Development of a viscoelastic continuum damage model for cyclic loading

A previously developed spectrum model for linear viscoelastic behavior of solids is used to describe the rate-dependent damage growth of a time dependent material under cyclic loading. Through the use of the iterative solution of a special Volterra integral equation, the cyclic strain history is described. The spectrum-based model is generalized for any strain rate and any uniaxial load history to formulate the damage function. Damage evolution in the body is described through the use of a rate-type evolution law which uses a pseudo strain to express the viscoelastic constitutive equation with damage. The resulting damage function is used to formulate a residual strength model. The methodology presented is demonstrated by comparing the peak values of the computed cyclic strain history as well as the residual strength model predictions to the experimental data of a polymer matrix composite.     

A continuum damage model for asphalt cement and asphalt mastic fatigue

An analytical model is developed for the mechanical degradation of asphalt cement and mastic under repeated loading. The model is derived by applying the strain decomposition principle to consider linear viscoelastic, nonlinear viscoelastic, and damage mechanisms. The experimental processes to isolate the behaviors and the analytical functions used to model each are described. It is found that the Schapery type damage approach is capable of modeling the fatigue process of these materials once appropriate consideration is taken for their nonlinear viscoelastic responses. Fatigue in asphalt mastics is also found to occur due to physical damage occurring in the asphalt cement.     

A model for anisotropic viscoelastic damage in composites

A model for continuous damage combined with viscoelasticity is proposed. The starting point is the formulation connecting the elastic properties to the tensor of damage variables. A hardening law associated with the damage process is identified from available experimental information and the rate-type constitutive equations are derived. This elastic damage formulation is used to formulate an internal variable approximation to viscoelastic damage in the form of a non-linear Kelvin chain. Elastic and viscoelastic equations are implemented into a finite element procedure. The code is verified by comparison with closed-form solutions in simplified configurations, and validated by fitting results of experimental creep tests.     

A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material

A bilinear cohesive zone model (CZM) is employed in conjunction with a viscoelastic bulk (background) material to investigate fracture behavior of asphalt concrete. An attractive feature of the bilinear CZM is a potential reduction of artificial compliance inherent in the intrinsic CZM. In this study, finite material strength and cohesive fracture energy, which are cohesive parameters, are obtained from laboratory experiments. Finite element implementation of the CZM is accomplished by means of a user-subroutine which is employed in a commercial finite element code (e.g., UEL in ABAQUS). The cohesive parameters are calibrated by simulation of mode I disk-shaped compact tension results. The ability to simulate mixed-mode fracture is demonstrated. The single-edge notched beam test is simulated where cohesive elements are inserted over an area to allow cracks to propagate in any general direction. The predicted mixed-mode crack trajectory is found to be in close agreement with experimental results. Furthermore, various aspects of CZMs and fracture behavior in asphalt concrete are discussed including: compliance, convergence, and energy balance.     

On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.     

Buckling analyses of viscoelastic structures considering ageing and damage effects

The durability of structures made of composite materials is affected by diverse factors, among which creep deformation, ageing and damage. Ageing is related to elapsed time (with different effects in different environmental conditions); damage is related to microstructural modifications due stress and/or strain inputs.The formal definition of these effects and the corresponding constitutive formulations are presented. These formulations are used to obtain analytical solutions and also to implement a Finite Element programme for viscoelastic analysis of laminar structures in a large displacement with small strains context. Then, the effects of ageing and damage on both the short and the long term stability of beam columns are analyzed. Some examples for verification of the formulation and for the comparison of effect are presented.     

A structural experimental technique to characterize the viscoelastic behavior of concrete under restrained deformations

An innovative variable restraint frame is proposed to characterize the viscoelastic behavior of concrete under tensile stresses induced by restraints to shrinkage deformations (mainly due to drying). Two concrete specimens with the same cross section are used, subjected to equal thermal and moisture conditions: one is made of plain concrete, to assess the “free” deformations due to shrinkage and temperature; the other is reinforced with two steel threaded rods, which induce a manually controlled axial restraint to shrinkage. The restrained specimen is installed on a reaction frame, being stretched in force control mode. The concrete and the rods are instrumented with strain gauges and temperature sensors, which allow separation of the different components of concrete strains with the aid of equations based on equilibrium and compatibility conditions. This permits identifying the elastic and tensile creep concrete strains, as well as the concrete tensile stresses induced by the restrained shrinkage. The device also allows assessing the concrete modulus of elasticity during the test and remains operational even upon concrete cracking, features of great interest for the intended material characterization.     

