Anisotropic Viscoelasticity Research Articles

Evaluation of Anisotropic Viscoelasticity by Indentation Test

Evaluation of Anisotropic Viscoelasticity by Indentation Test

Rock-physics models for heterogeneous creeping rocks and viscous fluids

Rock-physics models are used to explore how small-scale heterogeneity can affect the larger scale viscoelasticity of rocks. Applications include mixtures of creeping clay and elastic quartz, mixtures of different creeping materials (e.g., clay and kerogen), or viscous fluids containing bubbles or solid fines. We have found that elastic inclusions in a Maxwell viscoelastic background change the effective viscosity and the high-frequency limiting elastic modulus. The viscosity response was similar to that observed for a Newtonian fluid, and the high-frequency elastic modulus varied as predicted by elastic effective media models. The characteristic frequency of the effective medium scales with the ratio of effective modulus and effective viscosity. Inclusions also distribute the relaxation times, converting the Maxwell material to resemble a Cole-Cole material. Elastic inclusions in a creeping background decrease the effective viscoelastic Poisson’s ratio of the composite. As with elastic media, geometric alignment of phases with contrasting properties leads to viscoelastic anisotropy. Our modeling has illustrated how the amount of heterogeneity and the microgeometry of heterogeneity affects anisotropy; for example, aligned oblate elastic inclusions can increase the amount of creep in the symmetry direction while decreasing creep normal to the symmetry direction. We have developed a suggested interpretation template for how creep function parameters vary with the amount and microgeometry of elastic phases. Interpretation also depends strongly on the material properties of the creeping phase in the absence of elastic inclusions. Extrapolating from dynamic to quasi-static viscoelastic response is intrinsically nonunique without knowledge of the material microstructure. Dominant relaxation mechanisms can be different at different measurement scales and at different measurement strain amplitudes. For example, the observed dynamic response can be fit with an infinite number of microgeometries, each of which has a different long-term behavior.

A Three-Dimensional Boundary Element Approach for Transient Anisotropic Viscoelastic Problems

This paper presents a three-dimensional direct boundary element approach for solving transient problems of linear anisotropic elasticity and viscoelasticity. In order to take advantage of the correspondence principle between viscoelasticity and elasticity the formulation is given in the Laplace domain. Anisotropic viscoelastic fundamental solutions are obtained using the correspondence principle and anisotropic elastic Green’s functions. The standard linear solid model is used to represent the mechanical behavior of viscoelastic material. Solution in time domain is calculated via numerical inversion by modified Durbin’s method. Numerical example is provided to validate the proposed boundary element formulation.

Fully anisotropic finite strain viscoelasticity based on a reverse multiplicative decomposition and logarithmic strains

In this paper we present a novel formulation for phenomenological anisotropic finite visco-hyperelasticity. The formulation is based on a multiplicative decomposition of the equilibrated deformation gradient into nonequilibrated elastic and viscous contributions. The proposal in this paper is a decomposition reversed respect to that from Sidoroff allowing for anisotropic viscous contributions. Independent anisotropic stored energies are employed for equilibrated and non-equilibrated parts. The formulation uses logarithmic strain measures in order to be teamed with spline-based hyperelasticity. Some examples compare the results with formulations that use the Sidoroff decomposition and also show the enhanced capabilities of the present model.

The spectral theory of anisotropic linear viscoelasticity of polymers

The spectral theory of anisotropic linear viscoelasticity of polymer liquids is developed on the basis of the spectral decomposition of the relaxation tensor, which characterizes their anisotropic rheological properties. A definition of fading memory for anisotropic liquids is given. The oscillating shear and tension flows of liquids with uniaxial anisotropy are considered. The dependence of their dynamic characteristics on the direction is studied.

Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

In this paper a purely phenomenological formulation and finite element numerical implementation for quasi-incompressible transversely isotropic and orthotropic materials is presented. The stored en...

Non-linear material modeling of fiber-reinforced polymers based on coupled viscoelasticity–viscoplasticity with anisotropic continuous damage mechanics

A meso-scale material modeling of the fiber-reinforced polymer composites is presented. This model is based on coupled anisotropic viscoelasticity–viscoplasticity with anisotropic continuous damage mechanics. The constitutive equations are derived for three-dimensional statement and integrated implicitly by using return-mapping algorithm. Viscoelasticity model implies time dependent material properties. Viscoplasticity model is based on modified Hoffman criterion with combination of the Perzyna model. Anisotropic damage model is based on extended three-dimensional damage model. Developed material model is implemented in ABAQUS/Standard and is applied for modeling glass and carbon fiber laminate composite plates with various stacking sequences. Obtained results are in high agreement with already published experimental data.

