Strain dependent damping function

The equation leads to the definition of a time and strain-dependent memory fimction which can be further factorized into a time-dependent part (the linear memory function) and a strain-dependent damping function. Though on one hand, there is some experimental evidence for this in limited time ranges, on the other hand, a few experiments might question this strong hypothesis since, for example, the damping function obtained fi um step shear rate data is found to be different from that in step shear strain. 

In the same way, but much more complicated, with a damping function depending on the Hencky strain, it proved to be possible to calculate the transient extensional viscosity as a function of qe. The result is illustrated in Fig. 15.30 for the same polymer. It shows that extensional viscosity remains finite and increases with increasing strain rate up to a maximum at qe = 2 s, after which it decreases again. The calculated lines coincide quite well with the experiments, but the calculated viscosities are somewhat too high. 

In this work the dependency of the maximum shear modulus upon the effective stress, and relationship between strain and damping ratio are studied. Based on the laboratory experiment, the function of pore water pressure buildup versus the number of stress cycles is obtained. 

The damping function, g(s), in Eq. (6.30) accounts for lack of proportionality between stress and strain. The product, g(e)e, quantifies the nonlinear elasticity (g(e) = 1 for linear viscoelastic behavior). Separability of time and strain is illustrated for 1,4-polyisoprene in Figures 6.4 and 6.5 the time-dependence of the stress relaxation is the same for shear strains of varying amplimde and for different modes of deformation (Fuller, 1988). 

Uniaxial extension is an axi-symmetric deformation in which a tensile stress is appHed in one direction, we will call it the z-direction, while the free surfaces of the sample are under a uniform normal stress, usually one atmosphere of compression. The quantity measured is the net tensile stress t7g defined as (- a ), which is the applied axial stress minus that acting on the free surface. One could, in principle, carry out step-strain (stress relaxation) in extension, and if the tensile relaxation modulus (t,e) can be separated into time and strain-dependent contributions, a damping function could be determined as a function of strain. 

The damping of the stress oscillations presumably arises from a gradual loss of spatial coherence in the phase of the tumbling orbit across the sample. In a plate-and-plate rheometer, the strain is linearly dependent on the radial distance from the axis of rotation. As a result, the gap-averaged director orientation varies as a function of radial position in the sample. When this source of inhomogeneity in the tumbling orbit accounted for by integrating the torque contributions predicted by Eq. (10-31) over... 

The effect of the fillers on the dynamic mechanical property of NR material was analysed by DMA in this work. The elastic modulus ( ") and the loss factor (tan 5) of the neat NR and NR composites were characterized as functions of temperature. Under an oscillating force, the resultant strain in specimen depends upon both elastic and viscous behaviour of materials. The storage modulus reflects the elastic modulus of the rubber materials which measures t recoverable strain energy in a deformed specimen, and the loss factor is related to the energy damped due to energy dissipation as heat. 

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