Software development for simulation of Auxetic structures

An auxetic structure as a substrate material in sensor applications improves sensitivity performance due to lateral expansion under tensile loading. The presented stretchable, highly sensitive at-low-strain piezoresistive sensor was manufactured by mixing the silicone rubber and chopped carbon fibers in an auxetic re-entrant structure form. Auxetic re-entrant die was printed by using a 3D printing technique. The main feature of this sensor is the high sensitivity for strains lower than 6%, in which previous sensors could not recognize this range of strain well. In order to justify the excellent performance of the sensor, the deformation modes of the auxetic re-entrant structures were investigated and also connected to piezoresistive sensitivity. The shifting strain is defined as strain value, where the Poisson’s ratio of structure shifts from negative to positive Poisson’s ratio. Our study revealed that auxetic sensors have excellent sensitivity performance until the shifting strain due to having negative Poisson’s ratio, and after that, their sensitivity performance is going to be weak due to having positive Poisson’s ratio. In the present work, silicone rubber as the substrate material was used. This is a very soft material and made it possible to have low shifting strain resulting in perfect sensitivity performance for low-strain applications. The presented sensor has applications in many fields which are in low-strain conditions such as measuring the Vocal Cord Dysfunction (VCD), wrist pulse, or even earth vibration.

The behavior of Auxetic structures is highly dependent on the geometric parameters of the unit cell. To achieve the desired behavior, it is necessary to perform a parametric study on the unit cell. A conventional parametric study (which includes modeling and analysis with different parameters) is very time consuming and error prone. The Auxetica plugin was produced to solve this problem. Auxetica is an Abaqus plugin developed to estimate Auxetic structures' performance. In this paper, the features and instructions of this plugin are presented. This tool can automatically generate and analyze re-entrant, chiral, (Tri-chiral, Tetra-chiral, Hexa-chiral) and anti-chiral (Tri-anti-chiral and Tetra-anti-chiral) in planar and cylindrical geometries. The plugin tasks can be categorized as follows: the first task is to generate a model based on parametric input. The second task is an automatic analysis and extraction of the target output. The third task is to generate models that are ready for 3D printing and testing. To validate the plugin, an experimental setup is prepared and samples which are made by 3D printing are tested. The simulation result is validated with experimental data before any parametric study would be carried out. Moreover, to understand the plugin functionality better, a parametric study has been done. This plugin helps to perform the parametric study by the user in the shortest time and with the most accuracy with the desired inputs.

In this study, some new 2D auxetic metamaterials were investigated and called octagonal auxetic metamaterials. The structures were examined by numerical and experimental approaches and 3D printing additive manufacturing technique was employed to fabricate the structures from thermoplastic polyurethane elastomer (TPU) which is considered as a hyperelastic material. Auxetic behavior was caused by adding small triangles and squares to the vertices of the octagonal structure and applying high compressive strain. Although the octagonal structure showed negative Poisson’s ratio at high compressive strain, the results suggested that adding triangles to the vertices of the octagonal structure as well as increasing the triangle edge length led to higher negative Poisson's ratio. In contrast, with small squares adding to the vertices of the octagonal structure, Poisson’s ratio became slightly more negative. In addition, by increasing the square edge length, Poisson’s ratio measured near zero or even positive values. Moreover, a parametric study was carried out by Python 3.6.5 programming language to find the best triangle and square edge length which caused the most auxeticity.

Poisson Voronoi (PV) tessellations as artificial microstructures are widely used in investigations of material deformation behaviors. However, a PV structure usually describes a relative homogeneous field. This work presents a simple numerical method for generating 2D/3D artificial microstructures based on hierarchical PV tessellations. If grains/particles of a phase cover a large size span, the concept of “artificial phases” can be used to create a more realistic size distribution. From case to case, detailed microstructural features cannot be directly achieved by commercial or free softwares, but they are necessary for a deep or thorough study of the material deformation behavior. PV tessellations created in our process can fulfill individual requirements from material designs. Another reason to use PV tessellations is due to the limited experimental data. Concerning the application of PV microstructures, four examples are given. The FE models and results will be presented in consecutive works, i.e. “part II: applications”.

