Continuum Microviscoelasticity Model for Aging Basic Creep of Early-Age Concrete

We propose a micromechanics model for aging basic creep of early-age concrete. Therefore, we formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste (composed of cement, water, hydrates, and air), and one related to concrete (composed of cement paste and aggregates). Homogenization of the “nonaging” elastic and viscoelastic properties of the material’s contituents involves the transformation of the aforementioned viscoelastic boundary value problems to the Laplace-Carson (LC) domain. There, formally elastic, classical self-consistent and Mori-Tanaka solutions are employed, leading to pointwisely defined LC-transformed tensorial creep and relaxation functions. Subsequently, the latter are back-transformed, by means of the Gaver-Wynn-Rho algorithm, into the time domain. Temporal derivatives of corresponding homogenized creep and relaxation tensors, evaluated for the current maturation state of the material (in terms of current volume fractions of cement, water, air, hydrates, and aggregates; being dependent on the hydration degree, as well as on the water-cement and aggregate-cement ratios) and for the current time period since loading of the hydrating composite material, allow for micromechanical prediction of the aging basic creep properties of early-age concrete.     

Time-Dependent Response of an Axially Loaded Elastic Bar in a Multilayered Poroelastic Medium

This paper considers load transfer from an axially loaded long elastic bar into a multilayered poroelastic half-space. The problem is analyzed by decomposing the bar-half-space system into an extended half-space governed by Biot’s theory of poroelasticity and a one-dimensional fictitious bar. The interaction problem is formulated in the Laplace transform domain. Vertical displacement of the bar is approximated by an exponential series with a set of arbitrary functions. The arbitrary functions are determined by using a variational method. The vertical displacement influence function of a multilayered half-space subjected to a buried uniform vertical patch load is required in the variational formulation. The required influence function is obtained by employing a previously developed exact stiffness matrix method. Time domain solutions are computed by using a numerical Laplace inversion scheme. Selected numerical results are presented to portray the influence of the bar length–radius ratio, layer configuration, poroelastic material parameters, and loading time history on the time dependent response of a bar.     

Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling

The linear viscoelastic properties of bituminous mixtures are used to design pavement structure. Usually, only complex moduli E* (complex Young modulus) or G* (complex shear modulus) characterizing the stiffness of the materials in one direction (1D) are measured by classical tests. In this paper, the three-dimensional (3D) behavior is investigated. The complex Poisson's ratio (ν*) is introduced. Its evolution with temperature and frequency is studied for a bitumen, a mastic, and a mix. Experimental results show that the time–temperature superposition principle is applicable in the 3D case. The same shift factor applies for E* and ν*. The Di Benedetto–Neifar model developed at Ecole Nationale des Travaux Publics de l’Etat to simulate so far the 1D thermo-elastoviscoplastic behavior of bituminous materials has been extended to simulate their 3D isotropic behavior. Calibration of the model and comparison between simulations in the linear viscoelastic domain and experimental data are proposed.     

Numerical Model for Time-Dependent Fracturing of Concrete

A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.     

Dynamic Response Solution in Transient State of Viscoelastic Road under Moving Load and Its Application

In order to study the dynamic response of an asphalt road, a dynamic model of the road under a moving load is proposed, in which the viscoelastic characteristics of the base and pavement are all considered, the pavement is regarded as an infinite beam on a Kelvin viscoelastic base. By using Green’s functions, Laplace transforms, and Fourier transforms, the analytical solution in transient is deduced. As the viscosity of the pavement is included in the model, the analytical solution can be used to investigate more of the factors that affect the dynamic response, such as vehicle speed, temperature, and road material properties. Using this analytical solution, some numerical calculations are given to illustrate the effects of vehicles’ speeds and different damping on the deflection with the displacement.     

Dynamic Viscoelastic Beam Model for Finite Element Method

A finite element formulation is presented for the viscoelastic dynamic responses of Euler‐Bernoulli beams. A time‐stepping procedure based on New‐mark's method is employed. The changes in creep strain during a time step are treated as additional fictitious body forces for the next time step. A uniaxial Norton‐type strain‐hardening material law is employed. The aims of the proposed formulation are model simplicity, efficiency of the solution procedure, and ease of application. Quasi‐static and dynamic viscoelastic responses for beams under quasi‐static and earthquake motion are obtained. The results are compared with existing alternate solutions to demonstrate the validity of the present work.     