Determination of parameters of viscoelastic anisotropy from ray velocity and ray attenuation: Theory and numerical modeling

We have developed and numerically tested a method for determining parameters of homogeneous viscoelastic anisotropy from measurements of wavefields generated by point sources. The method is based on complex algebra and consists of several steps. First, a complex energy velocity surface is constructed from the directionally dependent velocity and attenuation measured along a set of ray directions. Second, a complex slowness surface is computed using the relation of polar reciprocity between the energy velocity and slowness vectors. The energy velocity vectors are homogeneous, but the corresponding slowness vectors are inhomogeneous. Finally, the complex phase velocity surface is calculated and inverted using the Christoffel equation. The inversion is nonlinear and can be performed in iterations. Numerical tests for the P-wave in transversely isotropic media showed that the method performed well for a wide range of models covering strong as well as weak velocity anisotropy and various levels of attenuation. The method was compared with a simplified approximate inversion when the inhomogeneity of the complex slowness vector is neglected. The neglect of the slowness vector inhomogeneity results in a significantly lower accuracy of the retrieved attenuation parameters. Accuracy with errors less than 10% is achieved only if the attenuation anisotropy is weak. This condition is, however, strongly restrictive because attenuation anisotropy is usually significant being more pronounced than the velocity anisotropy for most of rocks.

A review of basic to clinical studies of quantitative ultrasound of cortical bone

The use of quantitative ultrasound (QUS) for bone has increased sharply over the last two decades. QUS offers potential benefits over other diagnostic modalities which include (1) ex vivo non-destructive testing, (2) in vivo non-ionizing testing, and (3) the ability to assess important cortical bone quality factors which cannot easily be captured with X-ray techniques. These advantages have stimulated widespread interest in basic through clinical studies. For instance, resonant ultrasonic spectroscopy (RUS) has provided gains in ex vivo assessment of the anisotropic stiffness and viscoelasticity of bone despite strong damping. RUS is prone to provide answers to questions that remain open regarding the determinants of cortical bone elastic properties. In vivo QUS technologies using guided waves (GW) have the potential to reveal cortical bone strength-related factors such as the cortical thickness and porosity. These properties can be estimated by comparing the measured dispersion curves with an appropriate...

Viscoelasticity in Achilles tendonopathy: quantitative assessment by using real-time shear-wave elastography.

To investigate the differences in viscoelastic properties between normal and pathologic Achilles tendons (ATs) by using real-time shear-wave elastography (SWE). The institutional review board approved this study, and written informed consent was obtained from 25 symptomatic patients and 80 volunteers. One hundred eighty ultrasonographic (US) and SWE studies of ATs without tendonopathy and 30 studies of the middle portion of the AT in patients with tendonopathy were assessed prospectively. Each study included data sets acquired at B-mode US (tendon morphology and cross-sectional area) and SWE (axial and sagittal mean velocity and relative anisotropic coefficient) for two passively mobilized ankle positions. The presence of AT tears at B-mode US and signal-void areas at SWE were noted. Significantly lower mean velocity was shown in tendons with tendonopathy than in normal tendons in the relaxed position at axial SWE (P < .001) and in the stretched position at sagittal (P < .001) and axial (P = .0026) SWE. Tendon softening was a sign of tendonopathy in relaxed ATs when the mean velocity was less than or equal to 4.06 m · sec(-1) at axial SWE (sensitivity, 54.2%; 95% confidence interval [CI]: 32.8, 74.4; specificity, 91.5%; 95% CI: 86.3, 95.1) and less than or equal to 5.70 m · sec(-1) at sagittal SWE (sensitivity, 41.7%; 95% CI: 22.1, 63.3; specificity, 81.8%; 95% CI: 75.3, 87.2) and in stretched ATs, when the mean velocity was less than or equal to 4.86 m · sec(-1) at axial SWE (sensitivity, 66.7%; 95% CI: 44.7, 84.3; specificity, 75.6%; 95% CI: 68.5, 81.7) and less than or equal to 14.58 m · sec(-1) at sagittal SWE (sensitivity, 58.3%; 95% CI: 36.7, 77.9; specificity, 83.5%; 95% CI: 77.2, 88.7). Anisotropic results were not significantly different between normal and pathologic ATs. Six of six (100%) partial-thickness tears appeared as signal-void areas at SWE. Whether the AT was relaxed or stretched, SWE helped to confirm and quantify pathologic tendon softening in patients with tendonopathy in the midportion of the AT and did not reveal modifications of viscoelastic anisotropy in the tendon. Tendon softening assessed by using SWE appeared to be highly specific, but sensitivity was relatively low.

