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A mathematical model for stimuli-sensitive hydrogels in a water-alcohol solution is presented and analyzed, in which a new polymer-solvent interaction parameter is proposed to capture the deformation of the hydrogel due to changes in the external alcohol content and temperature. The nature of this parameter is determined in the limit of pure dilatation for poly(N-isopropylacrylamide) hydrogels immersed in tempered water-methanol and -ethanol solutions. Overall, good agreement between the resulting model predictions and experiments is achieved; the transition temperatures and "re-entrant phenomenon" are also captured reasonably well. The herein derived expression for the polymer-solvent interaction parameter can be introduced into more generic transient models that also account for fluxes of the relevant field variables.

A mathematical model integrating analytical method with numerical method was established to simulate the multi-pass plate hot rolling process, predicting its strain, strain rate, stress and temperature. Firstly, a temperature analytical model was derived through series function solution, the coefficients in which for successive processes were smoothly transformed from the former process to the latter. Therefore, the continuous computation of temperature for multi-operation and multi-pass was accomplished. Secondly, kinematically-admissible velocity function was developed in Eulerian coordinate system according to the principle of volume constancy and characteristics of metal flow during rolling with undetermined coefficients — which were eventually solved by Markov variational principle. Thirdly, strain rate was calculated through geometric equations and the difference-equations for solving strain and a subsequent recurrent solution were established. Fourthly, rolling force was calculated on the base of Orowan equilibrium equation, considering the contribution to flow stress of strain, strain rate and temperature, rather than taking the flow stress as a constant. Consequently, the thermo-mechanics and deformation variables are iteratively solved. This model was employed in the simulation of an industrial seven-pass plate hot rolling schedule. The comparisons of calculated results with the measured ones and the FEM simulation results indicate that this mathematical model is able to reasonably represent the evolutions of various variables during hot rolling so it can be used in the analysis of practical rolling. Above all, the greatest advantage of the presented is the high efficiency. It costs only 12 seconds to simulate a seven-pass schedule, more efficient than any other numerical methods.

A phenomenological model for stimuli sensitive hydrogels immersed in water subject to changes in temperature is presented and analyzed. In short, the model takes into account conservation of mass and momentum for polymer network and interstitial fluid with an expression for permeability to capture the rigid skin formation during shrinking. The nature of this expression is secured from the observation of and validation with experimental deformation kinetics. Overall, good agreement is achieved between model predictions and their experimental counterparts; the rigid skin formation and rigid core presence are also captured reasonably well. The model can be extended to account for arbitrary-shaped hydrogels as well as for other types of stimuli-sensitive hydrogels that exhibit rigid-skin formation during shrinking.

The polymer yield behavior is affected by temperature, strain rate and pressure. In this work, tensile yield stress of polyetheretherketone (PEEK) is characterized for temperature ranging between $223^{\circ }\mathrm{\text{K}}$ and $433^{\circ }\mathrm{\text{K}}$ ($-50^{\circ }$C and $160^{\circ }$C). The tensile yield stress is decreasing in terms of temperature. Two temperature transitions are observed: $320^{\circ }\mathrm{\text{K}}$ ($\sim 37^{\circ }$C) and the glass transition temperature. The temperature sensitivity is well captured by the modified-Eyring equation proposed by the authors. This paper completes three previous works where the PEEK’s yield behavior was described under compression on wide ranges of strain rate and temperature and under tension on a wide range of strain rates. Thus, the pressure effect is analyzed in terms of temperature and strain rate. Using either the experimental data or the modified-Eyring equation, the effect of the hydrostatic pressure is increasing with temperature and decreasing with strain rate.

We study the redistribution of mobile charge carriers in a composite fiber of piezoelectric dielectrics and non-piezoelectric semiconductors in extensional deformation under a uniform temperature change. The macroscopic theory of piezoelectricity and the drift-diffusion theory of semiconductor are used, coupled by doping and mobile charges. A one-dimensional model for extension is developed. Through a theoretical analysis, it is shown that under a temperature change the mobile charges in the semiconductor redistribute themselves under the polarization and electric field produced through thermoelastic, pyroelectric and piezoelectric effects. The results suggest the possibility of using composite structures for thermally manipulating mobile charges in semiconductors and have potential applications in piezotronics.