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Free volume and nonlinear viscoelasticity in supercrystalline nanocomposites: A nanoindentation driven modelling analysis

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MATERIALS & DESIGN 2025年 252卷

作者： Yan, Cong Hirschmann, Eric Geers, Marc G. D. Giuntini, Diletta Eindhoven Univ Technol Dept Mech Engn Rondom 70 NL-5612 AP Eindhoven Netherlands Helmholtz Zentrum Dresden Rossendorf Inst Radiat Phys D-01328 Dresden Germany

Supercrystalline nanocomposites (SCNCs) are a new class of hybrid materials consisting of organically functionalized nanoparticles that are arranged into periodic architectures, featuring multi-functional properties. While their mechanical behavior is starting to be assessed, the time-dependent aspects thereof, and especially creep, remain unexplored. This lack of understanding is an obstacle towards future implementation of SCNCs into devices. It is therefore imperative not only to capture experimentally the creep behavior of SCNCs, but also to develop models that accurately predict its evolution. Here, a model is proposed to capture the nanoindentation creep behavior of SCNCs, using both rheological models and free volume theory. The creep compliance derived from the rheological model shows a stress-dependent trend, indicating nonlinear viscoelasticity. The presence of free volume is experimentally detected in SCNCs via positron annihilation lifetime spectroscopy. It decreases in size with increasing degrees of crosslinking of the organic phase, a phenomenon attributed to the shrinkage of superlattices. The creep compliance is predicted by introducing a shift factor to account for the evolution of the relaxation time caused by the change in free volume. A free volume-based creep model is proposed to predict the creep behavior of SCNCs, and its applicability is validated through new nanoindentation creep tests at varying loads.

关键词： Supercrystals Creep nonlinear viscoelasticity Free volume Positron annihilation lifetime spectroscopy

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Stress relaxation and viscous energy in nonlinear viscoelasticity: A rational extended thermodynamics framework

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2025年 196卷

作者： Amabili, Marco Arima, Takashi Ruggeri, Tommaso Westlake Univ Sch Engn Hangzhou Zhejiang Provin Peoples R China Natl Inst Technol Tomakomai Coll Dept Engn Innovat Tomakomai 0591275 Japan Univ Bologna Dept Math Via Saragozza 8 I-40123 Bologna Italy Acad Nazl Lincei Rome Italy

We investigate uniaxial stress relaxation under constant strain using a recent hyperbolic model of nonlinear viscoelasticity based on the principles of Rational Extended Thermodynamics, as proposed in Ruggeri (2024). We determine the viscous dissipated energy such that the stress decays over time as a combination of exponential functions (Prony Series) with different relaxation times. We show that the obtained viscous energy satisfies all the requirements of the model such that the original system is symmetric hyperbolic and in particular satisfy the dissipation principle. According to the model, which requires that the viscous energy depends solely on the viscous stress, we are able to determine the analytical form of the coefficients in terms of the initial step deformation. This approach allows us to predict the decay of the viscous stress for any deformation jump, relying only on the fitting coefficients obtained from an experiment. This fully nonlinear viscoelastic model can be applied in conjunction with any hyperelastic law for the quasi-static stress component. We successfully applied our results to reproduce experimental data from uniaxial relaxation tests of a woven Dacron fabric currently used in aortic grafts.

关键词： Stress relaxation viscoelasticity nonlinear viscoelasticity Rational extended thermodynamics nonlinear elasticity

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Analysis of steady-state frictional rolling contact problems in Schapery-nonlinear viscoelasticity

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART J-JOURNAL OF ENGINEERING TRIBOLOGY 2019年第6期233卷 911-926页

作者： Abdelrahman, Alaa A. El-Shafei, Ahmed G. Mahmoud, Fatin F. Zagazig Univ Dept Mech Design & Prod Coll Engn Zagazig Egypt

In the context of an updated Lagrangian formulation, a computational model is developed for analyzing the steady-state frictional rolling contact problems in nonlinear viscoelastic solids. Schapery's nonlinear viscoelastic model is adopted to simulate the viscoelastic behavior. In addition to the material nonlinearity, the model accounts for geometrical nonlinearities, large displacements, and rotations with small strains. To satisfy the steady-state rolling contact condition, a spatially dependent incremental form of the viscoelastic constitutive equations is derived. Consequently, the dependence on the past history of the strain rate in the stress-strain law is expressed in terms of the spatial variation of the strain. The contact conditions are exactly satisfied by employing the Lagrange multiplier approach to enforce the contact constraints. The classical Coulomb's friction law is used to simulate friction. The developed model is verified and compared and good agreement is obtained. The applicability of the developed model is demonstrated by analyzing the steady-state rolling contact response of viscoelastically walled-wheel over rigid foundation. Moreover, the obtained results show remarkable effects of the rotational velocity and the viscoelastic material parameters on the mechanical response of steady-state frictional rolling contact.

