Hysteretic behaviour of uniaxially thermoformed auxetic foams under 3-point bending low-frequency vibration

The work describes experiments and models related to auxetic (negative Poisson’s ratio) foams subjected to low-frequency and variable amplitude 3-point bending loading. A custom 3-point bending vibration test rig is designed and used to perform the dynamic test of auxetic PU foam beams within low-frequency range (1–20 Hz) and 5 different displacement amplitudes. The auxetic foams tested in this work are manufactured using a simplified and relatively low-cost uniaxially thermoforming compression technique, which leads to the production of foams with transverse isotropic characteristics. Auxetic foam beam samples with two different cutting orientations and different thermoforming compression ratios rc (20–80%) are tested and compared, also with the use of theoretical Euler–Bernoulli-based and finite element models. The dynamic modulus of the foams increases with rc, ranging between 0.5 and 5 MPa, while the dynamic loss factor is marginally affected by the compression ratio, with overall values between 0.2 and 0.3. The auxetic PU foam has a noticeable amplitude-dependent stiffness and loss factors, while the dynamic modulus increases but slightly decreases with the frequency. The dynamic modulus is also 20–40% larger than the quasi-static one, while the dynamic and static loss factors are quite close. A modified Bouc–Wen model is also further developed to capture the amplitude and frequency-dependent properties of the conventional and auxetic foams with different volumetric compression ratios. The model shows a good agreement with the experimental results.