On the Fundamental Solution of Dynamic Poroelastic Boundary Integral Equations in the Time Domain

In this article, boundary integral equations (BIE) and Laplace transform domain fundamental solutions to the u‐p formulation of two‐dimensional dynamic poroelasticity are derived. Time domain fundamental solutions have been derived based on the Cleary reciprocal theorem. A set of numerical results is presented to highlight the salient features of the transient fundamental solutions, their components, and accuracies of proposed approximations. Several comparisons with Chen’s solution are made.     

Field-Scale In-Situ Compliance of Arctic First-Year Sea Ice

This paper presents the experimental results and analysis of the creep recovery and cyclic loading crack-opening-displacement measurements recorded on level first-year sea ice at Barrow, Alaska. This was the third of a three-trip program to track the seasonal evolution of the mechanical and physical properties of first-year S2 sea ice. Seven large-scale in-situ experiments were completed covering a size range of 1:30 with the largest test having dimensions of 30 m × 30 m. The creep recovery response from the largest test specimen is examined in this paper to determine the compliance of a precracked square-plate test geometry via a nonlinear viscoelastic∕viscoplastic formulation. This model is then applied to the cyclic loading, and a monotonic ramp to fracture, to quantify its ability to predict the behavior for a variety of loading paths.     

Consolidation of a Finite Transversely Isotropic Soil Layer on a Rough Impervious Base

A semianalytical solution to axisymmetric consolidation of a transversely isotropic soil layer resting on a rough impervious base and subjected to a uniform circular pressure at the ground surface is presented. The analysis uses Biot’s fully coupled consolidation theory for a transversely isotropic soil. The general solutions for the governing consolidation equations are derived by applying the Hankel and Laplace transform techniques. These general solutions are then used to solve the corresponding boundary value problem for the consolidation of a transversely isotropic soil layer. Once solutions in the transformed domain have been found, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore-water pressure and fluid discharge can finally be obtained by direct numerical inversions of the integral transforms. The accuracy of the present numerical solutions is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Further, some numerical results are presented to show the influence of the nature of material anisotropy, the surface drainage condition, and the layer thickness on the consolidation settlement and the pore pressure dissipation.     

Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry

A magnetic bead microrheometer has been designed which allows the generation of forces up to 10(4) pN on 4.5 micron paramagnetic beads. It is applied to measure local viscoelastic properties of the surface of adhering fibroblasts. Creep response and relaxation curves evoked by tangential force pulses of 500-2500 pN (and approximately 1 s duration) on the magnetic beads fixed to the integrin receptors of the cell membrane are recorded by particle tracking. Linear three-phasic creep responses consisting of an elastic deflection, a stress relaxation, and a viscous flow are established. The viscoelastic response curves are analyzed in terms of a series arrangement of a dashpot and a Voigt body, which allows characterization of the viscoelastic behavior of the adhering cell surface in terms of three parameters: an effective elastic constant, a viscosity, and a relaxation time. The displacement field generated by the local tangential forces on the cell surface is visualized by observing the induced motion of assemblies of nonmagnetic colloidal probes fixed to the membrane. It is found that the displacement field decays rapidly with the distance from the magnetic bead. A cutoff radius of Rc approximately 7 micron of the screened elastic field is established. Partial penetration of the shear field into the cytoplasm is established by observing the induced deflection of intracellular compartments. The cell membrane was modeled as a thin elastic plate of shear modulus mu * coupled to a viscoelastic layer, which is fixed to a solid support on the opposite side; the former accounts for the membrane/actin cortex, and the latter for the contribution of the cytoskeleton to the deformation of the cell envelope. It is characterized by the coupling constant chi characterizing the elasticity of the cytoskeleton. The coupling constant chi and the surface shear modulus mu * are obtained from the measured displacements of the magnetic and nonmagnetic beads. By analyzing the experimental data in terms of this model a surface shear modulus of mu * approximately 2 . 10(-3) Pa m to 4 . 10(-3) Pa m is found. By assuming an approximate plate thickness of 0.1 micron one estimates an average bulk shear modulus of mu approximately (2 / 4) . 10(-4) Pa, which is in reasonable agreement with data obtained by atomic force microscopy. The viscosity of the dashpot is related to the apparent viscosity of the cytoplasm, which is obtained by assuming that the top membrane is coupled to the bottom (fixed) membrane by a viscous medium. By application of the theory of diffusion of membrane proteins in supported membranes we find a coefficient of friction of bc approximately 2 . 10(9) Pa s/m corresponding to a cytoplasmic viscosity of 2 . 10(3) Pa s.     