A three-dimensional micromechanical model to predict the viscoelastic behavior of woven composites

Polymer matrix based cloth composites are increasingly used in engineering applications. For such composites, significant viscoelastic behavior can be observed for dynamic load conditions. The viscoelastic effect is primarily due to the polymeric matrix used as most of the fibers used in structural applications are elastic. Matrix does not show a major contribution in the axial properties of composites, thus in the traditional modeling its viscoelastic nature is often ignored. However, the effective out of plane properties are influenced by the matrix material and exhibit significant damping characteristics. Therefore, a complete three-dimensional (3-D) model considering the viscoelastic nature of matrix is needed for better understanding of cloth composites. An analytical 3-D micromechanical model based on classical laminate theory (CLT) is verified, in this paper for the prediction of effective elastic and viscoelastic properties of a cloth composite. The method is shown to be accurate. This model is extended to the viscoelastic regime with the use of Laplace transform and correspondence principle. Prony series coefficients for composite cloth are obtained for different volume fractions of fibers in yarn. It is observed from the hysteresis plots that dissipation in out of plane normal and shear modes is significantly higher than the normal directions.     

An analysis of dynamic fracture in concrete with a continuum visco-elastic visco-plastic damage model

We present a rate-dependent continuum model for the dynamic modelling of concrete. Rate dependency is included by means of visco-elastic and visco-plastic constitutive relationships. The inclusion of the Stefan effect, described by a visco-elastic model, results in an increased tensile strength with increasing loading rate. An additional rate effect comes from the visco-plastic contribution which, from a mechanical standpoint, can be related to the micro-inertia of the material surrounding the crack tip. Static and dynamic examples show the capabilities of the model with respect to localization, hysteresis and dissipation of energy.     

Viscoplastic modeling of asphalt mixes with the effects of anisotropy, damage and aggregate characteristics

This paper presents an approach for constitutive modeling of the viscoplastic behavior of asphalt mixes. This approach utilizes an anisotropic non-associated flow rule based on the Drucker–Prager yield surface. The selection of this yield surface is motivated by the field stress paths and material properties associated with permanent deformation at high temperatures. The efficacy of the model is demonstrated by analyzing data from compressive triaxial tests conducted at different confining pressures and strain rates for three different mixes. The model parameters are related to the experimental measurements of aggregate shape characteristics, aggregate surface energy, inherent anisotropic distribution of aggregates, and microstructure damage measured using X-ray computed tomography and image analysis techniques. Establishing the relationship between the model parameters and material properties is important in order to optimize the mix properties, and achieve desirable mix performance.     

Numerical modeling of micro- and macro-behavior of viscoelastic porous materials

This paper presents a numerical method for solving the two-dimensional problem of a polygonal linear viscoelastic domain containing an arbitrary number of non-overlapping circular holes of arbitrary sizes. The solution of the problem is based on the use of the correspondence principle. The governing equation for the problem in the Laplace domain is a complex hypersingular boundary integral equation written in terms of the unknown transformed displacements on the boundaries of the holes and the exterior boundaries of the finite body. No specific physical model is involved in the governing equation, which means that the method is capable of handling a variety of viscoelastic models. A truncated complex Fourier series with coefficients dependent on the transform parameter is used to approximate the unknown transformed displacements on the boundaries of the holes. A truncated complex series of Chebyshev polynomials with coefficients dependent on the transform parameter is used to approximate the unknown transformed displacements on the straight boundaries of the finite body. A system of linear algebraic equations is formed using the overspecification method. The viscoelastic stresses and displacements are calculated through the viscoelastic analogs of the Kolosov–Muskhelishvili potentials, and an analytical inverse Laplace transform is used to provide the time domain solution. Using the concept of representative volume, the effective viscoelastic properties of an equivalent homogeneous material are then found directly from the corresponding constitutive equations for the average field values. Several examples are given to demonstrate the accuracy of the method. The results for the stresses and displacements are compared with the numerical solutions obtained by commercial finite element software (ANSYS). The results for the effective properties are compared with those obtained with the self-consistent and Mori–Tanaka schemes.     

