Dissipated Energy Approach Research Articles

Temperature Wave Fatigue Damage and Dissipated Energy Approach to Flow Number Estimation of Asphalt Concrete

Abstract The effect of sinusoidal temperature on the fatigue life of asphalt concrete (AC) under continuous loading was investigated. The traditional failure criteria of 50 % loss in stiffness, stiffness ratio, and dissipated energy ratio were employed to analyze the AC fatigue test results. Dissipated energy approach and dissipated energy ratio were also extended to estimate the flow number (FN) of AC. The varying temperature induces a continuously changing temperature gradient across the AC beam. This, in turn, triggers the formation of continuously alternating weaker and harder outer layer relative to the beam core, thus creating a stiffness undulation. The combined effect of the load and temperature cycles resulted in a stiffness diminishing trend similar to that of damped harmonic vibration energy. The bottom of the beam is subjected to additional tensile strain/stress for a negative temperature gradient, while the top of the AC beam is subjected to additional compressive strain/stress for a positive temperature gradient. The temperature amplitude and period have a significant influence on the diminishing trend of the stiffness. Results from all the fatigue life estimation and prediction methods employed showed that the fatigue life of AC under variable temperature is shorter than that under constant temperature. However, the effect of the variable temperature is felt much more at lower strain loading. Nonrecovered strain energy method was successfully employed to estimate the AC FN.

Analytical modeling of fatigue crack propagation based on cyclic hardening and a characteristic damage length

An analytical fatigue crack growth model is developed, which combines effectively a cyclic energy dissipation approach and the strain energy density theory. The model uses cyclic material properties and relies on cyclic hardening for fatigue crack growth rate prediction. Fatigue crack propagation occurs incrementally by a characteristic damage length, which is in the length scale of striation spacing in commercial aluminum alloy, supporting the model’s physical background. Analytical crack propagation rates correlate well with existing experimental data, in material with uniform strength and strength gradient, showing the ability of the model to account for strength variation at the crack path.

Frequency domain CNN and dissipated energy approach for damage detection in building structures

Recent developments tools and techniques for structural health monitoring allow the design of early warning systems for the damage diagnosis and structural assessment. Most methods to damage detection involve vibration data analysis by using identification systems that generally require a mathematical model and much information about the system, such as parameters and states that are mostly unknown. In this paper, a novel frequency domain convolutional neural network (FDCNN) proposed aims to design an identification system for damage detection based on Bouc–Wen hysteretic model. FDCNN, unlike other works, only requires acceleration measurements for damage diagnosis that are very sensitive to environmental noise. In contrast to neural network (NN) and time domain convolutional neural network, FDCNN reduces the computational time required for the learning stage and adds robustness against noise in data. The FDCNN includes random filters in the frequency domain to avoid measurement noise using a spectral pooling operation, which is useful when the system bandwidth is unknown. Incorrect filtering can produce unwanted results, as a shifted and attenuation signal relative to the original. Moreover, FDCNN allows overcoming the parameterization problem in nonlinear systems, which is often difficult to achieve. In order to validate the proposed methodology, a comparison between two different architectures of convolutional neural networks is made, showing that proposed CNN in frequency domain brings better performance in the identification system for damage diagnosis in building structures. Experimental results from reducing scale two-storey building confirm the effectiveness of the proposed.

Fatigue performance evaluation of bitumen mastics reinforced with polyolefins through a dissipated energy approach

Polymers are known to improve the fatigue resistance of sphalt mastics. However, undesirable results can be obtained if the polymer is not successfully integrated into the bitumen binder. The goal of this work is to evaluate the effect of the addition of three selected polyolefins on their mastic’s fatigue performance. Low and high density polyethylenes (LDPE and HDPE) and polypropylene (PP) were chosen and used at the concentration of 4 wt.%. A dissipated energy approach was used in order to analyze the fatigue resistance, at 25 ºC, of the three composites studied. Dynamic time sweeps at and above the linear viscoelastic threshold were carried out. Based on that, the results demonstrated a better improvement when the LDPE was considered. For that binder, fluorescence optical microscopy observations at 25 ºC provided morphological evidence of a more homogeneous bitumen-polymer distribution which could be behind the improved fatigue behavior.

Thermoelastic damping in strain gradient microplates according to a generalized theory of thermoelasticity

This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results obtained by SGT are compared with those predicted by the modified couple stress theory (MCST) and the classical continuum theory. Furthermore, through a number of parametric studies, the effects of some variables on the amount of TED, such as microplate thickness, type of material and boundary conditions are discussed.

