The Physics of Rubber Elasticity (J. Meixner)

Mechanical responses of Ecoflex silicone rubber: Compressible and incompressible behaviors

In this paper, a micromechanical model for rubber elasticity is proposed on the basis of analytical network-averaging of the tube model and by applying a closed-form of the Rayleigh exact distribution function for non-Gaussian chains. This closed-form is derived by considering the polymer chain as a coarse-grained model on the basis of the quantum mechanical solution for finitely extensible dumbbells ( Ilg et al., 2000 ). The proposed model includes very few physically motivated material constants and demonstrates good agreement with experimental data on biaxial tension as well as simple shear tests.

Analytical network-averaging of the tube model:: Rubber elasticity

Nowadays the most common approach to model elastic behavior at large strains is through hyperelasticity. Hyperelastic models usually specify the shape of the stored energy function. This shape is modulated by some material parameters that are computed so the predicted stresses best fit the experimental data. Many stored energy functions have been proposed in the literature for isotropic and anisotropic materials, either compressible or incompressible. What-You-Prescribe-Is-What-You-Get (WYPIWYG) formulations present a different approach which may be considered an extension of the infinitesimal framework. The shape of the stored energy is not given beforehand but computed numerically from experimental data solving the equilibrium equations. The models exactly fit the experimental data without any material parameter. WYPIWYG procedures have comparable efficiency in finite element procedures as classical hyperelasticity. In this work we present a WYPIWYG numerical procedure for compressible isotropic materials and we motivate the formulation through an equivalent infinitesimal model.

WYPIWYG hyperelasticity for isotropic, compressible materials

An auxetic structure as a substrate material in sensor applications improves sensitivity performance due to lateral expansion under tensile loading. The presented stretchable, highly sensitive at-low-strain piezoresistive sensor was manufactured by mixing the silicone rubber and chopped carbon fibers in an auxetic re-entrant structure form. Auxetic re-entrant die was printed by using a 3D printing technique. The main feature of this sensor is the high sensitivity for strains lower than 6%, in which previous sensors could not recognize this range of strain well. In order to justify the excellent performance of the sensor, the deformation modes of the auxetic re-entrant structures were investigated and also connected to piezoresistive sensitivity. The shifting strain is defined as strain value, where the Poisson’s ratio of structure shifts from negative to positive Poisson’s ratio. Our study revealed that auxetic sensors have excellent sensitivity performance until the shifting strain due to having negative Poisson’s ratio, and after that, their sensitivity performance is going to be weak due to having positive Poisson’s ratio. In the present work, silicone rubber as the substrate material was used. This is a very soft material and made it possible to have low shifting strain resulting in perfect sensitivity performance for low-strain applications. The presented sensor has applications in many fields which are in low-strain conditions such as measuring the Vocal Cord Dysfunction (VCD), wrist pulse, or even earth vibration.

Highly sensitive, piezoresistive, silicone/carbon fiber-based auxetic sensor for low strain values

Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach

Correlation of modern finite element methods (FEM) with advanced experimental techniques for elastomers, biomedical materials, and living organs requires study and modification of the behavior of these materials In this study, the mechanical behavior of a commonly-used elastomer, silicone rubber, which provides excellent biocompatibility, was examined under different applied loading configurations, and large deformations were investigated through both experiment and simulation The stress-strain behaviors of silicone rubber were tested, using multiple homogeneous experiments, including uniaxial extension and equibiaxial tension, the load-apex displacement response, and digitized deformed shapes of two of the most-used structures for nonlinear hyperelasticity—the inflation of a clamped circular membrane, and indentation of the membrane by a spherical indenter Uniaxial and equibiaxial data were evaluated simultaneously, characterized by various constitutive models for implementation in the FE simulation These constitutive models examined the prediction of the FE simulations for the inflation and indentation tests in comparison to the results of experiments at various load-apex displacement levels The results showed that the constitutive models calibrated with the uniaxial and equibiaxial tests, predicted nearly the same results as the actual experimental results, particularly for the applied loads that generated moderate strain However, when the FE simulations based on the constitutive models were adjusted, employing only uniaxial or equibiaxial tests, they predicted different results, where the degree of their correlations with experimental results was incomplete or in some states simply poor The simulations suggested that the inverse FE procedure should not be restricted to the choice of material models, while more attention should be given to the choice of ranges of deformation

On the Correlation of FEM and Experiments for Hyperelastic Elastomers

It is apparent from the literature that the matrix–fiber mechanical interaction, as a result of interfacial adhesive bonds at the interface, significantly contribute to the macroscopic constitutive response of hyperelastic fiber-reinforced materials. This study bridges the degradation of macroscopic mechanical properties to the microscopically visible matrix–fiber interfacial debonding for cyclically deformed soft composites. The present work is an initial attempt to model matrix–fiber interfacial debonding in the context of pseudoelasticity by evaluating inelastic phenomena such as discontinuous Mullins softening and residual strain due to matrix damage , fiber rupture , and matrix–fiber interfacial debonding. The pseudoelastic model is based on hyperelastic strain energy functions consisting of two damage variables for each matrix, fiber, and matrix–fiber mechanical interaction. Each material and damage parameter is characterized independently by performing a comprehensive set of monotonic loading and cyclic tensile tests , respectively. Furthermore, finite element analysis is implemented using a user-defined subroutine, and the computationally calculated results are compared with the experimental data. 

M. R. Mansouri

Papers

Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach

On the Correlation of FEM and Experiments for Hyperelastic Elastomers

Matrix–fiber interfacial debonding in soft composite materials: Cyclically behavior modeling and microstructural evolution