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Mar 2013

Volume 57, Issue 2, pp. 365-717


Review of algorithms for estimating the gap error correction in narrow gap parallel plate rheology

Olena Kravchuk and Jason R. Stokes

J. Rheol. 57, 365 (2013); http://dx.doi.org/10.1122/1.4774323 (11 pages)

Online Publication Date: 07 Jan 13

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Parallel plate geometry at narrow gaps allows one to perform rheology at high shear rates and with small volumes of fluid. The results from this analysis have to be corrected for a systematic error in the actual gap between the plates. We review the statistical and error analysis methodology for such applications and demonstrate that the process for estimating the gap error significantly impacts the overall accuracy of the analysis at narrow gaps. It is shown that the standard linear regression approach to the estimation of the gap correction is unsound and must not be used in practice. We highlight alternative methods and illustrate their accuracy with typical examples from narrow gap rheology.
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47.57.Qk Rheological aspects
66.20.-d Viscosity of liquids; diffusive momentum transport
01.30.Rr Surveys and tutorial papers; resource letters

Comparative study of interphase viscoelastic properties in polyethylene/polyamide blends compatibilized with clay nanoparticles or with a graft copolymer

Isabelle Labaume, Pascal Médéric, Jacques Huitric, and Thierry Aubry

J. Rheol. 57, 377 (2013); http://dx.doi.org/10.1122/1.4774322 (16 pages) | Cited 1 time

Online Publication Date: 08 Jan 13

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The linear viscoelastic properties of immiscible polyethylene/polyamide blends filled with clay nanoparticles or compatibilized by a copolymer, exhibiting identical nodular morphologies, have been studied. The apparent compatibilizing effect of clay nanoparticles, exclusively located at the interface, was evidenced and compared to the more classical organic compatibilization due to the formation of a macromolecular interphase. The results show that there are some analogies between the two types of compatibilization, but mainly highlight significant differences in rheological properties of the two types of interphase involved in the compatibilization mechanisms. The major differences in interphase viscoelastic properties were evidenced not only directly from the experimental data but also indirectly by using the Palierne's model for different clay or compatibilizer contents.
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81.40.Jj Elasticity and anelasticity, stress-strain relations
83.60.Bc Linear viscoelasticity
64.75.Bc Solubility
61.46.Df Structure of nanocrystals and nanoparticles ("colloidal" quantum dots but not gate-isolated embedded quantum dots)
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances
68.03.Cd Surface tension and related phenomena

Melt fracture and wall slip of metallocene-catalyzed bimodal polyethylenes in capillary flow

Yong Woo Inn

J. Rheol. 57, 393 (2013); http://dx.doi.org/10.1122/1.4774397 (14 pages) | Cited 1 time

Online Publication Date: 10 Jan 13

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The melt fracture and wall slip behaviors of three metallocene-catalyzed bimodal polyethylene (PE) resins and one unimodal PE resin were investigated and critically compared. By comparing the flow curve observed by capillary rheology measurements with the linear viscoelastic (LVE) data, it was observed that the apparent slip increased with content of low molecular weight (MW) component. The bimodal resins that had higher content of low MW component first showed a matte surface at lower stresses. The matte surface remained until the extrudate converted to a wavy appearance before the stick-slip transition as shear rates were increased. The plateau modulus estimated from the LVE data decreased with the increase in low MW content. It was observed that the onset stress of the matte surface (or sharkskin) melt fracture was proportional to the plateau modulus. It was proposed that the distinct separation of the two modes of the bimodal PE resin and the high content of small chains could cause the significant wall slip and the unusual melt fracture behaviors.
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83.50.Rp Wall slip and apparent slip
83.80.Sg Polymer melts
61.25.hk Polymer melts and blends
47.50.Ef Measurements
62.10.+s Mechanical properties of liquids

Linear viscoelastic properties of ethylene–octene copolymer/nanosilica composites investigated over a broad range of frequencies