钢筋混凝土微平面本构模型及其算法研究

阐述文献[1]的第二部分。第一部分在Ba ant Z.P.等人提出的混凝土微平面模型的基础上引入钢筋的影响提出了一个适用于配筋混凝土的微平面动态本构模型。混凝土模型采用能够反映各种复杂受力行为并被试验充分验证的微平面模型,钢筋采用Cowper-Symonds型率相关的双线性模型。该模型可用于钢筋混凝土的静力和动力显式分析。这一部分将给出模型的显式算法和试验验证。     

Development and calibration of shear-based rutting model for asphalt concrete layers

This study improves a shear-based rutting model for asphalt concrete (AC) layers and calibrates the model with field data. With dynamic modulus-based material parameters, the laboratory rutting prediction model was improved and determined by the wheel tracking test and full-scale accelerated pavement test. Through the field survey on several in-service pavements, the rutting model was calibrated to be applied to AC layers. In the improved rutting prediction model, the ratio of maximum shear stress to shear strength was introduced to combine asphalt material design and pavement structural design. The speed correction coefficient and the new temperature processing method improve the accuracy of the rutting model. The calibrated rutting prediction model proves to be reasonable and accurate in predicting the rutting depth of AC layers.     

不同温度环境中沥青混凝土动态抗压性能试验研究

为研究沥青混凝土在不同温度环境中的动态力学特性,该研究在-20～30 ℃和10-5～10-2 s-1条件下对其进行了动态抗压试验研究.试验结果表明:温度和应变速率对沥青混凝土的力学性能有显著影响,降低温度或增加应变速率导致抗压强度和弹性模量增加,峰值应变减小;当温度大于20 ℃或小于-10 ℃时,应变速率由10-5 s...     

A creep model with damage based on internal variable theory and its fundamental properties

The creep damage is discussed within Rice irreversible internal state variable (ISV) thermodynamic theory. An ISV small-strain unified creep model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The proposed model can describe viscoelasticity and, preferably, three phases of creep deformation. Creep strain results from internal structural adjustment, and different creep stages accompany different thermodynamic properties in terms of flow potential function and energy dissipation rate. During the viscoelastic process, the thermodynamic state of the material system tends to equilibrate spontaneously. The thermodynamic state of the material system without damage tends to equilibrate or achieve steady state after loading. Kinetic equations of ISVs can be derived by one single flow potential function, and the energy dissipation rate decreases monotonically over time. In the entire creep damage process, multiple potentials are needed to characterise evolution of ISVs, rotational fluxes are presented in affinity space, and the thermodynamic state of material system tends to depart from the steady or equilibrium state. The energy dissipation rate can be a measure of the distance between the current thermodynamic state and the equilibrium state. The time derivative of the rate can characterise the development trend of the material, and the integral value in the domain may be regarded as indices to evaluate the long-term stability of the structure.     

A radial point interpolation meshless method extended with an elastic rate-independent continuum damage model for concrete materials

An advanced discretization meshless technique, the radial point interpolation method (RPIM), is applied to analyze concrete structures using an elastic continuum damage constitutive model. Here, the theoretical basis of the material model and the computational procedure are fully presented. The plane stress meshless formulation is extended to a rate-independent damage criterion, where both compressive and tensile damage evolutions are established based on a Helmholtz free energy function. Within the return-mapping damage algorithm, the required variable fields, such as the damage variables and the displacement field, are obtained. This study uses the Newton–Raphson nonlinear solution algorithm to achieve the nonlinear damage solution. The verification, where the performance is assessed, of the proposed model is demonstrated by relevant numerical examples available in the literature.     

LPG explosion damage of a reinforced concrete building: A case study in Sanliurfa,Turkey

Around the morning EET of 17 June 2011, at Karakopru town of Sanliurfa in Turkey, a LPG explosion at a petrol station took place and as a result of this explosion 1 person was died and 21 people were seriously wounded. The in situ investigation revealed that the explosion was originated by the ignition of an explosive atmosphere that had formed at the basement space of the building due to the LPG leakage. Although it is considered the risk of LPG release to be low, the potential consequences of such a leak is devastating. In the present study, the interesting damages of RC members and their mechanisms in the building exposed to the explosion were explained in conjunction with photos and drawings. Damages observed were so interesting that, they were far beyond the imagination of anyone. It is considered that the presented damages and their mechanisms will give a new insight to the people interested in explosion damages.     

