Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Fracture and viscoelastic properties of asphalt binders during fatigue and rest periods

Viscoelastic asphalt binder plays an important role in bonding individual aggregate particles and contributes to the durability and stability of asphalt pavement. When asphalt binder is subjected to cyclic loading, deformation and fracture may develop simultaneously within it, leading to the deterioration of material properties and eventually fatigue failure. Research has found that some degree of recovery may develop if rest periods are applied after fatigue deterioration. However, it is not clear whether such recovery is caused by fracture healing, viscoelastic recovery, or both. This paper presents an analysis to differentiate the contributions of fracture healing and viscoelastic recovery to the asphalt binder during rest periods. It also evaluates the damage caused by deformation and fracture during a fatigue process. It is found that viscoelastic recovery plays an important role in the instant increase in the dynamic shear modulus at the beginning of the rest period. The effect of fracture healing on dynamic shear modulus recovery is more dominant in the long term. A healing index is developed based only on the fracture healing of asphalt binder, excluding the effect of viscoelastic recovery. It can be used to evaluate the true healing properties of different asphalt binders. Copyright © 2014 by ASTM International.

Anisotropic viscoelastic properties of undamaged asphalt mixtures

A test protocol and a data analysis method are developed in this paper on the basis of linear viscoelastic theory to characterize the anisotropic viscoelastic properties of undamaged asphalt mixtures. The test protocol includes three nondestructive tests: (1) uniaxial compressive creep test, (2) indirect tensile creep test, and (3) the uniaxial tensile creep test. All three tests are conducted on asphalt mixture specimens at three temperatures (10, 20, and 30°C) to determine the tensile and compressive properties at each temperature and then to construct the master curve of each property. The determined properties include magnitude and phase angle of the compressive complex modulus in the vertical direction, magnitude and phase angle of the tensile complex modulus, and the magnitude and phase angle of the compressive complex modulus in the horizontal plane. The test results indicate that all tested asphalt mixtures have significantly different tensile properties from compressive properties. The peak value of the master curve of the tensile complex modulus phase angle is within a range from 65 to 85°, whereas the peak value of the compressive moduli phase angle in both directions ranges from 35 to 55°. In addition, the undamaged asphalt mixtures exhibit distinctively anisotropic properties in compression. The magnitude of the compressive modulus in the vertical direction is approximately 1.2 to ̃2 times of the magnitude of the compressive modulus in the horizontal plane. Dynamic modulus tests are performed to verify the results of the proposed test protocol. The test results from the proposed test protocol match well with those from the dynamic tests. © 2012 American Society of Civil Engineers.

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

Energy-based damage and fracture framework for viscoelastic asphalt concrete

A framework based on the continuum damage mechanics and thermodynamics of irreversible processes using internal state variables is used to characterize the distributed damage in viscoelastic asphalt materials in the form of micro-crack initiation and accumulation. At low temperatures and high deformation rates, micro-cracking is considered as the source of nonlinearity and thus the cause of deviation from linear viscoelastic response. Using a non-associated damage evolution law, the proposed model shows the ability to describe the temperature-dependent processes of micro-crack initiation, evolution and macro-crack formation with good comparison to the material response in the Superpave indirect tensile (IDT) strength test.

Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model

This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.

Measuring the dynamic mechanical response of hydrated mouse bone by nanoindentation

This study demonstrates a novel approach to characterizing hydrated bone's viscoelastic behavior at lamellar length scales using dynamic indentation techniques. We studied the submicron-level viscoelastic response of bone tissue from two different inbred mouse strains, A/J and B6, with known differences in whole bone and tissue-level mechanical properties. Our results show that bone having a higher collagen content or a lower mineral-to-matrix ratio demonstrates a trend towards a larger viscoelastic response. When normalized for anatomical location relative to biological growth patterns in the antero-medial (AM) cortex, bone tissue from B6 femora, known to have a lower mineral-to-matrix ratio, is shown to exhibit a significantly higher viscoelastic response compared to A/J tissue. Newer bone regions with a higher collagen content (closer to the endosteal edge of the AM cortex) showed a trend towards a larger viscoelastic response. Our study demonstrates the feasibility of this technique for analyzing local composition-property relationships in bone. Further, this technique of viscoelastic nanoindentation mapping of the bone surface at these submicron length scales is shown to be highly advantageous in studying subsurface features, such as porosity, of wet hydrated biological specimens, which are difficult to identify using other methods. © 2010 Elsevier Ltd.

Viscoelasticity and high buckling stress of dense carbon nanotube brushes

We report on the mechanical behavior of a dense brush of small-diameter (1–3 nm) non-catalytic multiwall (2–4 walls) carbon nanotubes (CNTs), with ~10 times higher density than CNT brushes produced by other methods. Under compression with spherical indenters of different radii, these highly dense CNT brushes exhibit a higher modulus (~17–20 GPa) and orders of magnitude higher resistance to buckling than vapor phase deposited CNT brushes or carbon walls. We also demonstrate the viscoelastic behavior, caused by the increased influence of the van der Waals’ forces in these highly dense CNT brushes, showing their promise for energy-absorbing coatings.

