Viscoelastic Relaxation Research Articles

Probing time-dependent afterslip and viscoelastic relaxation following the 2015 Mw7.8 Gorkha earthquake based on the 3-D finite-element model

We analyzed daily displacement time series from 34 continuous GPS stations in Nepal and 5 continuous GPS stations in South Tibet, China, and extracted the first 4.8 years of postseismic motion after the 2015 Mw7.8 Gorkha earthquake. With the longer duration GPS observations, we find that postseismic displacements mainly exhibit southward and uplift motion. To study the postseismic afterslip and viscoelastic relaxation, we built a 3-D spherical finite-element model (FEM) with heterogeneous material properties and surface topography across the Himalayan range, accounting for the strong variations in material properties and surface elevation along the central Himalayan arc. On the basis of the FEM, we reveal that the predicted viscoelastic relaxation of cm level moves southward to the north of the Gorkha earthquake rupture, but in an opposite direction to the observed postseismic deformation in the south; the postseismic deformation excluding viscoelastic relaxation is well explained by afterslip downdip of the coseismic rupture. The afterslip is dominant during 4.8 years after the 2015 Mw7.8 Gorkha earthquake; the contribution by the viscoelastic relaxation gradually increases slightly. The lack of slip on a shallow portion and western segment of the MHT during and after the 2015 Gorkha earthquake implies continued seismic hazard in the future.

Parameter identification for the simulation of the periodontal ligament during the initial phase of orthodontic tooth movement

The paper is concerned with simulation of the periodontal ligament response to force in the initial phase of orthodontic tooth movement. This is based on two previous investigations, a in vitro experiment with specimens of porcine mandibular premolars and a in vivo experiment on human upper first incisors. For the curve fit of the in vitro experiment a model function, assuming viscoelasticity, was introduced. The viscoelastic model function was augmented by a ramp rise time term, to account for observed dependence of the response on actuator velocity, and a previous load history term, to account for the effect of the previous tests on the current test. The correlation coefficient of a curve fit for all tests grouped together was Next, a curve fit of the in vivo experiment was done. Good correlation was found for a simplified model function, without viscoelastic term (). For both tests, in vitro and in vivo, the ramp rise time term improved correlation. A finite element model of the specimen of the in vitro experiment was created. For the PDL a hyperelastic constitutive model for compressible material was used and model parameters were identified. The present work indicates that the macroscopic response of the periodontal ligament to an external load can be simulated with a poro-visco-hyperelastic model. The simulation showed that poroelastic behaviour will gradually cease when viscoelastic relaxation progresses. This followed also from dimensionless analysis. As a consequence, for slow loading, or if initial response to fast loading is not of interest, a visco-hyperelastic model may suffice. To identify parameters of the finite element model several optimisation problems were solved. A model function, which can be regarded as a reduced order model, allowed a full factorial experiment (analysis) at low cost, to identify initial parameters. The thus found parameters were further refined with an optimum interpolation meta-model. That is, for limited number of parameter combinations the response was simulated with the finite element model and a refined parameter study was conducted by means of optimal interpolation. The thus found optimal parameters were verified by simulation with the finite element model. Optimal interpolation is computationally cheap, which allowed full factorial experiments at low cost.

On the Origin of Postseismic Deformation Processes in the Region of the Maule, Chile Earthquake of February 27, 2010