M. Bailly and M. Kontopoulou

J. Rheol. 57, 407 (2013); http://dx.doi.org/10.1122/1.4774405 (20 pages)

Online Publication Date: 14 Jan 13

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The interrelations between microstructure and rheology of melt compounded poly(ethylene-co-octene) (EOC) based nanocomposites containing low amounts of silica (SiO2) nanoparticles were studied. In the presence of a maleated EOC compatibilizer, hydrogen bonds are established between the silanol groups located on the surface of the particles and the succinic anhydride functionality of the compatibilizer, resulting in improved filler dispersion during compounding and the formation of a bound layer of polymer surrounding the particles. This layer alters the interface between the bulk polymeric matrix and the particles, influencing the linear viscoelastic (LVE) response. The compatibilized composites exhibited a more stable response in time sweeps and a higher critical strain for the onset of nonlinearity, compared to their noncompatibilized counterparts. Superposition of small angle oscillatory shear and creep/creep recovery experiments revealed enhancements in the LVE functions in the absence of a compatibilizer, which are attributed to the increased hydrodynamic effect due to increased propensity for particle aggregation, and to the direct interactions between the polymer chains and the surface of the filler. On the contrary these effects were moderated in the case of the compatibilized composites, due to the presence of the bound layer of polymer surrounding the particles.
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81.40.Jj Elasticity and anelasticity, stress-strain relations
81.40.Lm Deformation, plasticity, and creep
83.60.Bc Linear viscoelasticity
61.46.Df Structure of nanocrystals and nanoparticles ("colloidal" quantum dots but not gate-isolated embedded quantum dots)
62.20.Hg Creep
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances

Anisotropic thermal conduction in polymer melts in uniaxial elongation flows

Sahil Gupta, Jay D. Schieber, and David C. Venerus

J. Rheol. 57, 427 (2013); http://dx.doi.org/10.1122/1.4776237 (13 pages)

Online Publication Date: 16 Jan 13

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Anisotropic thermal conduction was measured in two amorphous polymers that were quenched immediately after being subjected to uniaxial elongation in the molten state. The quenching is performed so that the flow-induced orientation is retained and the samples are essentially in a stress-free state. A novel optical technique based on forced Rayleigh scattering is used to measure the two independent components of the thermal diffusivity tensor as a function of strain and strain rate. The thermal diffusivity is found to increase in the direction parallel, and decrease in the direction perpendicular, to the direction of elongation. Thermal diffusivity data along with measurements of the tensile stress at the point of quenching were used to evaluate the stress-thermal rule, which is analogous to the well-known stress-optic rule. The stress-thermal rule was found to be valid for both polymers over a range of strains and strain rates. Since the quenched samples have orientation only, it appears that the primary source of anisotropy in thermal conductivity is the anisotropy of polymer chain orientation.
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66.25.+g Thermal conduction in nonmetallic liquids
78.20.hb Piezo-optical, elasto-optical, acousto-optical, and photoelastic effects
47.57.Ng Polymers and polymer solutions
62.10.+s Mechanical properties of liquids
66.30.Xj Thermal diffusivity
78.35.+c Brillouin and Rayleigh scattering; other light scattering

High frequency linear rheology of complex fluids measured from their surface thermal fluctuations

Basile Pottier, Allan Raudsepp, Christian Frétigny, François Lequeux, Jean-François Palierne, and Laurence Talini

J. Rheol. 57, 441 (2013); http://dx.doi.org/10.1122/1.4776745 (15 pages)

Online Publication Date: 16 Jan 13

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We characterize the linear viscoelastic properties of complex fluids using a new technique, based on the measurement of surface fluctuations: surface fluctuation specular reflection (SFSR) spectroscopy. The thermally excited waves propagating on a free surface are measured through the deflection of a laser beam specularly reflected from that surface. Elastic and loss moduli of the complex fluids are inferred from the measured power spectrum density of thermal noise, with the implicit use of Kramers–Kronig relations. The technique, besides being noninvasive, provides rheological data in a large frequency range and at vanishing strains. It is therefore especially well suited for the rheological characterization of complex fluids. We present measurements of the viscoelastic modulus of supramolecular polymer solutions in a frequency range extending up to six decades. We compare the SFSR measurements with rheometric data at low and high frequencies, and show that they are in good agreement. Using supramolecular polymer solutions of different natures, exhibiting or not surface viscoelasticity, we furthermore show that SFSR provides a characterization of the bulk properties of the fluids. In addition, we discuss the accuracy of the measurements.
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62.10.+s Mechanical properties of liquids
61.25.he Polymer solutions
66.20.Ej Studies of viscosity and rheological properties of specific liquids
47.57.Ng Polymers and polymer solutions

Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology

R. N. Zia and J. F. Brady

J. Rheol. 57, 457 (2013); http://dx.doi.org/10.1122/1.4775349 (36 pages)

Online Publication Date: 17 Jan 13

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The motion of a single Brownian particle in a complex fluid can reveal material behavior both at and away from equilibrium. In active microrheology, a probe particle is driven by an external force through a complex medium and its motion studied in order to infer properties of the embedding material. Most work in microrheology has focused on steady behavior and established the relationship between the motion of the probe, the microstructure, and the effective microviscosity of the medium. Transient behavior in the near-equilibrium, linear-response regime has also been studied via its connection to low-amplitude oscillatory probe forcing and the complex modulus; at very weak forcing, the microstructural response that drives viscosity is indistinguishable from equilibrium fluctuations. But important information about the basic physical aspects of structural development and relaxation in a medium is captured by startup and cessation of the imposed deformation in the nonlinear regime, where the structure is driven far from equilibrium. Here, we study theoretically and by dynamic simulation the transient behavior of a colloidal dispersion undergoing nonlinear microrheological forcing. The strength with which the probe is forced, Fext, compared to thermal forces, kT/b, governs the dynamics and defines a Péclet number, Pe = Fext/(kT/b), where kT is the thermal energy and b is the colloidal bath particle size. For large Pe, a boundary layer (in which unsteady advection balances diffusion) forms at particle contact on the time scale of the flow, a/U, where a is the probe size and U its speed, whereas the wake forms over O(Pe) diffusive time steps. Similarly, relaxation following cessation occurs over several time scales corresponding to distinct physical processes. For very short times, the time scale for relaxation is set by a boundary layer of thickness δ ∼ (a+b)/Pe, and so τ ∼ δ2/Dr, where Dr is the relative diffusivity between the probe of size a and a bath particle. Nearly all stress relaxation occurs during this time. At longer times, the Brownian diffusion of the bath particles acts to close the wake on a time scale set by how long it takes a bath particle to diffuse laterally across it, τ ∼ (a+b)2/Dr. Although the majority of the microstructural relaxation occurs during this wake-healing process, it does so with little change in the stress. Also during relaxation, the probe travels backward in the suspension; this recovered strain is proportional to the free energy stored in the compressed particle configuration, an indicator that the stress is proportional to the free energy density stored entropically in the microstructure. Theoretical results are compared with Brownian dynamics simulation where it is found that the dilute theory captures the correct behavior even for concentrated suspensions. Two modes of forcing are studied: Constant force and constant velocity. Results are compared to analogous macrorheology results for suspensions undergoing simple shear flow.
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82.70.Dd Colloids
82.70.Kj Emulsions and suspensions
83.10.Mj Molecular dynamics, Brownian dynamics
66.20.Cy Theory and modeling of viscosity and rheological properties, including computer simulation
47.57.Qk Rheological aspects
62.10.+s Mechanical properties of liquids

Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices

Shao-Cong Dai, Erwan Bertevas, Fuzhong Qi, and Roger I. Tanner

J. Rheol. 57, 493 (2013); http://dx.doi.org/10.1122/1.4774325 (18 pages) | Cited 1 time

Online Publication Date: 23 Jan 13

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We present the results of measuring the three viscometric functions [the relative viscosity ηr, and the first (N1) and second (N2) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of ηr and N1−N2 were made with a parallel-plate rheometer, while we used the open semicircular trough method to give N2 directly. With the trough method measurements of N2 could be made down to a 10% concentration (φ = 0.1); measurements were continued up to 45% concentration. The trough surface shows visually that N2 is directly proportional to the shear stress τ, and the measurements of N2 agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for N1 show greater scatter. In the range 0.1 ≤ φ ≤ 0.45, our best estimate of N2/τ is −4.4φ3 and that of N1/τ is −0.8φ3. Hence, the magnitude of N2 is much greater than that of N1. Measurement uncertainties are given in the text—they depend on φ. We have also compared the new experiments with two sets of numerical simulations. There is considerable divergence, which remains to be explained, between some of the simulations and the experiments. However, agreement between experiment and some of the simulations of Bertevas et al. [Rheol. Acta 49, 53–73 (2010)] is reasonable.
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66.20.Cy Theory and modeling of viscosity and rheological properties, including computer simulation
62.10.+s Mechanical properties of liquids
68.03.Cd Surface tension and related phenomena
82.70.Kj Emulsions and suspensions

Role of linear viscoelasticity and rotational diffusivity on the collective behavior of active particles