Damage analysis four-point bending fatigue tests on stone matrix asphalt using dissipated energy approaches

Four-point bending tests under strain-controlled mode were conducted on a stone matrix asphalt. Fatigue properties were evaluated by comparing indexes and fatigue curves at different frequencies, temperatures, and strain levels. The results show the effects of temperature and strain level are more significant than that of frequency. The fatigue life is much longer under the conditions of high temperature or low strain level than those under other conditions. Stiffness ratio curve can be fitted well by the Weibull equations. The damage model expressed as a power exponential function for dissipated energy provides a reliable method for evaluating fatigue damage.

A heat energy dissipation approach to elastic-plastic fatigue crack propagation

A heat energy dissipation approach has been formulated to assess the crack propagation rate of mode I fatigue cracks in AISI 304L stainless steel specimens. The proposed experimental approach relies on the heat energy converted from the plastic strain hysteresis energy at the crack tip. Practically, the heat energy is estimated starting from temperature measurements in the vicinity of the crack tip, by means of an infrared camera. The approach evaluates the heat energy dissipated in a properly defined control volume surrounding the crack tip, reminiscent of Neuber’s structural volume, to account for stress gradient effects caused by notches. The investigation performed has revealed that the control volume size varies with fatigue lifetime, in that the longer the fatigue life is, the smaller the control volume size. However, a fixed control volume size proved to correlate well the available crack growth data. The proposed experimental method has also been compared with the theoretical approach, which assumes the plastic strain hysteresis energy evaluated inside the cyclic plastic zone as a crack driving force.

Laboratory investigation of fatigue parameters characteristics of aging asphalt mixtures: A dissipated energy approach

The objective of this paper is to reveal the effects of aging on the fatigue performance of asphalt mixture based on variation patterns of fatigue parameters with aging degrees. Specimens with different aging degrees were prepared by modified SHRP’s Long-Term-Oven Aging (LTOA) test method, in which five different aging durations, included 0, 1, 3, 5, 7 days, were adopted to substitute the fixed 5 days. The fatigue parameters, including stiffness modulus, fatigue life, phase angle, Plateau Value (PV), and cumulative dissipation energy of specimens with different aging degrees under different stress ratios were obtained by the tensile fatigue test. The relationship of fatigue parameters with aging degrees and stress ratios were established. It could be observed from the results that the aging degree and stress ratio had dramatic influences on the fatigue performance of asphalt mixture. Sensitivity analysis showed that aging had the most significant effect on the initial stiffness modulus of asphalt mixture, and should be used as a control index in fatigue design. Statistical models of the relation between (PV) and fatigue life (Nf) established by the Rate of Dissipated Energy Change (RDEC) approach has an effective correlation. The Plateau Value model eliminated the effects of aging degrees and reflected the uniqueness of material parameters. Also, it could provide novel ideas for effective prediction of the fatigue life of asphalt mixtures with different aging degrees based on plateau value.

Binder and Mixture Fatigue Performance of Plant-Produced Road Surface Course Asphalt Mixtures with High Contents of Reclaimed Asphalt

The aged properties of Reclaimed Asphalt (RA) binders are one of the main factors working against their utilisation in high-RA content (>30%) mixes for surface courses. Fatigue cracking is the main distress of surface courses that are manufactured with a high percentage of RA. This investigation presents results of the rheological and fatigue results of different asphalt mixtures and their recovered binders. The binders were recovered from asphalt mixtures that had been manufactured in asphalt plants using different amounts of RA with contents up to 60% with and without rejuvenators. Two different sources of RA were used, representing a moderately aged RA and an extremely aged RA. The Dynamic Shear Rheometer (DSR) was used to assess the fatigue-characteristics of the binders using time sweep tests while the fatigue characteristics of their mixtures were assessed using the Indirect Tensile Fatigue Test (ITFT). The fatigue data was analysed based on the cumulative dissipated energy approach in addition to traditional fatigue analysis. Results have shown that the ageing condition of RA significantly affects the fatigue properties of recovered binders. Binder and asphalt mixture fatigue results showed that RA contents up to 60% can produce comparable fatigue performance compared to lower percentages of RA in road surface course if the aged RA binder is sufficiently rejuvenated.

Experimental characterisation of fatigue damage in foamed bitumen stabilised materials using dissipated energy approach

Abstract Foamed bitumen stabilisation (FBS) of degraded pavements has become popular in recent times. Although the common failure mechanism of FBS materials under repeated heavy traffic loads has been identified as bottom-up fatigue cracking, further research is required to better model their performance characteristics. In this study, the four-point bending test was performed under both stress-controlled and strain-controlled modes to characterise the flexural fatigue performance of FBS beams. The dissipated energy (DE) approach was adopted to describe the flexural fatigue behaviour of FBS materials. This paper presents the issues in conventional DE calculation methods and suggests new empirical equations to more accurately determine the DE, the ratio of DE change, the plateau value and the cumulative dissipated energy (CDE) of FBS materials. The analysis of experimental results revealed that the CDE and the number of load cycles to the final flexural fatigue rupture of FBS beams are highly correlated.

