Modeling Payne effect on basis of linearization of a visco-hyperelastic model

The present work concerns the modeling of the Payne effect in nonlinear viscoelasticity. This effect is a characteristic property of filled elastomers. Indeed, under cyclic loading of increasing amplitude, a decrease is shown in the storage modulus and a peak in the loss modulus. In this study, the Payne effect is assumed to arise from a change of the material microstructure, i.e., the thixotropy. The so-called intrinsic time or shift time was inferred from solving a differential equation that represents the evolution of a material's microstructure. Then, the physical time is replaced by the shift time in the framework of a recent fractional visco-hyperelastic model, which was linearized in the neighborhood of a static pre-deformation. As a result, we have investigated the effects of static pre-deformation, frequency, and magnitude of dynamic strain on storage and loss moduli in the steady state. Thereafter, the same set of parameters identified from the complex Young's modulus was used to predict the stress in the pre-deformed configuration. Finally, it is demonstrated that the proposed model is reasonably accurate in predicting Payne effect.

A Transient Microsphere Model for Nonlinear Viscoelasticity in Dynamic Polymer Networks

Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the transient microsphere model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker–Planck equation that incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.

Finite Element Analysis for Nonlinear Unbonded Circular Fiber-Reinforced Elastomeric Bearings

In recent years, interest in low-cost seismic isolation systems has increased. The replacement of the steel reinforcement in conventional elastomeric bearings for a carbon fiber reinforcement is a possible solution and has garnered increasing attention. To investigate the response of fiber-reinforced elastomeric bearings (FREBs) under seismic loads, it is fundamental to understand its mechanical behavior under combined vertical and horizontal loads. An experimental investigation of the components presents complexities due to the high loads and displacements tested. The use of a finite element analysis can save time and resources by avoiding partially expensive experimental campaigns and by extending the number of geometries and topologies to be analyzed. In this work, a numerical model for carbon fiber-reinforced bearings is implemented, calibrated, and validated and a set of virtual experiments is designed to investigate the behavior of the bearings under combined compressive and lateral loading. Special focus is paid to detailed modeling of the constituent materials. The elastomeric matrix is modeled using a phenomenological rheological model based on the hyperelastic formulation developed by Yeoh and nonlinear viscoelasticity. The model aims to account for the hysteretic nonlinear hyper-viscoelastic behavior using a rheological formulation that takes into consideration hyperelasticity and nonlinear viscoelasticity and is calibrated using a series of experiments, including uniaxial tension tests, planar tests, and relaxation tests. Special interest is paid to capturing the energy dissipated in the unbonded fiber-reinforced elastomeric bearing in an accurate manner. The agreement between the numerical results and the experimental data is assessed, and the influence of parameters such as shape factor, aspect ratio, vertical pressure, and fiber reinforcement orientation on stress distribution in the bearings as well as in the mechanical properties is discussed.