Abstract—For the first time, we present a rupture surface model of the 2010 Maule earthquake, Chile, based on the combination of satellite geodesy, InSAR, and satellite gravimetry data. The regularization method used for constructing the model allowed us to find a uniform displacement field on rupture surface provided that a slip rake is close to a given one. On average, the displacements on the rupture surface are about 5 m with a maximum displacement of 13.1 m. The rupture zone extends south of the Arauco Peninsula and reaches a depth of 42 km along the plate surface. Using the constructed seismic rupture model, we have modeled the process of viscoelastic relaxation of stresses that emerged in the lithosphere and upper mantle as a result of the earthquake in order to estimate the contribution of this process in the observed postseismic displacements. Surface displacement velocities mainly depend on the viscosity value adopted for the asthenosphere. The comparison of the calculated and measured displacements at low viscosity of the asthenosphere shows that when the displacements are measured far from rupture surface as it is the case with the ocean–ocean subduction zone earthquakes, the observed displacements can be explained by the process of viscoelastic relaxation with a low viscosity of the asthenosphere. In the cases when there are data on the displacements above rupture surface, e.g., for the 2010 Maule earthquake, explaining the observed displacements by stress relaxation process in the near zone of the rupture is not possible at any viscosity: the displacements substantially differ both in amplitude and direction. At the same time, the postseismic creep models fairly well agree with the entire set of the existing data. Therefore, there is no need to accept the hypothesis of a low-viscous asthenosphere in the region of the 2010 Maule earthquake. Previously, we arrived at the similar conclusion considering the modeling results for the Sumatran earthquake of 2004, Simushir earthquakes of 2006, and a number of other large earthquakes in the subduction zones.

Rupture models and viscoelastic stress changes of three Mw ~ 6.3 earthquakes along the southern front of the Qilian Mountains, northeastern Tibetan plateau

Around the southern front of the Qilian Mountains, three Mw 6.3 strong earthquakes have occurred since 2003. The distances between the epicenters of these events range from 18 to 46 km. By collecting available datasets, including broadband waveforms, coseismic surface geodetic measurements and active fault mapping results, we invert rupture models for these strong earthquakes with a finite fault model approach in elastic half space. Constrained by these detailed rupture models, we then build a three-dimensional finite element model to calculate Coulomb stress change due to the coseismic displacement and postseismic viscoelastic relaxation. Combined with an effective friction coefficient of 0.2–0.8 and variable rheological characteristics, numerical results show that following the 2003 event, the Coulomb stress change along the 2008 rupture segment was positive with magnitudes between 1.8 × 103 Pa and 2.2 × 103 Pa. Among the stresses, the postseismic viscoelastic relaxation contributed 10.7% ~ 23.3%. Just prior to the occurrence of the 2009 earthquake, the total changes of the Coulomb stress around its hypocenter reached 2.71 × 104– 3.72 × 104 Pa, to which the 2003 event and the 2008 event contributed approximately 7 × 102– 1.5 × 103 Pa (2.58% ~ 4.03%) and 2.64 × 104– 3.57 × 104 Pa (95.97% ~ 97.42%), respectively. We believe that other postseismic behaviors, including afterslip and poroelastic rebound, could also yield extra changes in the Coulomb stress, which probably further enhance the triggering effect among the sequential earthquakes. The numerical results also show that the increased stress around the hypocenters of latter two events was mainly determined by the positive shear stress. After the three strong earthquakes, the Coulomb stress on some active faults increased and is still increasing, suggesting that great attention should be paid to the potential earthquake hazards in this region.

Altered mechanical behavior of demineralized bone following therapeutic radiation.

Post-radiotherapy (RTx) bone fragility fractures are a late-onset complication occurring in bone within or underlying the radiation field. These fractures are difficult to predict, as patients do not present with local osteopenia. Using a murine hindlimb RTx model, we previously documented decreased mineralized bone strength and fracture toughness, but alterations in material properties of the organic bone matrix are largely unknown. In this study, 4 days of fractionated hindlimb irradiation (4 × 5 Gy) or Sham irradiation was administered in a mouse model (BALB/cJ, end points: 0, 4, 8, and 12 weeks, n = 15/group/end point). Following demineralization, the viscoelastic stress relaxation, and monotonic tensile mechanical properties of tibiae were determined. Irradiated tibiae demonstrated an immediate (day after last radiation fraction) and sustained (4, 8, 12 weeks) increase in stress relaxation compared to the Sham group, with a 4.4% decrease in equilibrium stress (p < .017). While tensile strength was not different between groups, irradiated tibiae had a lower elastic modulus (-5%, p = .027) and energy to failure (-12.2%, p = .012) with monotonic loading. Gel electrophoresis showed that therapeutic irradiation (4 × 5 Gy) does not result in collagen fragmentation, while irradiation at a common sterilization dose (25 kGy) extensively fragmented collagen. These results suggest that altered collagen mechanical behavior has a role in postirradiation bone fragility, but this can occur without detectable collagen fragmentation. Statement of Clinical Significance: Therapeutic irradiation alters bone organic matrix mechanics and which contribute to diminished fatigue strength, but this does not occur via collagen fragmentation.

