Acoustic viscoelastic modeling by frequency-domain boundary element method

Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green＇s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.

Finite-difference modeling of Maxwell viscoelastic media developed from perfectly matched layer

In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.However,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in FDTD.To incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation costs.By modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the parameters.The proposed viscoelastic model is essentially equivalent to a Maxwell model.Compared with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much easier.The attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than 10.The numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity.

Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal environment.Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions.The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints.The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly.The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment.Considering the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping ratio.The effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

Travel time prediction with viscoelastic traffic model

Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.

EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION

This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system.

Prediction of Viscoelastic Behavior of Unidirectional Polymer Matrix Composites

To develop a novel method predicting the viscoelastic behavior of polymer matrix composites according to the viscoelasticity of the matrix, we used the viscoelastic model of the matrix to build new models for unidirectional composites in both 0° and 90° directions. Viscoelastic parameters for both new models were derived, and the obtained equations shared the same form as the viscoelastic constitutive equation of matrix material. The viscoelastic behaviors of matrix material and unidirectional composites were also tested. Results showed that fitting parameters of creep compliance equation were close to the theoretical values of viscoelastic constitutive parameters of the unidirectional composites, proving the validity of the models. A new method was obtained to predict the viscoelastic property of the unidirectional composites based on the viscoelastic property of composite matrix and elastic property of the unidirectional composites. This method provides a theoretical basis for future studies on the viscoelasticity of composite laminates.

Stability condition of finite difference solution for viscoelastic wave equations

The stability problem is a very important aspect in seismic wave numerical modeling. Based on the theory of seismic waves and constitutive equations of viscoelastic models, the stability problems of finite difference scheme for Kelvin- Voigt and Maxwell models with rectangular grids are analyzed. Expressions of stability conditions with arbitrary spatial accuracies for two viscoelastic models are derived. With approximation of quality factor Q≥5, simplified expressions are developed and some numerical models are given to verify the validity of the corresponding theoretical results. Then this paper summarizes the influences of seismic wave velocity, frequency, size of grid and difference coefficients, as well as quality factor on stability condition. Finally the prerequisite conditions of the simplified stability equations are given with error analysis.

Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation

The interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the theological characteristics of ground soil. Compared with conventional linear theology, the fractional calculus-based theory is a more powerful mathematical tool that can address this issue. This paper proposes a fractional Merchant model （FMM） to investigate the time-dependent behavior of a simply supported rectangular plate on viscoelastic foundation. The correspondence principle involving Laplace transforms was employed to derive the closed-form solutions of plate response under uniformly distributed load. The plate deflection, bending moment, and foundation reaction calculated using the FMM were compared with the results obtained from the analogous elastic model （EM） and the standard Merchant model （SMM）. It is shown that the upper and lower bound solutions of the FMM can be determined using the EM. In addition, a parametric study was performed to examine the influences of the model parameters on the time- dependent behavior of the plate-foundation interaction problem. The results indicate that a small fractional differential order corresponds to a plate resting on a sandy soil foundation, while the fractional differential order value should be increased for a clayey soil foundation. The long-term performance of a foundation plate can be accurately simulated by varying the values of the fractional differential order and the viscosity coefficient. The observations from this study reveal that the proposed fractional model has the capability to capture the variation of plate deflection over many decades of time.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and th

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

NONLINEAR RANDOM STABILITY OF VISCOELASTIC CABLE WITH SMALL CURVATURE

The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.

ON THE CALCULATION OF ENERGY RELEASE RATE FOR VISCOELASTIC CRACKED LAMINATES

The energy release rate(ERR) of crack growth as the energy change at the same time t between the two states of the structure is redefined, one is with crack length a under the loading σ(t), the other is the state with crack length a+ Δ a under the same loading condition. Thus the defined energy release rate corresponds to the released energy when a crack grows from a to a+ Δ a in an infinitesimal time. It is found that under a given loading history, the ERR is a function of time, and its maximum value should correspond with the critical state for delamination to propagate. Following William’s work, the explicit expressions of ERR for DCB experimental configurations to measure the interfacial fracture toughness have been obtained through the classical beam assumption.

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale（SGS） model based on coherent structures and temporal approximate deconvolution（MCT） is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation（LES） of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence（FHIT） with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation（DNS） results. Compared with the LES results using the temporal approximate deconvolution model（TADM） for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.

Traffic flow sensitivity to visco-elasticity

This letter reports traffic flow sensitivity to visco-elasticity, with the traffic flow modeling briefly described at first and then used to do traffic flow simulations whose results can reflect the properties of spatial-temporal evolution of ring traffic flow. It reveals that visco-elasticity plays crucial role in formation of traffic flow patterns, implying that self-organization of traffic flow is crucial in determining traffic flow status.

ANALYSIS MODEL ON GRADUAL CHANGE PRINCIPLE OF EFFECT ZONES OF LAYER FACE FOR ROLLED CONTROL CONCRETE DAM

The effect zones of layer face for RCC （rolled control concrete） dam have gradual change characteristics. Based on the analysis thought of complex material, a model was built to analyze above principle of RCC dam by use of series-wound and shunt-wound connection. Some methods were proposed to determine the instantaneous Young＇s modulus, delayed Young＇s modulus and viscosity coefficient of effect zones of layer face. Above models and methods were used to mine the principle of gradual change of key calculation parameters which can response the characteristics of effect zones. The principle of gradual change was described. A model was established to analyze the threedimensional viscoelastic problem of RCC dam. Above programs were developed. The examples show that the proposed models and methods to determine the key calculation parameters of effect zones can reflect the status of RCC dam accurately.

