Large Uniaxial Deformation Research Articles

Uni-axial reinforced dielectric elastomer actuators with embedded 3D printed fibers

Dielectric elastomer actuators (DEAs) can be described as compliant capacitors formed by a dielectric elastomer film sandwiched between two electrodes. An applied voltage results in a compressive Maxwell stress, a thickness reduction and thus an expansion in the other dimensions. In order to favor large uni-axial deformations, it is predicted that DEAs ought to be constrained in the other direction. This can be achieved by reinforcing the DEA with unidirectional fibers. In this paper, the behavior of uni-axial fiber-reinforced DEAs is established and the proposed model innovates by taking into consideration the fiber properties such as their Young’s modulus and dimensions, and is characterized by transversely isotropic models. A novel fabrication process is then presented for reinforced DEAs by using 3D printed fibers with four different materials, namely Nylon, PETG, ABS and PLA, and different coverages of fibers are considered. Fiber reinforcement is shown to increase uni-axial strain up to 75% in the manufactured DEAs when compared to traditional DEAs. This behavior corresponds to the one predicted by the proposed model.

A new mathematical model of compressive stress-strain behaviour of low viscosity and high viscosity bone cement with different strain rates

A new mathematical model of compressive stress-strain behaviour of low viscosity (LV) and high viscosity (HV) bone cement has been proposed to capture large uniaxial deformation under constant applied strain rate by incorporating three-term power law. The modeling capacity of the proposed model has been validated using uniaxial compressive test under eight different low strain rates ranging from 1.39 × 10-4 s-1 to 3.53 × 10-2 s-1 for low viscosity and high viscosity bone cement. The well agreement between the model and experimental response suggests that the proposed model can successfully predict rate dependent deformation behavior for Poly(methyl methacrylate) (PMMA) bone cement. Additionally, the proposed model was compared with the generalized Maxwell viscoelastic model and found to be in good agreement. The comparison of compressive responses over low strain rates for LV and HV bone cement reveals their rate-dependent compressive yield stress behaviour along with a higher value of compressive yield stress of LV bone cement compared to HV bone cement. For example, at the strain rate of 1.39 × 10-4 s-1 the mean value of compressive yield stress of LV bone cement was found to be 64.46 MPa, whereas for HV bone cement it was 54.00 MPa. Moreover, the modeling of experimental compressive yield stress with the Ree-Eyring molecular theory suggests that the variation of yield stress of PMMA bone cement can be predicted using two processes Ree-Eyring theory. The proposed constitutive model might be useful to characterize large deformation behaviour with high accuracy for PMMA bone cement. Finally, both variants of PMMA bone cement also exhibit ductile-like compressive behaviour below the strain rate of 2.1 × 10-2 s-1, whereas above this threshold strain rate, brittle-like compressive failure behavior is observed.

Deformation Driven Deswelling of Brush Gels

We studied equilibrium swelling in brush gels undergoing large uniaxial deformations in contact with solvent by using a combination of the Flory–Rehner and scaling models of gels and coarse-grained molecular dynamics simulations of swollen brush networks. Our analysis showed that the swelling ratio of the brush gels Qeq(λ), describing the volume change upon swelling, is a nonmonotonic function of the gel uniaxial deformation ratio λ characterizing the gel shape. It first increases with increasing strand elongation from its value for the free-standing gel then begins to decrease. This behavior is a result of the optimization of polymer/solvent interactions and conformational entropy of brush strands in the nonlinear deformation regime. The location of the maximum in the Qeq(λ) function is directly related to the value of the strain-stiffening parameter β. This parameter depends on the degree of polymerization of the brush backbone and the backbone Kuhn length defined by both the grafting density and degree of polymerization of the side chains. Analysis of the nonlinear gel modulus confirmed that the strain-stiffening parameter β is identical in both dry networks and gels. However, the structural modulus of the gels, Gs, is smaller than that of the dry networks, Gdr, by a factor equal to the ratio of the Kuhn length of brush strands in the dry state, bK, and in the gel, bK,s, such that Gs = GdrbK/bK,s.

Micromechanical quantification of elastic, twinning, and slip strain partitioning exhibited by polycrystalline, monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.

Young’s modulus evolution and texture-based elastic–inelastic strain partitioning during large uniaxial deformations of monoclinic nickel–titanium

The authors draw upon recent first-principles calculations of monoclinic NiTi elastic constants to develop a combined numerical–empirical, texture-based approach for calculating the Young’s modulus of polycrystalline, monoclinic nickel–titanium specimens. These calculations are carried out for load direction inverse pole figures measured in situ via neutron diffraction during tension–compression deformations to ∼18% true strain, as well as unloading events. As demonstrated by application to this empirical data set, the texture-based approach results in the ability to quantify the evolution of Young’s modulus and to micromechanically partition elastic and inelastic macroscopic strains for the entirety of non-linear and asymmetric uniaxial deformations, a result that had not been achieved previously for a monoclinic material.