Rhyolitic volcano dynamics in the Southern Andes: Contributions from 17 years of InSAR observations at Cordón Caulle volcano from 2003 to 2020

In this article I present a review of InSAR observations of ground deformation at Cordón Caulle volcano, whose 2011–2012 VEI 4-5 eruption is the best scientifically observed and instrumentally recorded rhyolitic eruption to date. I document a complete cycle of pre-eruptive uplift, co-eruptive subsidence and post-eruptive uplift with InSAR data between March 2003 and May 2020, and produced by a complex interplay of magmatic processes. Pre-eruptive data show ~0.5 m of ground uplift in three distinct episodes between 2003 and 2011, with uplift rates between ~3 and ~30 cm/yr. The uplift was likely caused by magma injection resulting in pressurization of the magmatic system at depths of 4–9 km. Data spanning the first 3 days of the eruption show ~1.5 m of deflation produced by two distinct sources at 4–6 km depth located 18 km from each other and up to 10 km from the eruptive vent -- suggesting hydraulic connectivity of a large magma mush zone. A third source of deformation was recorded during the rest of the eruption at a depth of ~5 km, resulting in a total subsidence of ~4.2 m during the whole eruption. On a much smaller spatial scale (~25 km2), InSAR-derived digital elevation models recorded ~250 m of uplift in the area of the eruptive vent interpreted as the intrusion of a shallow laccolith during the first 2.5 months of the eruption and time averaged lava discharge rates up to ~150 m3/s. The co-eruptive time series of reservoir pressure drop and extruded volume follow exponential trends that can be explained by a model of magma reservoir depressurization and conduit flow. Since the end of the eruption, the surface of the volcano was uplifted ~1 m in a sequence of three transient episodes of unrest during 2012 and 2019, with uplift rates between 6 and 45 cm/yr and lasting between 0.5 and 3.2 years. These pulses can be modeled by the same source, a sub-horizontal sill at a depth of ~6 km. Viscoelastic relaxation is not significant on these time scales, hence I interpret these uplift signals as being produced by episodic pulses of magma injection in the crystal mush that likely underlies the volcano. The episodic and abrupt changes of the ground deformation suggest a restless trans-lateral magmatic system at depths of 4–9 km, and active across multiple spatial and temporal scales. Finally, I also discuss challenges of the InSAR technology that should be addressed to detect ground deformation on short time scales, particularly under the low coherence conditions of Cordón Caulle.

Fault interactions in a complex fault system: insight from the 1936–1997 NE Lut earthquake sequence

SUMMARYCalculations of Coulomb stress changes have shown that moderate to large earthquakes may increase stress at the location of future earthquakes. Coulomb stress transfers have thus been widely accepted to explain earthquake sequences, especially for sequences occurring within parallel or collinear fault systems. Relating, under this framework, successive earthquakes occurring within more complex fault systems (i.e. conjugate fault system) is more challenging. In this study, we assess which ingredients of the Coulomb stress change theory are decisive for explaining the succession of three large (Mw 7+) earthquakes that occurred on a conjugate fault system in the NE Lut, East Iran, during a 30-yr period. These earthquakes belong to a larger seismic sequence made up of 11 earthquakes (Mw 5.9+) from 1936 to 1997. To reach our goal, we calculate, at each earthquake date, the stress changes generated by the static deformation of the preceding earthquakes, the following post-seismic deformation due to the viscoelastic relaxation of the lithosphere, and the interseismic deformation since 1936. We first show that accurately modelling the source and receiver fault geometry is crucial to precisely estimating Coulomb stress changes. Then we show that 7 out of 10 earthquakes of the NE Lut sequence, considering the uncertainties, are favoured by the previous earthquakes. Furthermore, the last two M7+ earthquakes of the sequence (1979 and 1997) have mainly been favoured by the moderate Mw ∼ 6 earthquakes. Finally, we investigate the link between the Coulomb stress changes due to previous earthquakes and the rupture extension of the next earthquake and show that a correlation does exist for some earthquakes but is not systematic.

