Mechanical behaviour of auxetic structures

Hyperelastic behaviour of auxetic structures in flexible 3D-printed polymers

A few decades ago, polymeric materials were considered to be low-quality, poorly manufactured plastics. Over the years, scientists and engineers have developed polymer materials with excellent mechanical properties that make them very reliable and high-tech. In fact, experiments and theoretical models of polymer mechanics have enabled new and better uses of polymers. As it is a multidisciplinary subject (e.g. in mechanical engineering, aerospace engineering, chemical engineering, materials science or bioengineering), it can be covered from different approaches, which generates complexity to the field of study.

The aim of the work in our institute is to investigate the material response of hyperelastic materials. This behaviour is observed in polymeric materials, among others.

Fig 1.: Stress-strain curve of a hyperelastic material
Fig 1.: Stress-strain curve of a hyperelastic material

The focus lies on auxetic geometries, i.e. structures with a negative transverse contraction number. An example of auxetic geometry cells is presented in Figure 2.

Fig 2.: Example of auxetic structures
Fig 2.: Example of auxetic structures

Experimentally, these complex structures can be created by 3D printing and tested in tensile tests to determine the strain field under load conditions. A technique called digital image correlation (DIC) offers a solution for this. The DIC system with a 2D non-contact optical measurement system (ARAMIS, GOM, Germany) is employed to assess in-plane displacement and determine strain fields in the specimen surface through the tensile test. To facilitate the measurement, the white surfaces of samples were painted black to form random but unique speckles. While post-processing the recorded images of deformed samples, a measuring zone inside the relevant region of the tested sample is developed. The averaged different strains can be determined. One feature of DIC is that it allows for the simultaneous acquisition of global and local strain fields on sample surfaces. The 2D DIC enables the simultaneous investigation of sample deformations by correlating measured strains and applied displacement. Full-field measurements close the gap between experiments and simulations and allow a direct comparison of displacement and strain. To proceed with the investigation, the following triangle themes need to be developed.

Nowadays, many mathematical models are available to reproduce the real behaviour of new materials such as polymers. Several constitutive laws for polymers are of great interest to the aircraft industry. In recent years, the need for verification and validation of simulation results gained importance. Nevertheless, the discrepancy between simulation results and real physical behaviour is still observed in many cases. Computers and especially the computational Finite Element Method (FEM) were a great revolution that improved not only the study of polymer mechanics, but also the analysis of components in general. Closed-form calculations using a simple material model, such as linear elasticity, are computationally efficient, but cannot be applied to complex geometries. Finite Element (FE) simulation using an advanced material model captures nonlinear geometric effects and can accurately capture the material response. However, these analysis techniques make material model calibration more difficult than FE simulation using a simple material model, and increase the computational cost.


To simulate the material behaviour of our auxetic structures, we use hyperelastic models such as Mooney-Rivlin, Odgen or Yeoh.

This image shows Berta Pi Savall

Berta Pi Savall


Research Assistant

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