Parameter Identification Procedure for Heterogeneous Viscoelastic Composites Using Iterative Functions

This paper presents a new numerical procedure for the determination of the viscoelastic compliance properties of a matrix phase from a simple three-point bending test on a composite beam. The composite is modeled as elastic inclusions randomly dispersed throughout a viscoelastic matrix. It is also assumed that the spatial distribution of the inclusions in the composite is known or can be determined. Zevin’s method of iterative functions is proposed for the determination of the matrix properties. Following a detailed explanation of the proposed scheme, a numerical verification is performed using three-dimensional finite-element (FE) analysis simulations. The proposed scheme was applied to the experimentally obtained creep compliance of the asphalt concrete beam. The obtained viscoelastic properties of the asphalt binder matrix phase were used as input into the FE model to simulate the behavior of the composite beam. An excellent comparison between the experimental data and the predicted beam deflections was observed. This shows that the proposed method is robust and it can be implemented to solve identification problems for viscoelastic composite materials.     

Creep Behavior of Hot-Mix Asphalt due to Heavy Vehicular Tire Loading

The objective of this study is to characterize the creep behavior of hot-mix asphalt (HMA) at intermediate (20°C) and at high temperatures (40°C). To accomplish this objective, a nonlinear time-hardening creep model, characterized through laboratory testing, was incorporated into a three-dimensional (3D) finite-element (FE) model, which was used to calculate permanent creep strains after applying repetitive vehicular loading cycles at the pavement surface. Two different tire configurations were simulated representing a typical dual-tire assembly and a newly introduced wide-base tire (dual-tire: 275/80R22.5 and wide-base tire: 455/55R22.5). Results of the 3D FE model were successfully verified against pavement response measurements in the field at the Virginia Smart Road. While the elastic or linear viscoelastic FE model may not simulate permanent deformation or shear creep strains after repetitions of vehicular loading, a nonlinear time-hardening creep model could predict primary rutting damage in HMA and shear creep strains at the edge of the tire imprint caused by different tire configurations.     

Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4

Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Ba?ant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.     

The viscoelastic nature of chorioamniotic membranes

This study establishes the viscoelastic nature of the human chorioamniotic membrane. Membrane tissue taken from term pregnancies was placed in a state of biaxial stress consistent with the condition in which membranes rupture in normal healthy patients. The phenomena of creep, stress relaxation, elastic recovery, and time-dependent load deformation relations were demonstrated. The experiments needed to produce these phenomena are described. The results are graphically reported. The experiments were performed using samples of fetal membranes and compared to gum rubber which is a known elastic material. From the results, one can conclude that fetal membranes are viscoelastic. The flow freely under applied stress, and they have elastic and viscous properties which are time dependent.     

Full Two-Dimensional Model for Rolling Resistance: Hard Cylinder on Viscoelastic Foundation of Finite Thickness

A new full two-dimensional semianalytical method is developed to rigorously and efficiently solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic foundation of finite thickness. In this new method, the solution is expanded into a set of Fourier series, the master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special boundary element based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. A verification example is given to validate the methodology. Several numerical examples are given to study the influences of various factors on rolling resistance. The method as well as the conclusions drawn from the examples may be of interest to roller and belt-conveyor designers. This approach can be easily generalized to solve the general rolling contact problems of two viscoelastic bodies.     