Postseismic Deformation Following the 2015 Mw7.8 Gorkha (Nepal) Earthquake: New GPS Data, Kinematic and Dynamic Models, and the Roles of Afterslip and Viscoelastic Relaxation

AbstractWe report Global Positioning System (GPS) measurements of postseismic deformation following the 2015 Mw7.8 Gorkha (Nepal) earthquake, including previously unpublished data from 13 continuous GPS stations installed in southern Tibet shortly after the earthquake. We use variational Bayesian Independent Component Analysis (vbICA) to extract the signal of postseismic deformation from the GPS time series, revealing a broad displacement field extending &gt;150 km northward from the rupture. Kinematic inversions and dynamic forward models show that these displacements could have been produced solely by afterslip on the Main Himalayan Thrust (MHT) but would require a broad distribution of afterslip extending similarly far north. This would require the constitutive parameter (a − b)σ to decrease northward on the MHT to ≤0.05 MPa (an extreme sensitivity of creep rate to stress change) and seems unlikely in light of the low interseismic coupling and high midcrustal temperatures beneath southern Tibet. We conclude that the northward reach of postseismic deformation more likely results from distributed viscoelastic relaxation, possibly in a midcrustal shear zone extending northward from the seismogenic MHT. Assuming a shear zone 5–20 km thick, we estimate an effective shear‐zone viscosity of ~3·1016–3·1017 Pa·s over the first 1.12 postseismic years. Near‐field deformation can be more plausibly explained by afterslip itself and implies (a − b)σ ~ 0.5–1 MPa, consistent with other afterslip studies. This near‐field afterslip by itself would have re‐increased the Coulomb stress by ≥0.05 MPa over &gt;30% of the Gorkha rupture zone in the first postseismic year, and deformation further north would have compounded this reloading.

Decadal Viscoelastic Postseismic Deformation of the 1964 Mw9.2 Alaska Earthquake

AbstractViscoelastic postseismic deformation after the 1964 Mw9.2 Alaska earthquake extends thousands of kilometers from the rupture region and lasts for decades, providing unique opportunities to better understand the three‐dimensional rheological properties of the Alaska subduction zone. We have optimized a three‐dimensional viscoelastic finite element model to study processes that control the postseismic deformation of the 1964 event. The model includes an elastic continental plate and an elastic oceanic plate, a two‐layered viscoelastic oceanic upper mantle, and a uniform viscoelastic mantle wedge. Stress‐driven afterslip is simulated by a thin weak shear zone. The viscoelastic relaxation of the upper mantle and shear zone is represented by the bi‐viscous Burgers rheology. The model has determined the viscosities of the mantle wedge and shear zone to be 3 × 1019 Pa s and 8 × 1016 Pa s, respectively. The afterslip takes place mostly within the first 5 years after the earthquake and is up to 4 m, equivalent to a modeled earthquake of Mw8.5. Model results reveal a spatial and temporal correlation between the afterslip distribution and later slow slip events. The model predicts that the surface deformation about 200 years after the earthquake will be controlled mostly by the relocking of the fault. Further tests on the impact of lateral variation in the mantle wedge viscosity indicate that the viscosity in the continental upper mantle thousands of kilometers from the rupture area may be about an order of magnitude higher than that of the mantle wedge in the subduction zone.

