The mechanical behavior of elastomeric materials is known to be rate-dependent and to exhibit hysteresis upon cyclic loading. Although these features of the rubbery constitutive response are well-recognized and important to its function, few models attempt to quantify these aspects of response perhaps due to the complex nature of the behavior and its apparent inconsistency with regard to current reasonably successful models of rubber elasticity. In this paper a detailed experimental investigation probing the material response of carbon black filled Chloroprene rubber subjected to different time-dependent strain histories is presented. Some of the key observations from the experiments are: (1) both filled and unfilled elastomers show significant amounts of hysteresis during cyclic loading; (2) the amount of carbon black particles does not strongly influence the normalized amount of hysteresis; (3) both filled and unfilled elastomers are strain-rate dependent and the rate dependence is higher during the uploading than during the unloading; (4) at fixed strain, the stress is observed to approach the same equilibrium level with relaxation time whether loading or unloading. Based on the experimental data a new constitutive model has been developed. The foundation of the model is that the mechanical behavior can be decomposed into two parts: an equilibrium network corresponding to the state that is approached in long time stress relaxation tests; and a second network capturing the non-linear rate-dependent deviation from the equilibrium state. The time-dependence of the second network is further assumed to be governed by the reptational motion of molecules having the ability to significantly change conformation and thereby relaxing the overall stress state. By comparing the predictions from the proposed three-dimensional constitutive model with experimental data for uniaxial compression and plane strain compression we conclude that the constitutive model predicts rate-dependence and relaxation behavior well.

https://polymerfem.com/polymer_files/Bergstrom_Boyce_model1.pdf

Constitutive modeling of the large strain time-dependent behavior of elastomers

In arthropods, evolution has created a remarkably sophisticated class of imaging systems, with a wide-angle field of view, low aberrations, high acuity to motion and an infinite depth of field. A challenge in building digital cameras with the hemispherical, compound apposition layouts of arthropod eyes is that essential design requirements cannot be met with existing planar sensor technologies or conventional optics. Here we present materials, mechanics and integration schemes that afford scalable pathways to working, arthropod-inspired cameras with nearly full hemispherical shapes (about 160 degrees). Their surfaces are densely populated by imaging elements (artificial ommatidia), which are comparable in number (180) to those of the eyes of fire ants (Solenopsis fugax) and bark beetles (Hylastes nigrinus). The devices combine elastomeric compound optical elements with deformable arrays of thin silicon photodetectors into integrated sheets that can be elastically transformed from the planar geometries in which they are fabricated to hemispherical shapes for integration into apposition cameras. Our imaging results and quantitative ray-tracing-based simulations illustrate key features of operation. These general strategies seem to be applicable to other compound eye devices, such as those inspired by moths and lacewings (refracting superposition eyes), lobster and shrimp (reflecting superposition eyes), and houseflies (neural superposition eyes).

Digital cameras with designs inspired by the arthropod eye

Soft fluidic actuators consisting of elastomeric matrices with embedded flexible materials are of particular interest to the robotics community because they are affordable and can be easily customized to a given application. However, the significant potential of such actuators is currently limited as their design has typically been based on intuition. In this paper, the principle of operation of these actuators is comprehensively analyzed and described through experimentally validated quasi-static analytical and finite-element method models for bending in free space and force generation when in contact with an object. This study provides a set of systematic design rules to help the robotics community create soft actuators by understanding how these vary their outputs as a function of input pressure for a number of geometrical parameters. Additionally, the proposed analytical model is implemented in a controller demonstrating its ability to convert pressure information to bending angle in real time. Such an understanding of soft multimaterial actuators will allow future design concepts to be rapidly iterated and their performance predicted, thus enabling new and innovative applications that produce more complex motions to be explored.

Modeling of Soft Fiber-Reinforced Bending Actuators

Buckling is exploited to design a new class of three-dimensional metamaterials with negative Poisson's ratio. A library of auxetic building blocks is identified and procedures are defined to guide their selection and assembly. The auxetic properties of these materials are demonstrated both through experiments and finite element simulations and exhibit excellent qualitative and quantitative agreement.

3D Soft Metamaterials with Negative Poisson's Ratio

/pdf/feap-a-finite-element-analysis-program-qvz36simr5.pdf

FEAP - - A Finite Element Analysis Program

According to Rivlin's Phenomenological Theory of Rubber Elasticity, the elastic properties of a rubber may be described in terms of a strain energy function which is an infinite power series in the strain invariants I1, I2 and I3. The simplest forms of Rivlin's strain energy function are the neo-Hookean, which is obtained by truncating the infinite series to just the first term in I1, and the Mooney-Rivlin, which retains the first terms in I1 and I2. Recently, we proposed a strain energy function which is a cubic in I1. Conceptually, the proposed function is a material model with a shear modulus that varies with deformation. In this paper, we compare the large strain behavior of rubber as predicted by these forms of the strain energy function. The elastic behavior of swollen rubber is also discussed.

Some Forms of the Strain Energy Function for Rubber

A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy ...

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

The Ogden strain-energy function for rubber appears to be gaining popularity among users of finite element analysis. This paper discusses some of the special features of this material mode...

On the Ogden Strain-Energy Function

An approximate theory for calculating the strain-energy release rate (tearing energy) for the propagation of penny-shaped cracks and predicting the life of model composites has been outlined. Fatigue studies on two model composites consisting of sheets of carbon-black-Filled natural rubber vulcanizates and rabberized steel card fabrics show experiment and theory to be in semiquantitative agreement

O. H. Yeoh

Papers

Some Forms of the Strain Energy Function for Rubber

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

On the Ogden Strain-Energy Function

Crack Initiation and Propagation in Model Cord-Rubber Composites