Thermo-mechanical large deformation responses of Hydrogenated Nitrile Butadiene Rubber (HNBR): Experimental results

A comprehensive study on the large uniaxial deformation responses of two elastomers, Hydrogenated Nitrile Butadiene Rubbers (HNBR A and HNBR B), over wide ranges of strain rates ( 10 - 4 ⩽ ε ˙ ⩽ 5 × 10 3 s - 1 ) and temperatures (348 ⩽ T ⩽ 450 K) are presented. The material is found to be non-linearly dependent on strain-rate and temperature. The large deformation responses of HNBR are determined to be almost purely viscoelastic. It is observed that, the instantaneous stress drop during the stress relaxation is dependent on the strain-rate. The relaxation and creep responses during the equilibrium state (a state where there is no drop in stress during relaxation and no increase in strain during creep) are dependent on strain/stress level at which the phenomenon is started.

Stages of Structural Ordering Leading to Stress Induced Crystallization of PEEK Films: A Mechano-Optical Study on Deformation, Relaxation and Retraction

Influence of rubbery state large uniaxial deformation followed by relaxation and retraction stages on the mechano-optical behavior of cast amorphous poly(ether ether ketone) films was investigated. At early stage of stretching the birefringence remains linearly proportional to stress. In this linear optical regime, the material remains amorphous. Beyond a critical stress level, a deviation from linearity is observed where a small fraction of the material exhibit extreme preferred orientation with substantial translational disorder resembling nematic-like order. The onset of this deviation also coincides with the onset of strain hardening. Stretching beyond this transition leads to stress induced crystallization. Films stretched to deformation levels well below the onset of strain hardening, remain amorphous before and after the relaxation stages. The entropy reduction gained through deformation of the polymer chains is not sufficient to form crystalline order at short time scales. Once the initial deformation increased beyond the onset of strain hardening, a long-range network of connected crystallites establishes itself.

A nonlinear fractional derivative model for large uni-axial deformation behavior of polyurethane foam

In uni-axial quasi-static tests, flexible polyurethane foam undergoing large compressive loading and unloading deformation exhibits highly nonlinear and viscoelastic behavior. In particular, the response in the first cycle is observed to be significantly different from the response in subsequent cycles. In addition, the stresses in the loading paths are higher than those in unloading paths. This quasi-static response is modeled as an additive sum of a nonlinear elastic and a linear viscoelastic response. The nonlinear elastic behavior is modeled as a polynomial function of compressive strain, while the viscoelastic behavior is modeled as a parallel combination of five-parameter fractional derivative models. The focus of this paper is to develop a multi-element fractional derivative model that can capture the multi-cycle behavior. A parameter estimation procedure based on separating the contributions of the viscoelastic elements and the nonlinear elastic component is developed. This approach is applied to both simulation and experimental data. The combination of a nonlinear elastic component and a two-element fractional derivative model is found to predict the observed responses reasonably well. The results for two distinct foams from tests with different compression rates are compared and discussed.

Electro-Mechanical Properties of Knitted Fabric Made From Conductive Multi-Filament Yarn Under Unidirectional Extension

A theoretical model for electro-mechanical properties of intrinsically conductive knitted fabrics made from stainless steel multi-filament yarns under large uniaxial deformation is presented. The investigations are focused on the relationship between the load and electrical resistance of the fabric under uniaxial extension. A circuit network is proposed based on the loops configuration and fabric structure. The equivalent resistance of the fabric is obtained by solving the circuit equations of the network. In order to simplify the calculation of the contacting forces on the overlapped yarns, a two-dimensional hexagon model is used to represent the loop configurations. An image-capturing system is employed to record the images of the loop configurations during the extension process and the relationship between the configurations of the loops and the load imposed on the fabric is obtained. From the theoretical analysis and experimental investigations, it is found that the contacting resistance of the overlapped yarns in the fabric is the key factor that governs the sensitivity of the fabric sensor. In addition, the fabric structure that determines the structure of the circuit network is also an important factor affecting the characteristics of the fabric sensor.

Demixing in Wheat Doughs—Its Influence on Dough and Gluten Rheology

ABSTRACTReshaping of relaxed wheat doughs leads to an increase in firmness that significantly changes the results of rheological measurements involving large uniaxial deformations of the dough, whereas the gluten properties remain unaffected. Microscopic investigations reveal that directly after kneading, starch and gluten are thoroughly mixed. However, the shaping procedure of a relaxed dough or shear‐flow during rheological measurements cause a separation of gluten and starch. The dilatant behavior of the starch granules and the capacity of gluten to aggregate account for the observed dough‐hardening.

Total energy and spin susceptibility of paramagnetic Cr and Fe under large uniaxial deformation

The total energy, pressure and spin susceptibility of paramagnetic Cr and Fe are calculated as functions of a large tetragonal deformation using the local density and local spin density approximations. The electronic structures, structural stabilities, elastic constants and their volume derivatives, theoretical tensile strength and strain dependence of the spin susceptibility are discussed on the basis of the results. Although the muffin-tin approximation is used for the charge and potential distributions, the calculated results agree essentially with the elastic properties observed.

Electrical conductivity of silicon under large uniaxial deformations

An analysis of the behavior of the electrical conductivity of electronic silicon under large uniaxial deformations is presented in this paper. The experimentally observed peculiarities in the behavior of the electrical conductivity are explained on the basis of anisotropic scattering theory, with account taken of the additional rearrangement of the impurity levels under the action of the deformation. A calculation is performed of the dependence of the anisotropy coefficient of the mobility on the impurity concentration with account taken of scattering by impurity ions and acoustic vibrations of the lattice.