Tunable Mechanical Metamaterial with Constrained Negative Stiffness for Improved Quasi‐Static and Dynamic Energy Dissipation

This paper presents the computational design, fabrication, and experimental validation of a mechanical metamaterial in which the damping of the material is significantly increased without decreasing the stiffness by embedding a small volume fraction of negative stiffness (NS) inclusions within it. Unlike other systems that dissipate energy primarily through large‐amplitude deformation of nonlinear structures, this metamaterial dissipates energy by amplifying linear strains in the viscoelastic host material. By macroscopically tuning the pre‐strain of the metamaterial via mechanical loading, the embedded NS inclusions operate about a constrained buckling instability. When further macroscopic vibrational excitation is applied, the inclusions amplify the strains of the surrounding viscoelastic medium. This results in enhanced dissipation of mechanical energy when compared to voided or neat comparison media. Microstereolithography, an emerging high‐resolution additive manufacturing (AM) technology, is employed to fabricate the deeply subwavelength inclusions which ensures broadband damping behavior. The mechanically induced broadband energy dissipation and manufacturing approach further differentiate the metamaterial from other approaches that exploit resonances, large deformations, or non‐mechanical instabilities. The computational design, fabrication, and experimental evaluation reported is the first dynamic demonstration of such a mechanically tunable NS metamaterial, potentially enabling components with integrated structural and damping capabilities.

Fretting wear accumulation in partial-slip circular Hertzian contact

An axisymmetric Hertzian type elastic contact under a constant normal and oscillating tangential loading is considered in the framework of Archard’s law of wear. The dissipated energy approach is employed for modeling the volume wear rate, and a simple two-parameter regression model has been introduced, which accounts for the wear rate’s non-monotonicity. After fixing one of its parameters based on the numerical solution available in the literature, the developed model does not contain any free parameters, since the other one is determined by matching to the final (limiting) contact configuration, which evolves as a result of fretting wear.

Evaluation of fatigue behavior of asphalt binders containing reclaimed asphalt binder using simplified viscoelastic continuum damage approach

Several fatigue damage analysis approaches have been introduced for asphalt binders and mixtures. In this study, using three modifiers including softer bitumen, a rejuvenator and waste polymer modified bitumen, fatigue behavior of RAB-containing binder mixes was evaluated based on the simplified viscoelastic continuum damage mechanics (S-VECD). In addition, correlations between the S-VECD parameters and the other fatigue failure criteria were investigated. For this purpose, the time sweep test was used to evaluate fatigue behavior of various asphalt binders in controlled-strain mode. Results showed that the rejuvenator and softer bitumen had the greatest effect in terms of prioritization on the improvement of the fatigue resistance of the RAB-containing binder mixes. Moreover, the results showed that good unique relationships between plateau value (PV) and Nf50 and between rate of change of total released pseudo strain energy (GR) and Nf50 were established in the RAB-containing binder mixes. Furthermore, there was a good relationship between the two concepts of the dissipated energy approach used for determination of the PV and the dissipated pseudo strain energy approach which used for calculation of the GR values.

A dissipated energy model of shock evolution in the simulation of the dynamics of DGM’s of railway compositions

One of the major challenges for the simulation of the longitudinal dynamics of heavy-haul trains is modeling the in-train forces. The freight cars draft gear mechanisms (DGM) are known for its highly non-linear behavior, with fast force transitions between the loaded and unloaded operational stages. Accurate models that represent the constructive characteristics of DGMs, including friction simulation, demand high computational power and are not viable for the simulation of long trains with several freight cars. To overcome such an issue, simplified models were developed to estimate in-train forces based on intermediate stiffness and/or smoothing techniques that ensure numerical stability and low computational cost for the model. In this paper, a new technique to calculate the DGM intermediate transition forces, based on the dissipated energy approach is developed. The proposed methodology is compared to two well-known techniques presented in the literature and the results show expressive improvement in computational cost and numerical stability of in-train forces estimation.

Size-Dependent Strain Gradient-Based Thermoelastic Damping in Micro-Beams Utilizing a Generalized Thermoelasticity Theory

The small-scale effects on the thermoelastic damping (TED) in Euler–Bernoulli micro-beams is investigated in this study. To this purpose, by utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model, the coupled equations of motion and heat conduction are derived. By solving these equations simultaneously and using the Galerkin method, the real and imaginary parts of the frequency and the amount of TED in thin micro-beams are obtained. The results predicted by SGT are compared with those given by the modified couple stress theory (MCST) and the classical continuum theory. In addition, TED is calculated on the basis of energy dissipation approach which shows that the difference between the obtained results and those evaluated based on the frequency approach is negligible. Some numerical results are also presented in order to study the effects of different parameters of the micro-beams as well as the type of the boundary conditions on TED and the critical thickness; these parameters include the micro-beam height, its aspect ratio and type of the material.

