Stress relaxation theoretical results

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

Dilational rheological experiments are based on area changes by keeping the shape of the interface constant. Models for the exchange of matter, which sets in after a compression or expansion of the interface, are generally applicable to both harmonic and transient types of relaxations (178). Stress-relaxation experiments may yield results different from those obtained from measurements on small disturbances as the composition of the surface layer can vary (179). Overviews on experimental and theoretical aspects of dilational rheology were given recently in Refs 180—182. 

Cavitation evolution dynamics in cylindrical liquid volumes under the axial loading by an exploding wire is studied experimentally aind theoretically. The method of dynamic head registration is used to study the structure of two phase flows formed and evaluate characteristic time of cavitation liquid fracture. As a result of numerical simulation of the experiments, which was performed in a single-velocity two-phase model approximation, the energy transformation mechanism is determined at shock interaction with a free real liquid surface. A two-phase model is suggested to describe the irreversible development of a cavitation zone formed as a result of the mentioned interaction. The model is based on practically instantaneous tensile--stress relaxation in a centered rarefaction wave and further inertial evolution of the process. 

The material behavior above-described refers to the quasi-static response. However, elastomers subjected to real world loading conditions possess fluid-like characteristics typical of a viscoelastic material. When loaded by means of a stepwise strain, they stress-relax, i.e., the reaction force resulting from the application of an initial peak falls to an asymptotic value, which is theoretically reached after an infinite time [69]. Moreover, if an external force is suddenly applied, creep is observed and the strain begins to change slowly towards a limiting value. 

In this research, by using a real geometric model of tibia, according to its complex and unique geometry, the effects of different mechanical properties of tibia on the stress analysis under a transversal impact load has been investigated. The maximum stress was seen in the case of viscoelastic model of tibia while the minimum was found with the transversely isotropic property. In agreement with previous studied [7 and 8], the maximum amount of stress reached by the transversely isotropic model of tibia was closer to the results of theoretical and experimental works by other researchers. The dependency of the viscoelastic material property to the time caused the maximum stress to be seen in the last increment of the impact cycle. But, for the elastic behavior of tibia, the maximum stress was seen in the increment with the maximum applied force. The stress relaxation was seen by a reduction in the maximum amount of stress just after the impact load was over because of the constant strain rate in the tibial shaft. 

As mentioned above, it is very difficult, for experimental reasons, to measure the relaxation modulus or the creep compliance at times below 1 s. In this time scale region, dynamic mechanical viscoelastic functions are widely employed (5,6). However, in these methods the measured forces and displacements are not simply related to the stress and strain in the samples. Moreover, in the case of dynamic experiments, inertial effects are frequently important, and this fact must be taken into account in the theoretical methods developed to calculate complex viscoelastic functions from experimental results. 

We want to emphasize that a logarithmic time dependence of d and w, and the corresponding decrease of V, are not expected for a Newtonian liquid [42]. Moreover, our results cover times shorter than the longest relaxation time in equilibrated bulk samples (i.e., the reptation time). Thus, the visco-elastic properties of PS certainly affect our dewetting experiments. Thus, a detailed theoretical model has been developed that takes into account residual stresses, interfacial friction (i.e., slippage), and visco-elasticity [42,44,46],... 

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