Auxetic foams have a variety of unique properties due to their negative Poisson ratio such as high energy absorption and fracture toughness for applications such as sports safety equipment, packing material, and shoe soles. The viscoelastic behavior of this relatively new material has not been extensively studied and modeled. Better knowledge of the viscoelastic behavior over a broad range of deformation rates is critical when considering the mechanical properties of the material. Previous modeling for positive Poisson ratio materials has been completed successfully to characterize the behavior. This same modeling was applied to auxetic foams with less success. The influence of nonlinear compressibility effects greatly improved calibration and prediction. Model simulations across several orders of magnitude in deformation rates are validated against data. All results are statistically validated using maximum entropy methods to obtain posterior densities for the hyperelastic and fractional order parameters. Importantly, a maximum entropy algorithm is used such that heterogeneous data can be fused to inform and validate the model and quantify its uncertainty.
Dielectric elastomers exhibit novel electromechanical coupling that has been exploited in many adaptive structure applications. Whereas the quasi-static, one-dimensional constitutive behavior can often be accurately quantified by hyperelastic functions and linear dielectric relations, accurate predictions of electromechanical, rate-dependent deformation during multiaxial loading is non-trivial. In this paper, an overview of multiaxial electromechanical membrane finite element modeling is formulated. Viscoelastic constitutive relations are extended to include fractional order. It is shown that fractional order viscoelastic constitutive relations are superior to conventional integer order models. This knowledge is critical for transition to control of legged robotic structures that exhibit advanced mobility.