Prediction of electrical contact endurance subject to micro-slip wear using friction energy dissipation approach

Fretting wear is a common cause of failure of an electrical contact (EC). In this study, we analyzed in detail the failure of EC induced especially by sliding using the representative electrical terminals. Furthermore, combining the friction energy dissipation theory, we proposed a prediction model to evaluate the electrical connector endurance (ECE) based on the contact stress and geometrical changes during the wear process obtained from a numerical model. The study helps establish that the friction energy dissipation theory is a powerful tool to analyze a contact failure due to wear. The proposed model proves to be effective in predicting the ECE for all considered cases such as micro-slip amplitude, contact force, overturning angle, superficial layer thickness, and friction/wear coefficients.

Analysis of fatigue on surface course using dissipated energy approach

As an important transportation infrastructure, pavement is subjected to repeated vehicle loads that may cause fatigue, which often leads to cracking. The point when this cracking initiates can be determined from the energy dissipated during the loading. This research investigates fatigue in Adi Soemarmo Airport mix-design using bitumen Pen 60/70 + EVA (Ethyl Vinyl Acetate) polymer. An Indirect Tensile Fatigue Test (ITFT) was conducted using stress-controlled loading mode to determine its fatigue life. The stress levels were 500, 600, and 700 kPa, while the loading frequency and the temperature were 10 Hz and 20°C, respectively. The test exhibits strain levels for each loading cycle, which were used to determine the dissipated energy (DE). The result indicates that the DE increases when the number of loading cycles increases, due to progress of the strain levels. The values of DE are 7122.8, 8614.3, and 2654.9 J/m3 for loading levels of 500, 600, and 700 kPa, respectively, whereas the failure points for stress levels of 500, 600, and 700 kPa are 8171, 5161, and 841 cycles, respectively. Thus, the longer the time until the pavement failure point is reached (fatigue life), the greater the amount of energy that is dissipated.

Characteristics of dissipated energy of concrete subjected to cyclic loading

Based on dissipated energy approach (DEA), the energy dissipation characteristics of concrete samples subjected to uniaxial cyclic loading have been investigated. The effect of different cyclic load levels on energy dissipation is quantitatively analyzed by different damage indicators during cyclic fatigue tests. It is concluded that the cumulative speed of energy dissipation and increasing growth-rate of damage indicators in Continuum Damage Theory (CDT) follow an exponential function in relation to the maximum cyclic load level and follow a logarithmic function in relation to the minimum cyclic load level. The loading strategy has an effect on total energy dissipated during fatigue tests, in other words: Energy dissipation and damage evolution are stress path dependent.

Outrigger tuned inertial mass electromagnetic transducers for high-rise buildings subject to long period earthquakes

This paper proposes outrigger tuned inertial mass electromagnetic transducer (TIMET) systems for high-rise buildings subject to long period earthquake excitations. The proposed outrigger TIMET systems consist of the outrigger and TIMET parts. The outrigger damping systems have been proposed as a novel energy dissipation approach to high-rise buildings, in which control devices are installed vertically between the outrigger and perimeter columns to achieve large energy dissipation. While the TIMET has been developed based on the mechanism of the tuned viscous mass damper (TVMD) which can improve energy absorbing capability by taking advantage of resonance effect. However, instead of a viscous material, the damping of the TIMET is provided by a motor which can convert mechanical energy to electrical energy. The focus of this study is to investigate the structural control performance and energy harvesting efficiency of the proposed outrigger TIMET system for high-rise buildings subjected to long period earthquakes through numerical simulations.

An energy dissipation approach on complete loading-unloading and dynamic impact predictions with experimental verification for rubber anti-vibration component

Accurate evaluations of a completed loading-unloading cycle and dynamic impact response for rubber anti-vibration components have been very challenging for industry over many years. In this article, we have altered the classic hyperelastic models to predict complete loading-unloading response using an energy dissipation approach. In addition, we proposed NFR (Natural Frequency Region) approach to simulate a dynamic impact event instead of using the usual viscoelastic methodology, as results from different viscoelastic models may vary widely and to avoid complex parameter fitting procedures. The proposed approaches have been validated in laboratory experiments using industrial anti-vibration components. We have also detailed a procedure for engineers to implement this approach in commercial finite element software without writing intricate user subroutines, as simulation based on finite element method has been routinely used in industry to support design of new products. It is suggested that these methodologies could be used for a design stage in engineering applications.