Detection and Localization of Delaminations in Thin Carbon Fiber Reinforced Composites with the Ultrasonic Polar Scan

In this paper, the hybrid compliance-stiffness matrix method for simulating wave propagation in (delaminated) multilayered media with viscoelastic anisotropy has been confronted with high-quality amplitude and phase experiments on delaminated composites, obtained using the ultrasonic polar scan setup (UPS) in transmission by considering harmonic as well as pulsed ultrasound. Results are presented for multiple thin carbon/epoxy laminates with an artificial edge delamination induced by a foil insert, showing a good agreement between experimental recording and numerical modeling. The obtained results further reveal the feasibility of the harmonic UPS to detect and even locate the depth-position of multiple delaminations in fiber reinforced composites. Considering that the harmonic UPS method does not rely on the detection of different echoes like the classical C-scan, but rather expounds the conditions for efficient stimulation of guided waves in the solid, the method is found to be highly suited for inspecting thin composite materials for the presence of delaminations.

Living liquid crystals

Collective motion of self-propelled organisms or synthetic particles, often termed "active fluid," has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here, we introduce a class of active matter--living liquid crystals (LLCs)--that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena, caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence-enabled visualization of microflow generated by the nanometers-thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.

Seismic Rheological Model and Reflection Coefficients of the Brittle–Ductile Transition

It is well established that the upper—cooler—part of the crust is brittle, while deeper zones present ductile behaviour. In some cases, this brittle–ductile transition is a single seismic reflector with an associated reflection coefficient. We first develop a stress–strain relation including the effects of crust anisotropy, seismic attenuation and ductility in which deformation takes place by shear plastic flow. Viscoelastic anisotropy is based on the eigenstrain model and the Zener and Burgers mechanical models are used to model the effects of seismic attenuation, velocity dispersion, and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. The P- and S-wave velocities decrease as depth and temperature increase due to the geothermal gradient, an effect which is more pronounced for shear waves. We then obtain the reflection and transmission coefficients of a single brittle–ductile interface and of a ductile thin layer. The PP scattering coefficient has a Brewster angle (a sign change) in both cases, and there is substantial PS conversion at intermediate angles. The PP coefficient is sensitive to the layer thickness, unlike the SS coefficient. Thick layers have a well-defined Brewster angle and show higher reflection amplitudes. Finally, we compute synthetic seismograms in a homogeneous medium as a function of temperature.

Interface corners in linear anisotropic viscoelastic materials

In this study, an extended Stroh formalism for two-dimensional linear anisotropic viscoelasticity is developed for the problems of interface corners between two dissimilar viscoelastic materials. In this formalism, the solutions for the displacements and stress functions in the time domain can be written in the form of a matrix function using complex variables. The correspondence relations for viscoelastic analysis are then obtained and verified for material eigenvectors, displacement and stress eigenfunctions, singularity orders of stresses, and stress intensity factors. Explicit solutions for the material eigenvector matrices in the Laplace domain are also obtained for standard linear and isotropic linear viscoelastic solids. To calculate the singularity orders and stress intensity factors of the interface corners, four different approaches are proposed. Through numerical examples on cracks, interface cracks, and interface corners, an approach using the path-independent H-integral in the Laplace domain with an elastic near-tip solution, which takes the correspondence relations for singularity orders and stress intensity factors, is demonstrated to be better than the other three approaches.

A numerical analytic method for solving boundary-value problems of linear anisotropic viscoelasticity

The paper proposes an approach to solving boundary-value problems for linear viscoelastic orthotropic bodies based on the method of operator continued fractions and the boundary-element method. A problem-solving algorithm and a procedure to estimate the possible error are outlined. The solution for a viscoelastic orthotropic plate with a rigid circular inclusion under uniaxial tension is obtained as an example and compared with available ones

Cones of material response functions in one-dimensional and anisotropic linear viscoelasticity

Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. These conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspondence between the viscoelastic response functions is expressed in terms of cone-preserving mappings and their inverses. The theory covers scalar- and tensor-valued viscoelastic response functions.

