenon, one should use a gradient (vector) analysis of the deformations and stresses increase in the mesh surface. At this point, it should be emphasized that in case of unfavorable distributions, in particular stress distribution, a more complex structure of the anisotropic barrier mesh can be considered.