Yaser Bozorgi and Patrick T. Underhill

J. Rheol. 57, 511 (2013); http://dx.doi.org/10.1122/1.4778578 (23 pages)

Online Publication Date: 23 Jan 13

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A linear dynamics scheme has been used to quantify the impact of viscoelasticity of the suspending fluid on the collective structure of active particles, including rotational diffusivity. The linear stability examines the response near an isotropic state using a mean-field theory including far-field hydrodynamic interactions of the swimmers. The kinetic model uses three possible constitutive models, the Oldroyd-B, Maxwell, and generalized linear viscoelastic models inspired by fluids like saliva, mucus, and biological gels. The perturbation growth rate has been quantified in terms of wavenumber, translational diffusivity, rotational diffusivity, and material properties of the fluids. A key dimensionless group is the Deborah number, which compares the relaxation time of the fluid with the characteristic timescale of the instability. An advantage of the model formalism is the ability to calculate some properties analytically and others efficiently numerically in the presence of rotational diffusion. The different constitutive equations examined help illustrate when and why the dispersion relation can have a peak at a particular wavenumber. The fluid properties can also change the role of rotational diffusion; diffusion always stabilizes a system in a Newtonian fluid but can destabilize a system in a Maxwell fluid.
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83.60.Bc Linear viscoelasticity
83.60.Wc Flow instabilities
66.10.C- Diffusion and thermal diffusion
66.20.Cy Theory and modeling of viscosity and rheological properties, including computer simulation

Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions

Marat Andreev, Renat N. Khaliullin, Rudi J. A. Steenbakkers, and Jay D. Schieber

J. Rheol. 57, 535 (2013); http://dx.doi.org/10.1122/1.4788909 (23 pages)

Online Publication Date: 31 Jan 13

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The discrete slip-link model (DSM) was developed to describe the dynamics of flexible polymer melts. The model is able to predict linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. The model also shows good agreement with dielectric relaxation experiments, except for the single data set available for bidisperse linear systems with a small volume fraction of long chains. In this work, both shear and elongational flow predictions obtained using the DSM without parameter adjustment are shown. Model predictions for shear flow agree very well with experimental results. The DSM is able to capture the transient response as well as the steady-state viscosity. However, for elongational flow, agreement is unsatisfactory at large strains. The DSM captures the onset of strain hardening, but after a Hencky strain between 2 and 3, it predicts transient strain softening, whereas experiments show only monotonic growth. We explore a number of assumptions and approximations of the model and their effect on flow predictions. The approximations are related to the neglect of these phenomena, which are expected to be more sensitive in elongational flow: finite extensibility, convective constraint release, and deformation of dangling ends. We indeed find that shear flow predictions are insensitive to these approximations, but elongational flow is affected. However, none of these effects is able to bring prediction in line with experiments. We conclude that the currently accepted view of entanglement dynamics is incomplete.
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47.57.Ng Polymers and polymer solutions
47.57.Qk Rheological aspects
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics
47.45.Gx Slip flows and accommodation
47.50.Cd Modeling

Necking in extrusion film casting: The role of macromolecular architecture

Harshawardhan V. Pol, Sumeet S. Thete, Pankaj Doshi, and Ashish K. Lele

J. Rheol. 57, 559 (2013); http://dx.doi.org/10.1122/1.4788911 (25 pages)

Online Publication Date: 01 Feb 13

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Extrusion film casting (EFC) is used on an industrial scale to produce several thousand tons of polymer films and coatings. While significant research has been carried out on necking of films of viscoelastic melts in EFC, the influence of macromolecular chain architecture on the necking behavior is not yet fully understood. In the present research, we have explored experimentally and theoretically the effects of long chain branching and molecular weight distribution on the extent of necking during EFC. Polyethylenes of essentially linear architecture but having narrow and broad molecular weight distributions, and polyethylenes having long chain branching were used for experimental studies. The EFC process was analyzed using the one-dimensional flow model of Silagy et al. [Polym. Eng. Sci. 36(21), 2614–2625 (1996)] in which multimode molecular constitutive equations namely the “extended pom-pom” equation (for long chain branched polymer melts) and the “Rolie–Poly (Rouse linear entangled polymers)” equation (for linear polymer melts) were incorporated. We show that the model qualitatively captures the salient features of the experimental data thereby elucidating the role of chain architecture on the extent of necking.
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62.10.+s Mechanical properties of liquids
68.15.+e Liquid thin films
81.05.Lg Polymers and plastics; rubber; synthetic and natural fibers; organometallic and organic materials
81.10.Fq Growth from melts; zone melting and refining
61.25.hk Polymer melts and blends
47.57.Ng Polymers and polymer solutions

