Finite deformation and fractional order viscoelasticity of an auxetic foam

Abstract

Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

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“…To model and design with the effects of the viscoelastic property changes radiation exposure a linear viscoelastic finite element (FE) user material has been developed that includes both temperature and dose as model parameters. For similar viscoelastic materials, several approaches have been taken, for example, fractional derivative-based fitting [ 64 - 66 ], generalized Maxwell models with non-linear elements for large deformations [ 4 ], and modifications of the multi-parameter Odgen-type model (the so-called “Hyperfoam”) [ 67 , 39 ].…”

Assessment of frequency and amplitude dependence on the cyclic degradation of polyurethane foams

“…[24][25][26] The DMA technique is used to characterize the viscoelasticity of materials across temperature and frequency within the linear viscoelastic regime. [27][28][29] For most elastomers, nonlinearity in the stress response increases with DMA amplitude and frequency. 30 To simplify analysis and interpretation, standard DMA calculations assume that the stress response remains in the linear single order regime containing only the excitation frequency, ω.…”

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