OS1003 傷害予測のための異方損傷と粘弾性を考慮した皮質骨構成式の定式化(生体と材料力学,オーガナイズドセッション)

OS1003 傷害予測のための異方損傷と粘弾性を考慮した皮質骨構成式の定式化(生体と材料力学,オーガナイズドセッション)

On modelling of anisotropic viscoelasticity for soft tissue simulation: Numerical solution and GPU execution

Efficient and accurate techniques for simulation of soft tissue deformation are an increasingly valuable tool in many areas of medical image computing, such as biomechanically-driven image registration and interactive surgical simulation. For reasons of efficiency most analyses are based on simplified linear formulations, and previously almost all have ignored well established features of tissue mechanical response such as anisotropy and time-dependence. We address these latter issues by firstly presenting a generalised anisotropic viscoelastic constitutive framework for soft tissues, particular cases of which have previously been used to model a wide range of tissues. We then develop an efficient solution procedure for the accompanying viscoelastic hereditary integrals which allows use of such models in explicit dynamic finite element algorithms. We show that the procedure allows incorporation of both anisotropy and viscoelasticity for as little as 5.1% additional cost compared with the usual isotropic elastic models. Finally we describe the implementation of a new GPU-based finite element scheme for soft tissue simulation using the CUDA API. Even with the inclusion of more elaborate constitutive models as described the new implementation affords speed improvements compared with our recent graphics API-based implementation, and compared with CPU execution a speed up of 56.3 x is achieved. The validity of the viscoelastic solution procedure and performance of the GPU implementation are demonstrated with a series of numerical examples.

Real ray tracing in anisotropic viscoelastic media

Ray tracing equations applicable to smoothly inhomogeneous anisotropic viscoelastic media are derived. The equations produce real rays, in contrast to previous ray-theoretical approaches, which deal with complex rays. The real rays are defined as the solutions of the Hamilton equations, with the Hamiltonian modified for viscoelastic media, and physically correspond to trajectories of high-frequency waves characterized by a real stationary phase. As a consequence, the complex eikonal equation is satisfied only approximately. The ray tracing equations are valid for weakly and moderately attenuating media. The rays are frequency-dependent and must be calculated for each frequency, separately. Solving the ray tracing equations in viscoelastic anisotropy is more time consuming than in elastic anisotropy. The main difficulty is with determining the stationary slowness vector, which is generally complex-valued and inhomogeneous and must be computed at each time step of the ray tracing procedure. In viscoelastic isotropy, the ray tracing equations considerably simplify, because the stationary slowness vector is homogeneous. The computational time for tracing rays in isotropic elastic and viscoelastic media is the same. Using numerical examples, it is shown that ray fields in weakly attenuating media (Q higher than about 30) are almost indistinguishable from those in elastic media. For moderately attenuating anisotropic media (Q between 5–20), the differences in ray fields can be visible and significant.

A MICROMECHANICALLY MOTIVATED MODEL FOR THE ANISOTROPIC VISCOELASTICITY OF SOFT TISSUES

Soft biological tissues are in general characterised by time dependent and in particular viscoelastic properties. This becomes apparent in mechanical testing where these materials reveal e.g. stress relaxation when stretched to a constant level and rate dependent hysteresis in cyclic loading. These characteristics depend considerably on the direction of loading and are thus of an anisotropic nature. In order to take this anisotropic viscoelasticity into account in constitutive modelling, we propose a micromechanically motivated approach. This is based on the assumption that the viscoelastic properties are the result of an interaction between the collagen fibres and the surrounding matrix constituents. Accordingly, fibres and the nearby ground substance are regarded as a structural unit with nonlinear viscoelastic properties. The constitutive equations describing the viscoelastic behaviour are based on the multiplicative decomposition of the stretch in fibre direction into an elastic and a viscous part. Therefore, the model is able to account for finite deformations. Anisotropy is included by a non-uniform spatial distribution of the fibre-matrix units. The model is applied and compared to recent experimental data from cyclic loading and relaxation tests on different tissues.