Dissipative particle dynamics modeling of low Reynolds number incompressible flows

N. Mai-Duy, D. Pan, N. Phan-Thien, and B. C. Khoo

J. Rheol. 57, 585 (2013); http://dx.doi.org/10.1122/1.4789444 (20 pages)

Online Publication Date: 01 Feb 13

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This paper is concerned with the numerical modeling of a slow (creeping) flow using a particle-based simulation technique, known as dissipative particle dynamics (DPD), in which the particles' mass is allowed to approach zero to simultaneously achieve a high sonic speed, a low Reynolds number, and a high Schmidt number. This leads to a system of stiff stochastic differential equations, which are solved efficiently by an exponential time differencing (ETD) scheme. The ETD-DPD method is first tested in viscometric flows, where the particle mass is reduced down to 0.001. The method is then applied for the modeling of rigid spheres in a Newtonian fluid by means of two species of DPD particles, one representing the solvent particles and the other, the suspended particle. Calculations are carried out at particle mass of 0.01, with corresponding Mach number of 0.08, Reynolds number of 0.05, and Schmidt number of 6.0×103. Stokes results are used to determine the DPD parameters for the solvent-sphere interaction forces. The method obeys equipartition and yields smooth flows around the sphere with quite uniform far-field velocities.
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47.15.G- Low-Reynolds-number (creeping) flows

Uniaxial extensional rheology of well-characterized comb polymers

H. Lentzakis, D. Vlassopoulos, D. J. Read, H. Lee, T. Chang, P. Driva, and N. Hadjichristidis

J. Rheol. 57, 605 (2013); http://dx.doi.org/10.1122/1.4789443 (21 pages)

Online Publication Date: 04 Feb 13

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We present a detailed systematic investigation of the transient uniaxial extensional response of a series of well-characterized, anionically synthesized comb polystyrenes and polyisoprenes. The comb architecture consists of a linear chain backbone with multiple branches of equal molar mass, and represents an excellent model branched polymer. The linear viscoelastic response has been studied already in great detail. Our results indicate that the strain hardening becomes more important as the Hencky strain rate is increased. In general, the larger the number of entanglements of the segments between branches and/or of the branches, the stronger the strain hardening and the smaller the characteristic rate for its onset. The key molecular parameter appears to be the number of entanglements per branch. By varying it, one can tailor the amount and onset of strain hardening. This can be rationalized by accounting for the combined effect of backbone tube dilation and extra friction, brought about by the branches. In fact, we define an effective “stretch time” of the comb as the timescale for stretch relaxation along the dilated backbone tube when accounting for the large friction that comes from the branches and suggest that extension hardening occurs at rates equal to or greater than its inverse. The good comparison of this prediction to experimental data is a promising guide toward a universal framework for understanding the effects of branches on extensional rheology, and hence providing some insight into the behavior of long-chain branched polyolefins.
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81.40.Jj Elasticity and anelasticity, stress-strain relations
61.41.+e Polymers, elastomers, and plastics
62.20.Qp Friction, tribology, and hardness
81.40.Ef Cold working, work hardening; annealing, post-deformation annealing, quenching, tempering recovery, and crystallization
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances
81.40.Pq Friction, lubrication, and wear

Apparent elongational yield stress of soft matter

L. Martinie, H. Buggisch, and N. Willenbacher

J. Rheol. 57, 627 (2013); http://dx.doi.org/10.1122/1.4789785 (20 pages)

Online Publication Date: 04 Feb 13

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Apparent elongational yield stresses of soft matter including polymer gels, highly concentrated emulsions, and aggregated suspensions have been determined from step stretch experiments. Materials display apparent shear yield stresses in the range 1–100 Pa and large but finite shear relaxation times tR. For all investigated fluids, the Laplace pressure within the stretched filaments is essentially constant during an initial period of time after the step strain. Then, it increases rapidly and finally the filaments break. Filament lifetime tf strongly increases with decreasing stretching ratio ε. The apparent elongational yield stress is identified as the initial value of the Laplace pressure obtained at a critical stretching ratio εc corresponding to a Deborah number De = tR/tf = 1. For all fluids, the ratio of this elongational yield stress to shear yield stress is math in agreement with the von Mises plasticity criterion, irrespective of the physical nature of structural breakdown. Elongational experiments performed at different ε or tf covering Deborah numbers between 0.1 and 100 reveal a universal relationship between the initial plateau value of the Laplace pressure normalized to the shear yield stress and De. This stress ratio varies between 0.5 and 5, and equals math only for De ≈ 1.
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82.70.Gg Gels and sols
82.70.Kj Emulsions and suspensions
62.10.+s Mechanical properties of liquids
61.25.H- Macromolecular and polymers solutions; polymer melts