关键词： Steady-state rolling contact nonlinear viscoelasticity Schapery's model large deformation finite element method

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nonlinear viscoelasticity of PP/PS/SEBS blends

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RHEOLOGICA ACTA 2005年第3期44卷 295-312页

作者： Macaúbas, PHP Demarquette, NR Dealy, JM Univ Sao Paulo Escola Politecn Dept Met & Mat Engn BR-05508900 Sao Paulo Brazil McGill Univ Dept Chem Engn Montreal PQ H3A 2B2 Canada

The nonlinear viscoelastic behavior of polypropylene/polystyrene (PP/PS) blends compatibilized or not with the linear triblock copolymer (styrene-ethylene-/butylene-styrene, SEBS) was investigated. Start-up of steady-shear at rates from 0.1 to 10 s(-1) supercript stopwas carried out using a controlled strain rotational rheometer and a sliding plate rheometer for strain histories involving one or several shear rates. The shear stress and first normal shear stress difference were measured as functions of time, and the morphologies of the samples before and after shearing were determined. For each strain history except that involving a single shear rate of 0.1 s(-1) the blends showed typical non-linear viscoelastic behavior: a shear stress overshoot/undershoot, depending on the history, followed by a steady state for each step. The first normal stress difference increased monotonically to a steady-state value. The values of the stresses increased with the addition of SEBS. The shear stress overshoot and undershoot and the times at which they occurred depended strongly on the strain history, decreasing for a subsequent shear rate step performed in the same direction as the former, and the time at which stress undershoot occurred increased for a subsequent shear rate step performed in the opposite direction, irrespective of the magnitude of the shear rate. This behavior was observed for all the blends studied. The time of overshoot in a single-step shear rate experiment is inversely proportional to the shear rate, and the steady-state value of N-1 scaled linearly with shear rate, whereas the steady-state shear stress did not. The average diameter of the dispersed phase decreased for all strain histories when the blend was not compatibilized. When the blend was compatibilized, the average diameter of the dispersed phase changed only during the stronger flows. Experimental data were compared with the predictions of a model formulated using ideas of Doi and Ohta (1991), Lac

关键词： nonlinear viscoelasticity polymer blends Doi and Ohta Theory flow-induced morphology

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nonlinear viscoelasticity and viscoplasticity of flax/polypropylene composites

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JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME 2006年第4期128卷 527-536页

作者： Marklund, Erik Varna, Janis Wallstrom, Lennart Lulea Univ Technol Div Polymer Engn SE-97187 Lulea Sweden

In tensile tests the flax/polypropylene composites clearly show nonlinear behavior in loading and hysteresis loops in unloading. In creep tests performed at different load levels the response was nonlinear viscoelastic, and after recovery, viscoplastic strains were detected. No degradation in stiffness could be seen and thus nonlinear viscoelasticity and viscoplasticity were assumed to be the main cause for the observed behavior The fracture surface of a specimen that experienced creep rupture at 24 MPa was investigated using a scanning electron microscope. The viscoplastic response was studied experimentally and described by a power law with respect to time and stress level in the creep test. The nonlinear viscoelasticity was described using Schapery's model. The application of Prony series and a power law to approximate the viscoelastic compliance was investigated. Both descriptions have accuracy sufficient for practical applications. However, at high stresses the attempts to describe the viscoelastic compliance by a power law with a stress-independent exponent failed and therefore stress dependence of this exponent was included in the data analysis. The accuracy within the considered stress range is good, but the thermodynamic consistency of this procedure has to be proven.