The role of organoclay in promoting co-continuous morphology in high-density poly(ethylene)/poly(amide) 6 blends

The effect of organically modified clay on the morphology, rheology and mechanical properties of high-density polyethylene (HDPE) and polyamide 6 (PA6) blends (HDPE/PA6 = 75/25 parts) is studied. Virgin and filled blends were prepared by melt compounding the constituents using a twin-screw extruder. The influence of the organoclay on the morphology of the hybrid was deeply investigated by means of wide-angle X-ray diffractometry, transmission and scanning electron microscopies and quantitative extraction experiments. It has been found that the organoclay exclusively places inside the more hydrophilic polyamide phase during the melt compounding. The extrusion process promotes the formation of highly elongated and separated organoclay-rich PA6 domains. Despite its low volume fraction, the filled minor phase eventually merges once the extruded pellets are melted again, giving rise to a co-continuous microstructure. Remarkably, such a morphology persists for long time in the melt state. A possible compatibilizing action related to the organoclay has been investigated by comparing the morphology of the hybrid blend with that of a blend compatibilized using an ethylene–acrylic acid (EAA) copolymer as a compatibilizer precursor. The former remains phase separated, indicating that the filler does not promote the enhancement of the interfacial adhesion. The macroscopic properties of the hybrid blend were interpreted in the light of its morphology. The melt state dynamics of the materials were probed by means of linear viscoelastic measurements. Many peculiar rheological features of polymer-layered silicate nanocomposites based on single polymer matrix were detected for the hybrid blend. The results have been interpreted proposing the existence of two distinct populations of dynamical species: HDPE not interacting with the filler, and a slower species, constituted by the organoclay-rich polyamide phase, which slackened dynamics stabilize the morphology in the melt state. In the solid state, both the reinforcement effect of the filler and the co-continuous microstructure promote the enhancement of the tensile modulus. Our results demonstrate that adding nanoparticles to polymer blends allows tailoring the final properties of the hybrid, potentially leading to high-performance materials which combine the advantages of polymer blends and the merits of polymer nanocomposites.

Anisotropic characterization of crack growth in the tertiary flow of asphalt mixtures in compression

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris' laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris' law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger n1 value (exponent of Paris' law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load. © 2014 American Society of Civil Engineers.

Characterizing permanent deformation and fracture of asphalt mixtures by using compressive dynamic modulus tests

Permanent deformation and fracture may develop simultaneously when an asphalt mixture is subjected to a compressive load. The objective of this research is to separate viscoplasticity and viscofracture from viscoelasticity so that the permanent deformation and fracture of the asphalt mixtures can be individually and accurately characterized without the influence of viscoelasticity. The undamaged properties of 16 asphalt mixtures that have two binder types, two air void contents, and two aging conditions are first obtained by conducting nondestructive creep tests and nondestructive dynamic modulus tests. Testing results are analyzed by using the linear viscoelastic theory in which the creep compliance and the relaxation modulus are modeled by the Prony model. The dynamic modulus and phase angle of the undamaged asphalt mixtures remained constant with the load cycles. The undamaged asphalt mixtures are then used to perform the destructive dynamic modulus tests in which the dynamic modulus and phase angle of the damaged asphalt mixtures vary with load cycles. This indicates plastic evolution and crack propagation. The growth of cracks is signaled principally by the increase of the phase angle, which occurs only in the tertiary stage. The measured total strain is successfully decomposed into elastic strain, viscoelastic strain, plastic strain, viscoplastic strain, and viscofracture strain by employing the pseudostrain concept and the extended elastic-viscoelastic correspondence principle. The separated viscoplastic strain uses a predictive model to characterize the permanent deformation. The separated viscofracture strain uses a fracture strain model to characterize the fracture of the asphalt mixtures in which the flow number is determined and a crack speed index is proposed. Comparisons of the 16 samples show that aged asphalt mixtures with a low air void content have a better performance, resisting permanent deformation and fracture. © 2012 American Society of Civil Engineers.

Using overlay test to evaluate fracture properties of field-aged asphalt concrete

Field material testing provides firsthand information on pavement conditions which are most helpful in evaluating performance and identifying preventive maintenance or overlay strategies. High variability of field asphalt concrete due to construction raises the demand for accuracy of the test. Accordingly, the objective of this study is to propose a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the overlay test (OT). The OT is selected because of its efficiency and feasibility for asphalt field cores with diverse dimensions. The fracture properties refer to the Paris’ law parameters based on the pseudo J-integral (A and n) because of the sound physical significance of the pseudo J-integral with respect to characterizing the cracking process. In order to determine A and n, a two-step OT protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. To ensure the accuracy of determined undamaged and fracture properties, a new analysis method is then developed for data processing, which combines the finite element simulations and mechanical analysis of viscoelastic force equilibrium and evolution of pseudo displacement work in the OT specimen. Finally, theoretical equations are derived to calculate A and n directly from the OT test data. The accuracy of the determined fracture properties is verified. The proposed methodology is applied to a total of 27 asphalt field cores obtained from a field project in Texas, including the control Hot Mix Asphalt (HMA) and two types of warm mix asphalt (WMA). The results demonstrate a high linear correlation between n and −log A for all the tested field cores. Investigations of the effect of field aging on the fracture properties confirm that n is a good indicator to quantify the cracking resistance of asphalt concrete. It is also indicated that summer climatic condition clearly accelerates the rate of aging. The impact of the WMA technologies on fracture properties of asphalt concrete is visualized by comparing the n-values. It shows that the Evotherm WMA technology slightly improves the cracking resistance, while the foaming WMA technology provides the comparable fracture properties with the HMA. After 15 months aging in the field, the cracking resistance does not exhibit significant difference between HMA and WMAs, which is confirmed by the observations of field distresses.