Fixed-point iteration for relaxation spectrum from dynamic mechanical data

Kwang Soo Cho and Gun Woo Park

J. Rheol. 57, 647 (2013); http://dx.doi.org/10.1122/1.4789786 (32 pages)

Online Publication Date: 04 Feb 13

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An algorithm was developed for the continuous spectrum of linear viscoelasticity. The algorithm is free from the possibility of negative relaxation intensity whereas most previous algorithms suffer from the problem. The algorithm is not only simpler than the nonlinear regularization of Honerkamp and Weese [Rheol. Acta 32, 65–73 (1993)] but is also as accurate as the nonlinear regularization. The basic concept of the algorithm is to use a fixed-point iteration, which transforms the initial spectrum to a new one that is closer to the least-square solution. The iteration algorithm regularizes the errors in data in a different manner of conventional regularization.
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83.60.Bc Linear viscoelasticity
02.60.-x Numerical approximation and analysis
02.70.Rr General statistical methods

Power series approximations of dynamic moduli and relaxation spectrum

Kwang Soo Cho

J. Rheol. 57, 679 (2013); http://dx.doi.org/10.1122/1.4789787 (19 pages)

Online Publication Date: 04 Feb 13

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We suggest a new algorithm for relaxation time spectrum, which is based on the power series approximation of dynamic modulus and relaxation time spectrum. Through the regression of dynamic modulus as a polynomial of the logarithm of frequency, the method converts the coefficients of the modulus to those of relaxation time spectrum. The algorithm provides relaxation time spectrum as stable as regularization method.
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81.40.Jj Elasticity and anelasticity, stress-strain relations
62.20.de Elastic moduli
62.40.+i Anelasticity, internal friction, stress relaxation, and mechanical resonances

Viscoelastic characterization of wood: Time dependence of the orthotropic compliance in tension and compression

Tomasz Ozyhar, Stefan Hering, and Peter Niemz

J. Rheol. 57, 699 (2013); http://dx.doi.org/10.1122/1.4790170 (19 pages)

Online Publication Date: 06 Feb 13

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This study is concerned with the viscoelastic behavior of wood. The time dependency of the orthotropic compliance for beech wood is investigated by performing tensile (Te) and compressive (Co) creep experiments in all wood's orthotropic directions. Time evolution of the creep strain in the axial and lateral directions is recorded using the digital image correlation technique, to determine the time dependent Young's moduli and the Poisson's ratios needed for the calculation of the diagonal and nondiagonal elements of the viscoelastic compliance matrix. The results of this study demonstrate the viscoelastic character of wood, revealing the significant time influence on the mechanical behavior. The unequal time dependency of the Young's moduli and the Poisson's ratios obtained for the individual directions highlights the orthotropic nature of the viscoelastic compliance. Differences between the time dependent behavior for the compliance determined in Te and Co further indicate that the viscoelastic behavior of wood depends on the loading modality. Supported by the unequal evolution of the Te and Co creep strain, the results suggest that the time dependent stress–strain relationship of wood is essentially different in Te and Co. Poisson's ratio values, which are shown to increase with time in Te and decrease in Co, demonstrated this fact. The substantially different time dependency of the nondiagonal elements of the compliance matrix further emphasizes the complexity of the viscoelastic character of wood. Visualized by the time evolution of the corresponding nondiagonal elements ratio, differences between the Te and Co viscoelastic behavior become particularly visible in the time dependency of the orthotropic compliance asymmetry.
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89.20.Kk Engineering
62.20.Hg Creep
81.40.Jj Elasticity and anelasticity, stress-strain relations
81.40.Lm Deformation, plasticity, and creep
81.70.Bt Mechanical testing, impact tests, static and dynamic loads
83.60.Bc Linear viscoelasticity
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