Viscoelastic–plastic damage model for porous asphalt mixtures: Application to uniaxial compression and freeze–thaw damage

Porous asphalt mixture increasingly used in highway pavement applications is an open graded composite material which has fewer fines and more air voids compared with conventional dense graded asphalt mixtures. The freeze thaw resistance of the mixture is crucial for the performance of porous asphalt pavement especially when clogging is unavoidable. A simple viscoelastic–plastic damage model is developed to evaluate the effects of freeze–thaw of porous asphalt mixtures. Generalized Maxwell and Drucker–Prager model are used to determine the viscoelastic and plastic responses respectively. The damage and its evolution is characterized by Weibull distribution function. Experimental data from uniaxial compressive strength tests, conducted at different strain rates and temperatures, are used to calibrate the model. The sensitivity of model parameters to loading conditions is identified. Simulation results suggest that loss of cohesion is the dominant mechanism of failure in porous asphalt mixtures under freeze–thaw cycles. Freeze–thaw effects also lead to changes of plastic potential surface and induce large volumetric strains under loading.     

Analytical modeling and experimental study of tensile strength of asphalt concrete composite at low temperatures

In this study, analytical modeling of the tensile strength of hot-mix asphalt (HMA) mixtures at low temperatures was developed. To do this, HMA mixtures were treated as a two-phase composite material with aggregates (coarse and fine) dispersed in an asphalt mastic matrix. A two-phase composite model, which was similar to Papanicolaou and Bakos's [J. Reinforced Plast. Compos. 11 (1992) 104] model with a particle embedded in an infinite matrix, was proposed. Unlike Papanicolaou and Bakos's model, an axial stress was introduced to the fiber end to consider the load transferred from the asphalt mastic the aggregate. Efforts were also made to consider the effect of aggregate gradation, asphalt mastic degradation, and interfacial damage between the aggregates and asphalt mastic matrix on the tensile strength of the HMA mixtures. Experimental investigations were conducted to validate the developed theoretical relations. A reasonable agreement was found between the predicted tensile strength and the experimental results at low temperatures. Parameters affecting the tensile strength of asphalt mixtures were discussed based on the calculated results.     

Viscoelastic behavior of opto-mechanical properties and its application to viscoelastic fracture studies

In experimental fracture studies of viscoelastic polymers presently available optical measurement methods need to be modified to account for the rate sensitivity of the physical properties. Here, photoviscoelastic behavior is examined for the purpose of determining the mechanical state of stress and strain at the tip of a crack moving through a viscoelastic solid. The linearly opto-mechanical constitutive relation is derived from mechanical and dielectric relaxation functions for thermorheologically simple solids via the Clausius-Mosotti-Lorentz-Lorenz (CMLL) relation, which derivation is consistent with the Maxwell-Neumann relation in the limit of elastic behavior; also, approximate functions in place of the CMLL relations are explored.Computations of the caustic, based on the square root singular stress field at the tip of a steadily propagating crack show that the crack speed has a pronounced effect on the size of the caustic but leaves the shape virtually unchanged. A knowledge of the phenomenological opto-mechanical properties of the polymer allows thus the determination of the stress intensity factor in (linearly) viscoelastic solids, though that determination must be effected through a de-convolution rather than through an algebraic computation as in the case of elastic solids.

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Résumé Dans les études actuellement disponibles sur la rupture des polymères viscoélastiques, les méthodes de mesure optique doivent être adaptées pour tenir compte de la sensibilité des propriétés physiques à la vitesse de sollicitation. Dans le présent travail, on examinera le comportement photo-viscoélastique dans le but de déterminer l'état mécanique des contraintes et des déformations à l'extrémité d'une fissure en progression dans un solide viscoélastique. La relation linéaire constitutive entre propriétés optiques et mécaniques est tirée de fonctions de relaxation mécaniques et diélectrique pour des solides thermoréologiquement simples, via la relation de Clausius-Mosotti-Lorentz-Lorentz (CMLL). Cette approche est cohérente avec la relation de Maxwell-Neumann dans les limites du comportement élastique. On explore également l'usage des fonctions approchées en lieu et place de la relation de CMLL.Les calculs de la caustique basés sur le champ de contraintes de singularité –1/2 à l'extrémité d'une fissure en propagation stable montrent que la vitesse de propagation a un effet prononcé sur la dimension de la caustique, bien que la forme en soit virtuellement inchangée. Ainsi, une connaissance des propriétés opto-mécaniques d'un polymère permet de déterminer un facteur d'intensité de contraintes dans des solides (linéairement) viscoélastiques, même si cette détermination doit être effectuée via une déconvolution plutôt que via un calcul algébrique, comme c'est le cas dans les solides élastiques.