Temperature Dependency of Dynamic Mechanical Properties of Cement Asphalt Paste by DMTA Method

We investigated the temperature dependency of the dynamic mechanical properties of cement asphalt paste by the dynamic mechanical thermal analysis（DMTA） method. The experimental results show that the dynamic mechanical properties of cement asphalt pastes are sensitive to temperature due to the inclusion of asphalt, and may go through different states within a temperature range of-40 ℃ to 60 ℃, which is different from that of pure cement and asphalt. As the temperature of the cement asphalt paste increases, a considerable change of dynamic mechanical properties, including storage modulus（E＇）, loss modulus（E＇＇） and loss factor（tand） is observed. Moreover, the influence of asphalt to cement（A/C） ratio on the temperature sensitivity of the dynamic mechanical properties of cement asphalt composites was investigated. The temperature dependency of cement asphalt composites is ascribed to the temperature dependency of the asphalt and its interaction with cement paste. A simple fractional model is proposed to describe the viscoelastic behavior of cement asphalt composites.

Rheology-based facial animation realistic face model

This paper presents a rheology-based approach to animate realistic face model. The dynamic and biorheological characteristics of the force member （muscles） and stressed member （face） are considered. The stressed face can be modeled as viscoelastic bodies with the Hooke bodies and Newton bodies connected in a composite series-parallel manner. Then, the stress-strain relationship is derived, and the constitutive equations established. Using these constitutive equations, the face model can be animated with the force generated by muscles. Experimental results show that this method can realistically simulate the mechanical properties and motion characteristics of human face, and performance of this method is satisfactory.

TRANSVERSAL INERTIAL EFFECT ON RELAXATION/RETARDATION TIME OF CEMENT MORTAR UNDER HARMONIC WAVE

Under dynamic loading, the constitutive relation of the cement mortar will be significantly affected by the transversal inertial effect of specimens with large diameters. In this paper, one-dimensional theoretical analysis is carried out to determine the transversal inertial effect on the relaxation/retardation time of the cement mortar under the harmonic wave. Relaxation time or retardation time is obtained by means of the wave velocity, attenuation coefficient and the frequency of the harmonic wave. Thus, the transversal inertial effect on the relaxation time from Maxwell model, as well as on retardation time from Voigt model is analyzed. The results show that the transversal inertial effect may lead to the increase of the relaxation time, but induce the decrease of the retardation time. Those should be taken into account when eliminating the transversal inertial effect in applications.

Mechanism on Moho offset induced by aseismic slip of deeply buried faults

Recent high-resolution deep seismic reflection profile across the Kunlun fault in northeastern Tibet shows clearly that the Moho is cut off by a complex thrust fault system. Moho offset is a general phenomenon, but little is known about the dynamic mechanism. In this study, contact models with Maxwell materials are used to simulate the mechanical process of Moho offset induced by the aseismic slip of deeply buried faults. Based on the seismic reflection data, we project a single fault model and a complex fault system model with two faults inter- secting. The deformations of the Moho, the aseismic slips, and contact stresses on faults in different models are discussed in detail. Results show that the Moho offset might be produced by aseismic slip of deeply buried faults, and the magnitude is influenced by the friction coefficient of faults and the viscosity of the lower crust. The maximum slip occurs near the Moho on the single fault or at the crossing point of two intersecting faults system. Stress concentrates mainly on the Moho, the deep end of faults, or the crossing point. This study will throw light on understanding the mechanism of Moho offset and aseismic slip of deeply buried faults. The results of complex fault system with two faults intersecting are also useful to understand the shallow intersecting faults that may cause earthquakes.

Workflow to numerically reproduce laboratory ultrasonic datasets

The risks and uncertainties related to the storage of high-level radioactive waste （HLRW） can be reducedthanks to focused studies and investigations. HLRWs are going to be placed in deep geological repositories,enveloped in an engineered bentonite barrier, whose physical conditions are subjected tochange throughout the lifespan of the infrastructure. Seismic tomography can be employed to monitor itsphysical state and integrity. The design of the seismic monitoring system can be optimized via conductingand analyzing numerical simulations of wave propagation in representative repository geometry.However, the quality of the numerical results relies on their initial calibration. The main aim of this paperis to provide a workflow to calibrate numerical tools employing laboratory ultrasonic datasets. The finitedifference code SOFI2D was employed to model ultrasonic waves propagating through a laboratorysample. Specifically, the input velocity model was calibrated to achieve a best match between experimentaland numerical ultrasonic traces. Likely due to the imperfections of the contact surfaces, theresultant velocities of P- and S-wave propagation tend to be noticeably lower than those a prioriassigned. Then, the calibrated model was employed to estimate the attenuation in a montmorillonitesample. The obtained low quality factors （Q） suggest that pronounced inelastic behavior of the clay has tobe taken into account in geophysical modeling and analysis. Consequently, this contribution should beconsidered as a first step towards the creation of a numerical tool to evaluate wave propagation innuclear waste repositories. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model

This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.