Interface-by-design in zirconia-polyurea matrix hybrid composites

This study investigates the incorporation of zirconia particles in polyurea matrix to form hybrid composites. Pristine zirconia particles in the monoclinic phase are first premixed with an oligomeric diamine−a reactant for polyurea−as an alternative method of surface functionalization that does not require the use of organosilanes. Interfacial interactions between the zirconia particles and polyurea are revealed via attenuated total reflectance-Fourier transform infrared spectroscopy, where a shift and broadening of the urea-carbonyl stretching and an increase in relative intensity of the corresponding disordered vs. ordered N–H stretching are shown in hybrid composites vs. bulk polyurea. The composition dependence of the viscoelastic relaxation characteristics and dynamic storage modulus in hybrid composites as determined by dynamic mechanical analysis are also elaborated upon. Additionally, we evaluate the potential of exploiting zirconia-polyurea hybrids to enabling dynamic impedance optimization at the interface of a select bi-layer construct, particularly when considering the material response under dynamic loading environments.

Gradient Flow Model of Mode-III Fracture in Maxwell-type Viscoelastic Materials

We formulate a phase field crack growth model for mode III fracture in a Maxwell-type viscoelastic material. To describe viscoelastic relaxation, a field variable of viscously flowed strain is employed in addition to a displacement field and damage phase field used in the original elastic model. Unlike preceding models constructed in the mechanical engineering community, our model is based only on the generic procedure for driving (uni-directional) gradient flow system from a physically natural system energy and employ no additional assumption such as the super-imposed relations for stress and strain (and their time derivatives) valid only for linear viscoelasticity. Numerical simulations indicate that the competition between increase in deformation by applied loading and the viscoelastic relaxation determines whether a distinct crack propagation has occurred from an initial crack. Furthermore, we consider the numerical results from an energetic perspective.

Logarithmic and exponential transients in GNSS trajectory models as indicators of dominant processes in postseismic deformation

Models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas with single or multiple timescales. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. It is now quite widely understood that one can model GPS/GNSS time series manifesting postseismic transient displacements almost equally well using trajectory models constructed using logarithmic or exponential transients. This is consistent with the consensus established by the late 1970s that it is difficult to use geodetic observations to distinguish between deep aseismic afterslip and more diffuse viscoelastic relaxation as the primary mechanism of postseismic deformation. In this paper, we assess the relative explanatory value of both logarithmic and exponential forms by focusing on GNSS time series measured with better than typical signal-to-noise ratios. We find that the double logarithmic transient typically provides much better fits than double exponential transient, when both models are given equal degrees of freedom. We also discuss the relative utility of the hybrid transient formulas in which the logarithmic component is assigned shorter decay timescale parameters than the exponential component. These models fit observed postseismic displacements almost as well as double logarithmic transients.

Analytical Investigation on CNT Based Maxwell Nano-fluid with Cattaneo–Christov Heat Flux Due to Thermal Radiation

At first, we derive a series form solution of the coupled highly nonlinear equations, which includes various conditions. Then, via the method of directly defined inverse mapping with the series form solution firstly reported in this paper, we can obtain theoretical and approximate analytical analysis about the transfer of heat as well as the magnetohydrodynamic flow of Maxwell nanofluid by the influence of convective heating with effects of thermal radiation. In the energy equation, heat flux model is adopted to develop the equations for viscoelastic relaxation over boundary layer flow. For this investigation, we considered base liquid as engine oil and other forms of carbon nanotubes such as single walled nanotubes and multi-walled nanotubes. Suitable similarity transformations are applied for transformation of given boundary layer flow equations. Results are compared numerically by Keller–Box method. It is found that for both singled and multi-walled carbon nanotube based nanofluids the thermal relaxation time and temperature function are inversely proportional. More interestingly it is noted that for the two types of nanofluids, fluid relaxation parameter exactly coordinates with heat transfer rate as well as skin friction investigated. Also shown that the base functions of solutions are highly convergence.