关键词： flax/PP composite nonlinear viscoelasticity viscoplasticity creep recovery

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nonlinear viscoelasticity of complex fluids: A kinetic network model

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RHEOLOGICA ACTA 2015年第1期54卷 53-67页

作者： Manero, Octavio Puig, Jorge E. Bautista, Fernando Paulo Garcia-Sandoval, J. Univ Nacl Autonoma Mexico Inst Invest Mat Mexico City 04510 DF Mexico Univ Guadalajara Dept Ingn Quim & Fis Guadalajara 44430 Jalisco Mexico

In this work, the rheological behavior of complex fluids is analyzed with a model based on the classical transient network formulation, in which the description of nonlinear viscoelasticity and time-dependent phenomena considers spatial and temporal variations of the entanglement density in the flow region. The entropic law of the segments that join entanglement points of macromolecules (or dispersed phase) is modeled with a Warner spring law with variable extensibility. The structure modification is described with a function that is dependent of a kinetic process that involves the formation of a more entangled microstate on one extreme, and a flow-induced degradation of the transient network with variable entanglement density on the other extreme (disentangled microstate). Predictions of the model under simple shear, inception of shear flow, stress relaxation, interrupted shear, and shear-thickening are compared with those of other models and with experiments.

关键词： Transient network Complex fluids Kinetic process nonlinear viscoelasticity

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nonlinear viscoelasticity of pre-compressed layered polymeric composite under oscillatory compression

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COMPOSITES SCIENCE AND TECHNOLOGY 2018年 162卷 188-197页

作者： Xu, Yangguang Tao, Ran Lubineau, Gilles KAUST COHMAS Lab Phys Sci & Engn Div Thuwal 239556900 Saudi Arabia CAEP Inst Syst Engn Mianyang 621999 Peoples R China

Describing nonlinear viscoelastic properties of polymeric composites when subjected to dynamic loading is essential for development of practical applications of such materials. An efficient and easy method to analyze nonlinear viscoelasticity remains elusive because the dynamic moduli (storage modulus and loss modulus) are not very convenient when the material falls into nonlinear viscoelastic range. In this study, we utilize two methods, Fourier transform and geometrical nonlinear analysis, to quantitatively characterize the nonlinear viscoelasticity of a pre-compressed layered polymeric composite under oscillatory compression. We discuss the influences of pre-compression, dynamic loading, and the inner structure of polymeric composite on the nonlinear viscoelasticity. Furthermore, we reveal the nonlinear viscoelastic mechanism by combining with other experimental results from quasi-static compressive tests and microstructural analysis. From a methodology standpoint, it is proved that both Fourier transform and geometrical nonlinear analysis are efficient tools for analyzing the nonlinear viscoelasticity of a layered polymeric composite. From a material standpoint, we consequently posit that the dynamic nonlinear viscoelasticity of polymeric composites with complicated inner structures can also be well characterized using these methods.

关键词： nonlinear viscoelasticity Layered polymeric composite Fourier transform Geometrical nonlinear analysis Oscillatory compression

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nonlinear viscoelasticity of cheese

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BIORHEOLOGY 1998年第3期35卷 171-191页

作者： Tariq, S Giacomin, AJ Gunasekaran, S Univ Wisconsin Rheol Res Ctr Madison WI 53706 USA Univ Wisconsin Dept Mech Engn Madison WI 53706 USA Univ Wisconsin Dept Biol Syst Engn Madison WI 53706 USA Univ Wisconsin Wisconsin Ctr Dairy Res Madison WI 53706 USA

Cheese viscoelasticity is commonly measured using steady uniaxial compression, steady uniaxial extension, shear and compressive creep, and stress relaxation in shear and compression. Viscoelastic properties for many cheeses have also been studied using small amplitude oscillatory shear (SAOS). However, there is little on the measurement of nonlinear viscoelastic properties. The large deformation test usually conducted on cheese to study nonlinear viscoelasticity is uniaxial compression, but this test hardly departs from linear behavior. In this work, the nonlinear viscoelasticity of four cheese varieties was studied using large amplitude oscillatory shear (LAOS). A sliding plate rheometer incorporating a shear stress transducer was used. The data were evaluated using spectral analysis, and results are presented mainly in the form of shear stress versus shear rate loops.

