Linear Viscoelastic Deformation Under Three-Dimensional Stresses

Author(s):  
Helmut Münstedt ◽  
Friedrich Rudolf Schwarzl
2016 ◽  
Vol 24 (11) ◽  
pp. 2180-2200 ◽  
Author(s):  
Smitadhi Ganguly ◽  
A Nandi ◽  
S Neogy

A new shaft element is proposed for viscoelastic rotors in a spinning frame considering the shear deformation in addition to bending deformation. The Maxwell–Wiechert model is considered here to replicate linear viscoelastic behavior. This model considers additional internal damping displacement variables between elastic and viscous elements and the stress depends not only on the elastic strain and elastic strain rate, but also on additional strains and their rates corresponding to the damping variables. The present work assumes that these additional strains can be derived from continuous fictitious displacement variables, which in turn are interpolated from their nodal values using the Timoshenko beam shape functions. Therefore, in addition to the standard degrees of freedom for a three-dimensional shaft, extra degrees of freedom are defined at the nodes. The finite element matrices are assembled in state space. The time domain equations are then used for stability analysis and computation of response to a unit step load and an unbalance.


2018 ◽  
Vol 32 (10) ◽  
pp. 1435-1449 ◽  
Author(s):  
Tomasz Zbigniew Osmałek ◽  
Anna Froelich ◽  
Barbara Jadach ◽  
Marek Krakowski

Purpose Most of the studies concerning gellan have been focused on its application as a food ingredient, however, gellan is often considered as a candidate for the development of novel pharmaceutical formulations. Taking into account that gellan is ion-sensitive, it can be assumed that its initial mechanical properties can change upon contact with body secretions. Therefore, the aim of the work was to investigate the rheological properties of pure high-acyl gellan gum hydrogel (0.4%) and its mixtures with selected simulated body fluids. Methods The rheological investigations were performed on rotational rheometer and included oscillatory temperature, amplitude, and frequency sweeping. The results enabled estimation of the linear viscoelastic regime, calculation of the cross-over points, and percentage of structure recovery. Results In the case of pure hydrogel no evidence of thermosensitivity was observed in the range of 20–40°C. In pH = 1.2 (NaCl/HCl) the hydrogel structure was almost entirely destroyed. Mixing with phosphate buffer (pH = 4.5) resulted in higher gel strength than after dilution with deionized water. The opposite effect was observed in the case of pH = 7.4. The studies performed for the mixture of GG hydrogel and mucin indicated interaction between the components. The hydrogel elasticity increased in the presence of simulated tear, but decreased in simulated saliva and vaginal fluid. Conclusions In this study, it was shown that the stability of a three-dimensional gellan structure may be affected by pH and the presence of mucin which most probably competed with gellan gum in divalent cations binding. The observations presented in this study may be important in terms of potential application of gellan gum as a potential carrier in drug delivery systems.


2020 ◽  
Vol 222 (2) ◽  
pp. 1013-1022 ◽  
Author(s):  
Nahidul Hoque Samrat ◽  
Matt A King ◽  
Christopher Watson ◽  
Andrew Hooper ◽  
Xianyao Chen ◽  
...  

SUMMARY We consider the viscoelastic rheology of the solid Earth under the Antarctic Peninsula due to ice mass loss that commenced after the breakup of the Larsen-B ice shelf. We extend the previous analysis of nearby continuous GPS time-series to include five additional years and the additional consideration of the horizontal components of deformation. They show strong uplift from ∼2002 to 2011 followed by reduced uplift rates to 2018. Modelling the GPS-derived uplift as a viscoelastic response to ongoing regional ice unloading from a new ice model confirms earlier estimates of low upper-mantle viscosities of ∼0.3–3 × 1018 Pa s in this region but allows a wide range of elastic lithosphere thickness. The observed and modelled north coordinate component shows little nonlinear variation due to the location of ice mass change to the east of the GPS sites. However, comparison of the observed and modelled east coordinate component constrains the upper-mantle viscosity to be less than ∼9 × 1018 Pa s, consistent with the viscosity range suggested by the uplift rates alone and providing important, largely independent, confirmation of that result. Our horizontal analysis showed only marginal sensitivity to modelled lithospheric thickness. The results for the horizontal components are sensitive to the adopted plate rotation model, with the estimate based on ITRF2014 suggesting that the sum of residual plate motion and pre-2002 glacial isostatic adjustment is likely less than ∼±0.5 mm yr−1 in the east component.


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