3D Structure and Mechanics of Silk Sponge Scaffolds Is Governed by Larger Pore Sizes

Three-dimensional scaffolds play an essential role in tissue engineering. Although essential, the tunability of the 3D scaffolds mechanical and transport properties remains a challenge. In this work, we present new approaches to advance the field. First, we applied our progressive pH acidification to mimic the natural silk gelation process before ice-templating (−20 and −80°C); second, we fitted the mechanical properties using a connectivity model; third, we fitted the scaffolds mechanical relaxation to understand the transport properties; and fourth we used micro-CT to correlate the process parameters to the scaffolds' performances. Our results suggested that the free shrinkage of the scaffolds determined their final properties. We found, however, that the porosity (above 90%) was anisotropic, similarly the tortuosity (between 1 and 1.3). We identified two major pore dimensions, the first one between 10 and 20 μm, and the second between 50 and 130 μm. Mechanically, our model suggested that the bulk modulus captured the elastic contribution and was controlled predominantly by the silk concentration. We tentatively associated the fractional modulus 1 to the collapse of the larger pores structures and was controlled mostly by the process temperature. We assigned the slow relaxation to the transport of fluid in the silk sponge scaffolds; and the fast relaxation with a viscoelastic relaxation. The silk concentration and process temperatures did not influence the latter. Overall, our use of the tomography, mechanical test, and detailed statistical analysis provides inroads into the interplay between process parameters (silk concentration and process temperature) and the multiple responses of the silk sponge scaffolds. The development of a new mechanical fitting for the compression test helped capture simply the different failure modes in the sponge scaffolds as well as correlating those events to relaxation and eventually transport properties. (Less)

Viscoelastic Relaxation within the Moon and the Phase Lead of Its Cassini State

AbstractAnalyses of Lunar Laser Ranging data show that the spin symmetry axis of the Moon is ahead of its expected Cassini state by an angle of ϕp = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid‐body tides and viscous core‐mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the center of the Moon can also account for a part of the observed phase lead angle ϕp. We build a rotational dynamic model of the Cassini state of the Moon that comprises an inner core, a fluid core, and a mantle and where solid regions are allowed to deform viscoelastically in response to an applied forcing. We show that the presence of an inner core does not change the global monthly Q of the Moon and, hence, that the contribution from solid‐body tides to ϕp is largely unaffected by an inner core. However, we also show that viscoelastic deformation within the inner core, acting to realign its figure axis with that of the mantle, can contribute significantly to ϕp through inner core‐mantle gravitational coupling. We show that the contribution to ϕp is largest when the inner core viscosity is in the range of 1013 to 1014 Pa s, when the inner core radius is large and when the free inner core nutation frequency approaches a resonance with the precession frequency of 2π/18.6 yr−1.

Effects of water absorption on the mechanical properties of GFRPs

This study reports on the effects of water absorption on the anisotropic mechanical response of an epoxy resin reinforced with E-glass fibres. Composite specimens were conditioned by immersion in pure water at 50 °C for different time durations, up to full saturation. Water-saturation resulted in reduction of stiffness and strength, in the range of strain rate 0.001–700s−1. Experiments on re-dried specimens after water saturation showed a limited recoverability of the original mechanical properties. Water absorption increased the sensitivity of the mechanical response of the GFRPs to the applied strain rate. Finite element simulations of the response of a unit cell of the unidirectional composite were performed to understand the role of the hygroscopic stresses induced by water absorption, and it was found that this is negligible due to the active mechanisms of viscoelastic relaxation.

Linear viscoelastic relaxation in the α and α+ regions of linear polymers, crosslinked polymers and small molecules

The dynamic linear viscoelastic behavior in the region above Tg was studied for a series of diglycidyl ether of bisphenol-A (DGEBA) based epoxy resins cured with 4,4′-methylenedianiline (MDA) and 4,4′-diaminodiphenyl sulfone (DDS) as well as a linear DGEBA-based polymer – phenoxy. Master curves were constructed from the frequency dependent storage and loss isotherms. The relaxation spectra were determined for the MDA and DDS cured systems and also, using the reported dielectric relaxation data (Casalini et al. Phys. Rev. B, 1997), for the DGEBA monomer. For the tighter DGEBA networks, a single broad relaxation peak was observed vs looser DGEBA networks and a phenoxy thermoplastic where two relaxation processes were observed: the main α-process and an α+-process that occurs at longer relaxation times and higher temperatures. The spectrum for DGEBA monomer exhibited only an α-process with a very abrupt end. The temperature dependence of logaT follows one of the two distinct branches when adjusted for Tg: the tight DGEBA networks all exhibit a steep response; in contrast, the DGEBA monomer, phenoxy and looser DGEBA networks exhibit a less steep response. Relaxation spectrum for the loosely crosslinked Epon1009-MDA system consists of α and α+ components; intriguingly, logaT for the α-process follows the steep branch vs the α+-process following the less steep branch.