关键词： cheese nonlinear viscoelasticity oscillatory shear

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nonlinear viscoelasticity and Viscoplasticity Characteristics of Virgin and Modified Asphalt Binders

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JOURNAL OF ENGINEERING MECHANICS 2023年第10期149卷 04023074-04023074页

作者： Li, Hui Ling, Jian Leng, Zhen Zhang, Yuqing Luo, Xue Southeast Univ Sch Transportat Nanjing 211189 Peoples R China Hong Kong Polytech Univ Dept Civil & Environm Engn Hung Hom Kowloon Hong Kong Peoples R China Zhejiang Univ Coll Civil Engn & Architecture 866 Yuhangtang Rd Hangzhou 310058 Zhejiang Peoples R China

Many engineering materials have coupled nonlinear viscoelasticity and viscoplasticity, which are affected by complex thermomechanical loadings. This study addressed the challenge of accurately separating the viscoplasticity and the nonlinear viscoelasticity and formulated the viscoplasticity by considering the effects of temperatures and loading levels. First, the nonlinear viscoelastic constitutive equation was adopted to accurately separate the viscoplasticity and the nonlinear viscoelasticity. Then a kinetics-based viscoplastic model and a new viscoplastic activation energy indicator are proposed to consider the effects of the temperature and loading level on the viscoplasticity. As typical nonlinear viscoelastic viscoplastic materials commonly used in pavement engineering, asphalt binders were selected to demonstrate the principles in this study. It was found that the proportion of the viscoplastic strain is larger than the nonlinear viscoelastic strain for virgin asphalt binders (VBs) and it increases with the temperature, whereas the opposite is true for high-viscosity modified asphalt binders (HVBs) and rubber asphalt binders (RBs). The logarithm of the viscoplastic strain rate increases linearly with the reciprocal of the temperature, and the viscoplastic strain rates at different temperatures are correlated and can be predicted based on the established viscoplastic strain kinetics model. The viscoplastic activation energy indicator can characterize the viscoplastic deformation resistance for nonlinear viscoelastic viscoplastic materials, and the order of the viscoplastic deformation resistances of the three binders was VB < HVB < RB, based on this indicator. (c) 2023 American Society of Civil Engineers.

关键词： Viscoplasticity nonlinear viscoelasticity Kinetics-based viscoplastic model Viscoplastic activation energy.

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nonlinear viscoelasticity of silicone carbide whisker-filled liquid crystalline polymer melts

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POLYMERS & POLYMER COMPOSITES 2002年第5期10卷 361-373页

作者： Katsuhiko, A Takeshi, K Takahiro, T Lengalova, A Saha, P Natl Inst Adv Ind Sci & Technol Res Ctr Macromol Technol Tsukuba Ibaraki 3058565 Japan Ind Technol Ctr Fukui Prefecture Fukui 9160273 Japan Maezawa Kasei Ind Ltd Oosato Saitama 366042 Japan Tomas Bata Univ Zlin Fac Technol Ctr Polymer Zlin 76273 Czech Republic

Dynamic viscoelasticity of melts of semi-aromatic liquid crystalline polymer (LCP) and its silicone carbide (SiC) whisker-filled compounds was measured to analyze quantitatively their nonlinear viscoelastic properties by Fourier expansion of the shear stress wave. For LCP the tertiary terms, G'(3) and G"(3), are considerably smaller than their primary terms, G'(1) and G"(1), i.e. their viscoelasticity is almost linear. Viscoelastic behaviour of the silicone carbide whisker-filled LCP system was compared with that of the carbon fiber (CF)- and glass fiber (GF)-filled LCP systems presented in [18]. The CF/LCP system shows a dependence of the oscillatory angle upon its G'(i) and G"(i), making both accordingly decrease with increasing i from 1 to 3 and 5. The G'(3) and G"(3) values of the polymer system, compared to its G'(1) and G"(1) counterparts, are sufficiently large not to be negligible, suggesting that the system's viscoelasticity is nonlinear. Furthermore, the SiC whisker-filled LCP system was examined for the dependence of the ratios G'i / G'(1) and G"(i) / G"(i) (i = 3, 5), and G(i) / G(1) (i = 3, 5, 7) as indicators of the degree of viscoelastic nonlinearity upon angular frequency. The results did not show any significant difference between G'(3) /G'(1) and G'(5) /G'(1) values, or between G"(3) /G"(1) and G"(5) /G''(1) values. The ratio G(i)/G(1) (i = 3, 5, 7), representing the nonlinearity of viscoelasticity of the system, however, is higher with an increase in the oscillatory angle.

关键词： viscoelasticity MELT nonlinear viscoelasticity dynamic viscoelasticity Liquid crystal polymers Silicones Viscoelastic properties Polymer melts

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