Isogeometric Shape Optimization of Auxetics in the Nonlinear Regime

Researchers: Deepak Pokkalla, Zhenpei Wang, Leong Hien Poh, Ser Tong Quek

Auxetics is a class of structural and/or functional materials that expand (contract) transversely when stretched (compressed) in the axial direction, exhibiting a negative Poisson’s ratio (NPR) phenomenon.

Auxetic material (NPR arises due to the underlying structural geometry and deformation mechanism) Andrew Alderson, 1999

Due to this counterintuitive behavior, auxetics boasts enhanced mechanical properties with many potential applications in civil, automotive, aerospace, and medical fields.

Auxetic soft network composite materials for tissue engineering and skin-mounted electronics applications. Jang et al., 2015

Smoothed petal auxetics with prescribed nonlinear deformation

The primary objective of my doctoral research is to develop an isogeometric shape optimization framework based on sensitivity analysis for designing smoothed petal auxetics with prescribed nonlinear deformation.

Smoothed Hexa-petals structure: The exterior boundary of the petal is optimized to achieve the target properties.

The versatility of the proposed shape optimization framework for smoothed petal auxetics is demonstrated here through two examples. The details can be found in the paper.

The first example focuses on designing the hexa-petals structure to achieve constant Poisson’s ratios ranging from null value to -0.5 to an effective tensile strain of 50%. The design optimization history for a targeted Poisson’s ratio of null value is presented below.

Design optimization history for a targeted Poisson’s ratio = 0

The optimized hexa-petals structures and deformed configurations at 25% and 50% longitudinal strains are depicted below.

(a) Optimized smoothed hexa-petals structures. Resultant displacement (U) contour plot of deformed optimized unit cells for a longitudinal strain of (b) 25% and © 50%. The dashed line represents the boundary of undeformed geometry

The performance of the optimized hexa-petals structures for different prescribed Poisson’s ratios of {0, -0.1, -0.2, -0.3, -0.4, -0.5} is summarized below, where the Poisson’s ratios are close to the target Poisson’s ratios in the desired interval.

Performance of the optimized structures with various prescribed constant Poisson’s ratios

The second example showcases the shape optimization of smoothed the hexa-petals structure under plane stress condition for targeted nonlinear deformation behavior of the cat’s skin up to 90% tensile strain. The deformation of an auxetic patch made up of optimized structure along with its performance is illustrated here:

Smoothed hexa-petals structure with similar deformation characteristics as of cat’s skin (Cat’s skin data extracted from Veronda and Westmann, 1970)

Missing rib auxetics with programmable Poisson’s ratios

In the second part, the isogeometric analysis (IGA) is combined with the genetic algorithm in MATLAB to further explore auxetic architectures. The objective is to obtain missing rib architectures with programmable Poisson’s ratios over large strains (~ 50%) in tension and perform experimental validation.

A comparison of simulation and experiment for a prescribed Poisson’s ratio of -0.6 to an effective tensile strain of 50% is presented here.

Comparison of simulation and experiment for a prescribed Poisson’s ratio = -0.6

The optimized missing rib architectures for different values of constant Poisson’s ratios together with the deformed configurations at 25% and 50% tensile strains are illustrated here.

(a) Optimized missing rib structures in tension. Resultant displacement (U) contour plots of deformed optimized unit cells for the longitudinal strain of (b) 25% and (c) 50% in tension. The dashed line represents the boundary of undeformed geometry. (d) Experimentally observed deformation of unit cells at longitudinal strain of 50% in tension.

The comparison between numerical and experimental Poisson’s ratios of missing rib architectures in tension is presented below and an excellent quantitative agreement between the numerical and experimental results is evident.

Comparison of numerical and experimental results for missing rib architectures with programmable Poisson’s ratios

Conclusion

The isogeometric shape optimization framework developed is a powerful tool to design metamaterials with prescribed nonlinear mechanical properties. In this work, the versatility of the sensitivity analysis and genetic algorithm based frameworks is demonstrated through various numerical examples and experimental validation on specimens fabricated using additive manufacturing. The optimized auxetic architectures can be used for stretchable electronics and tissue engineering applications. The optimization framework can be extended to design acoustic or phononic metamaterials for engineering applications such as shock absorption, acoustic imaging, and therapy devices.