The paper introduces a valuable new description of fatigue strength in relation to material properties and thus a new perspective on the overall understanding of the fatigue process. Namely, a relation between the endurance limits and the accompanying values of the critical resolved shear stress (CRSS) for various metallic materials has been discovered by means of a multiscale approach for fatigue simulation. Based on the uniqueness of the relation, there is a strong indication that it is feasible to relate the endurance limit to the CRSS, and not to the ultimate strength as often done in the past.

The structure and mechanical properties of the 09Mn2Si high-strength low-alloyed steel after the five-stage helical rolling (HR) were studied. It was revealed that the fine-grained structure had been formed in the surface layer ≈ 1 mm deep as a result of severe plastic strains. In the lower layers, the “lamellar” structure had been formed, which consisted of thin elongated ferrite grains oriented in the HR direction. It was shown that the five-stage HR resulted in the increase in the steel fatigue life by more than 3.5 times under cyclic tension. The highest values of the number of cycles before failure were obtained for the samples cut from the bar core. It was demonstrated that the degree of the elastic energy dissipation in the steel samples under loading directly depended on the area of the grain boundaries as well as on the grain shapes. The fine-grained structure possessed the maximum value of the average torsional energy among all the studied samples, which caused the local material structure transformation and the decrease in the elastic energy level. This improved the crack resistance under the cyclic mechanical loading. The effect of the accumulation of the rotational strain modes at the grain boundaries was discovered, which caused the local structure transformation at the boundary zones. In the fine-grained structure, the formation of grain conglomerates was observed, which increased the values of the specific modulus of the moment of force. This could be mutually compensated due to the small sizes of grains. At the same time, the coarse-grained structures were characterized by the presence of the small number of grains with a high level of the moments of forces at their boundaries. They could result in trans-crystalline cracking.

In this paper, the modified SIMP topology optimization (TO) method was used, to introduce diverse auxetic unit cells with different volume fractions, composing of the symmetric, chiral and re-entrant unit cells. The output results suggested that the geometry of the 2D auxetic structures were extremely dependent on the values of SIMP method parameters, including initial designs and volume fractions. The brilliant modes of deformation in the auxetic structures, whose unit cells are symmetric, are based on either buckling or bending. To validate the TO results, four structures containing symmetric unit cells were chosen, called structure 1, 2, 3 and 4. The auxetic structures were produced by using 3D printing, with TPU as a hyperelastic material as well. Under Compression, the dominating mode of deformation in structures 1 and 2 is based on bending, caused by the movement of the oblique struts between the unit cells. There is also a linear relationship between the vertical and horizontal displacements in structure 1, the structure with 50 % volume fraction and -0.55 Poisson’s ratio value. However, the deformation mechanisms in structures 3 and 4 are based on buckling, called shearing deformation, which is the result of the buckling of the vertical struts between the unit cells.

In this study, 2D triangular anti-trichiral structures and auxetic stents, under compression, were introduced. The cores of the anti-trichiral structures were the equilateral triangles. The deformation mechanisms in 2D structures were based on the rotation of the triangles and bending of the ligaments. A parametric study was carried out to investigate the dependence of the Poisson's ratio to the triangle edge lengths. The most auxeticity, with the values of υyz = −0.55 and υzy = −1.6, was obtained in the structure in which the triangle edge lengths were considered 13 mm. Next, the auxetic stents with the aims of uniform shrinkage behaviors as well as high energy absorption were introduced. For this purpose, the equilateral triangles were distributed on the cylindrical surfaces along with the peripheral and longitudinal directions. Under compression, the stent with 15mm triangle edge lengths possessed uniform shrinkage behavior, and the values of Poisson's ratio were measured υzx = −2.2 and υzy = −2.19. Finally, the comparisons between triangular and conventional anti-trichiral stents were performed. It was observed that the lateral displacements, as well as energy absorption of the triangular stents were twice and three times as high as the conventional anti-trichiral stents respectively.