基于虚拟材料复模量非均匀分布的螺栓连接薄板结构半解析建模

基于非均匀分布的虚拟材料模拟螺栓连接薄板搭接部分的力学特性,其中虚拟材料的材料参数用复模量表示,可直接生成复刚度矩阵以表示搭接部分的刚度及阻尼特性,省却了常规建模中生成结合部阻尼矩阵的步骤,在保证模型精确性的基础上简化了建模流程,以此建立了螺栓连接薄板结构的半解析模型并对其进行了动力学分析。首先描述了建模理念,将虚拟材料分别假定了三种复模量非均匀分布形式模拟螺栓搭接部分的力学特性,提出用反推辨识技术确定虚拟材料储能模量与耗能模量的方法。接着,基于能量法并用正交多项式假定模态,推导了螺栓连接薄板的半解析分析模型,并创新性地给出了求解半解析模型任意锤击点与拾振点处频响函数的公式。最后,以一个具体的螺栓连接薄板结构为对象进行了实例研究,结果表明:用所创建的半解析模型计算出的各阶仿真固有频率与实验测得的各阶固有频率的误差均在5%以内,计算得到的各阶仿真模态振型以及频响函数曲线与实测值均较为接近,从而证明了利用复模量非均匀分布的虚拟材料模拟螺栓搭接部分可有效简化螺栓结合部建模,亦可达到较高的仿真计算精度。      

PVA水凝胶在不同人体模拟液中的压缩蠕变行为

通过冷冻-解冻循环方法制备出聚乙烯醇（PVA）水凝胶人工髓核材料,研究了其在生理盐水和Hanks溶液两种模拟体液及去离子水中的压缩蠕变性能并进行了蠕变黏弹性模型分析.PVA水凝胶在不同模拟体液中都表现出良好的黏弹性能,达到蠕变平衡的快慢和应变量大小都与体液中的离子含量有关.等时线法的研究表明,水凝胶的力学行为符合线性黏弹性行为,选取的Kelvin-Voigt模型能够很好地模拟PVA水凝胶蠕变行为.拟合结果表明:体液中的一些盐离子抑制了水凝胶内部小尺寸单元的运动,蠕变平衡时间延长;体液中的Na+盐离子会促进水凝胶内部大尺寸单元的运动,使其快速达到蠕变平衡,满足临床医学使用要求.      

Full Two-Dimensional Model for Rolling Resistance. II: Viscoelastic Cylinders on Rigid Ground

Following the previous paper, “Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,” addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers.     

Multiple-Porosity Contaminant Transport by Finite-Element Method

An exponential finite-element model for multiple-porosity contaminant transport in soils is proposed. The model combines three compartments for dissolved contaminants: a primary compartment of diffusion–advection transport with nonequilibrium sorption, a secondary compartment with diffusion in rectangular or spherical soil blocks, and a tertiary compartment for immobile solutions within the primary compartment. Hence the finite-element model can be used to solve four types of mass-transfer problems which include: (1) intact soils, (2) intact soils with multiple sources of nonequilibrium partitioning, (3) soils with a network of regularly spaced fissures, and (4) structured soils. Hitherto, mobile/immobile compartments, fissured soils, and nonequilibrium sorption have been treated separately or in pairs. A Laplace transform is applied to the governing equations to remove the time derivative. A Galerkin residual statement is written and a finite-element method is developed. Both polynomial and exponential finite elements are implemented. The solution is inverted to the time domain numerically. The method is validated by comparison to analytical and boundary element predictions. Exponential elements perform particularly well, speeding up convergence significantly. The scope of the method is illustrated by analyzing contamination from a set of four waste repositories buried in fissured clay.     

Viscoelastic State for the Solutions of Spherically Symmetric Viscoelasticity Problems

The solutions of the spherically symmetric, linear, isothermal, and transient viscoelasticity problems via reciprocity theorem have been investigated for a specific material. The integral form of stress–strain relations has been used. The Laplace transform of a viscoelastic state, which is necessary for the integral equation arising as a result of reciprocity theorem, has been derived. This integral equation has been solved by Laplace transform. A sample problem has been solved to test the presented formulation. A numerical application of the analytic solution of this problem has been given.