Rheology of the Zagros Lithosphere from Post-Seismic Deformation of the 2017 Mw7.3 Kermanshah, Iraq, Earthquake

We use 2018–2020 Sentinel-1 InSAR time series data to study post-seismic deformation processes following the 2017 Mw 7.3 Kermanshah, Iraq earthquake. We remove displacements caused by two large aftershock sequences from the displacement field. We find that for a six month period the response is dominated by afterslip along the up-dip extension of the coseismic rupture zone, producing up to 6 cm of radar line-of-sight displacements. The moment magnitude of afterslip is Mw 5.9 or 12% of the mainshock moment. After that period, the displacement field is best explained by viscoelastic relaxation and a lower crustal viscosity of η l c = 1 − 0.4 + 0.8 × 10 19 Pas . The viscosity of the uppermost mantle is not constrained by the data, except that it is larger than 0.6 × 10 19 Pas . The relatively high lower crustal and uppermost mantle viscosities are consistent with a cold and dry lithosphere of the Zagros region.

On finite bending of visco-hyperelastic materials: a novel analytical solution and FEM

In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony series are utilized to define the strain-dependent and time-dependent parts of the visco-hyperelastic constitutive model, respectively. 3D finite element analysis of the problem is carried out using ABAQUS/Visco to verify the analytical solution results. Material parameters of polyurea are calibrated using an optimization framework for experimental results under five different strain rates, simultaneously. Two well-known tests of viscoelastic materials, stress relaxation and creep tests, are investigated both analytically and numerically. Distribution of the Cauchy stress components and the resultant bending moment versus time, and the variation of the mentioned results with different rise times and ultimate bent angles are provided for the stress relaxation test. Moreover, the strain and bending angle results are plotted in a creep test for different rise times and applied moments. Besides, a multi-step relaxation test and creep recovery test are performed for different loading conditions. Finite element method results confirm the analytical approach with great compatibility.

Viscoelastic relaxation attributed to the molecular dynamics of polyrotaxane confined in an epoxy resin network

The molecular dynamics of polyrotaxane (PR) dispersed homogeneously in a cross-linked epoxy resin were studied using dynamic mechanical analysis (DMA) and pulsed NMR spectroscopy. In PR, poly-e-caprolactone (PCL)-grafted α-cyclodextrins (CDs) are threaded on a polyethylene glycol (PEG) axis. At low temperatures, the PEG and PCL chains of the PR embedded in the epoxy network are in a glassy state. With increasing temperature, the PEG in the PR undergoes a glass-to-rubber transition and fluctuates in the glassy PCL-grafted CDs confined by the epoxy matrix, which causes viscoelastic relaxation. The glass transition temperature, Tg, of the PEG in the PR is much higher than that of pure PEG because of the strong confinement effect in the epoxy network. In addition, the Tg of the PEG drastically changes with coverage by the CDs on the PEG, suggesting that the topological constraint by the CDs also substantially influences the PEG dynamics. The viscoelastic relaxation ascribed to PEG enhances the deformability and toughness of the epoxy resin containing PR under uniaxial stretching. The molecular dynamics of PCL-grafted polyrotaxanes (PRs) homogeneously dispersed in a cross-linked epoxy network were investigated using viscoelastic mechanical measurements and relaxation time measurements with pulsed NMR spectroscopy. With increasing temperature, the PEG axial chains in the PRs exhibit a glass-rubber transition and start fluctuating in the CDs with glassy PCL graft chains, which causes viscoelastic mechanical relaxation.