Energy dissipation of a two-relaxation-time material

e-Polymers ◽  
2015 ◽  
Vol 15 (5) ◽  
pp. 329-333
Author(s):  
Tao-Tao Xu
Keyword(s):  
Relaxation Time ◽  
Energy Dissipation ◽  
Polymeric Materials ◽  
Dissipated Energy ◽  
External Loading ◽  
Model Parameters ◽  
Hysteresis Phenomenon ◽  
Time Model ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

AbstractEnergy dissipation in polymeric materials was studied using a two-relaxation-time model. A differential form of a constitutive relation was constructed with the viscoelasticity theory. Through the simulation of a cyclic loading and unloading test, the dependence of the dissipated energy on the model parameters and external loading variables was determined and analyzed. In particular, the characteristics of the hysteresis phenomenon of a material with more than one relaxation time were studied in detail.

scholarly journals Investigating the Mullins Effect and Energy Dissipation in Magnetorheological Polyurethane Elastomers

2020 ◽  
Vol 21 (15) ◽  
pp. 5318
Author(s):  
Alex Elías-Zúñiga ◽  
Luis M. Palacios-Pineda ◽  
Imperio A. Perales-Martínez ◽  
Oscar Martínez-Romero ◽  
Daniel Olvera-Trejo ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Magnetic Flux ◽  
Shear Modulus ◽  
Flux Density ◽  
Material Behavior ◽  
Dissipated Energy ◽  
Magnetic Flux Density ◽  
Polyurethane Elastomers ◽  
Residual Strains ◽  
Loading And Unloading

The aim of this article was to investigate the mechanical performance of magnetorheological polyurethane elastomers reinforced with different concentrations of carbonyl iron microparticles (CIPs) in which stress softening, energy dissipation, residual strains, microparticles orientation, and magnetic flux density effects will be considered. Other aspects, such as the determination of the dissipated energy during cyclic loading and unloading, were investigated by considering a pseudo-elastic network model that takes into account residual strains, magnetic field intensity, and the isotropic and anisotropic material behavior. Theoretical predictions confirmed that the material shear modulus becomes sensitive not only for higher concentrations of CIPs added into the elastomer material matrix, but also to the magnetic flux intensity that induces attractive forces between CIPs and to the strong bonds between these and the elastomer matrix. It was also found that the addition of CIPs when embedded into the polymer matrix with a predefined orientation enhances the material shear modulus as well as its capacity to dissipate energy when subjected to magnetic flux density in loading and unloading directions.

scholarly journals Study on Nonlinear Damage Creep Model for Rocks under Cyclic Loading and Unloading

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Liangliang Zhang ◽  
Xiaojian Wang
Keyword(s):  
Cyclic Loading ◽  
Superposition Principle ◽  
Three Dimensional ◽  
Creep Model ◽  
Model Parameters ◽  
Nonlinear Creep ◽  
Cyclic Loading And Unloading ◽  
In Series ◽  
Loading And Unloading ◽  
Stress States

To determine the nonlinear creep characteristics of rocks under cyclic loading and unloading conditions, a nonlinear Kelvin model and damage viscoplastic model are proposed. The models are connected in series with a linear elastic body to establish a nonlinear damage creep model. The differential damage constitutive equations of the proposed creep model under one-dimensional and three-dimensional stress states are derived based on the creep mechanics and elasticity theory. The damage and unloading creep equations are then obtained based on the superposition principle, and a simple and feasible method for determining the model parameters is determined. Finally, the step cyclic loading and unloading creep test data for lherzolite and limestone are used to verify the rationality and feasibility of the nonlinear damage creep model. The results show that the theoretical creep curves of the nonlinear damage creep model are consistent with the experimental curves which indicates that the proposed model can not only determine the creep properties of lherzolite and limestone under cyclic loading and unloading but also determine the nonlinear characteristics of rocks in the transient and steady-state creep stages and particularly within the accelerating creep stage.

An Experimental Assessment of the Hysteresis Behavior of Umbilical Cables Under Cyclic Traction

2017 ◽  
Author(s):  
Caio C. P. Santos ◽  
Celso P. Pesce ◽  
Rafael Salles ◽  
Guilherme R. Franzini ◽  
Rodolfo T. Gonçalves ◽  
...  
Keyword(s):  
Energy Dissipation ◽  
Flexible Structures ◽  
Hysteresis Loops ◽  
Polymeric Materials ◽  
Optical Tracking ◽  
Experimental Methodology ◽  
Substantial Part ◽  
Hysteresis Phenomenon ◽  
Cyclic Loads ◽  
Friction Mechanism

Umbilical cables are composed by several internal components helically disposed and externally protected by an outer polymeric sheath. With these elements wound in different directions, internal friction is a well-known structural feature, originating hysteretic loops when umbilicals are subject to cyclic loads. On the other hand, polymeric materials represent a substantial part of an umbilical composition. These materials present a viscoelastic character, introducing a second energy dissipation mechanism to these flexible structures. Therefore, this paper aims to assess the hysteresis phenomenon observed under different periodic axial loading conditions. The study is based on experimental campaigns carried out with two umbilical cables, proposing and testing a new experimental methodology based on standard instrumentation combined with optical tracking measurement. The hysteresis loops are evaluated considering ‘slow’ and ‘very-slow’ axial cyclic loads. The results indicates that an equivalent viscoelastic damping behavior could be adopted to model the umbilical cable response under ‘slow’ axial cyclic loads. In contrast, the ‘very-slow’ tests indicate that the energy dissipation process is dominated by a dry friction mechanism.

scholarly journals Fracture Characteristics and Fatigue Damage of Noncoplanar Fractured Rocklike Specimens under Uniaxial Graded Cyclic Loading and Unloading

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Gui-cheng He ◽  
Wen-yuan Wu ◽  
Yun Wang ◽  
Yong-ming Xue ◽  
Bing Dai ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Energy Dissipation ◽  
Cyclic Loading ◽  
Hysteresis Loop ◽  
Fatigue Damage ◽  
Damping Ratio ◽  
Fracture Characteristics ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading ◽  
Limit Stress

To study the fracture characteristics and fatigue damage of fractured rock masses, noncoplanar fractured rocklike specimens prepared using cement mortar were used for a graded cyclic loading–unloading test. The results showed that the two ends of the horizontal crack were the main stress concentration areas, and they inhibited crack initiation of the inclined fracture. With increasing crack inclination, the inhibitory effect became more obvious. Under the condition that the lower limit stress is constant, as the upper limit stress increases, energy dissipation of the specimen increases, becoming relatively stable in each stage of the cycle. With increasing crack inclination, the increase in the energy dissipation value decreases. Specimens with large changes in the shape of their hysteresis loop tend to exhibit large fluctuations in the elastic modulus. As the loading progressed, the elastic modulus exhibited a downward trend, and the damping ratio tended to be stable. The change in the damping ratio is affected by the dynamic elastic modulus and area of the hysteresis loop. Based on the Weibull probability distribution function, the evolution curve of the damage variable of the specimen can be obtained. This curve reflects the trend of the damage change of the rocklike specimens under various levels of cyclic loading and unloading.

scholarly journals Study on Permeability of Deep-Buried Sandstone under Triaxial Cyclic Loads

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingqiang Sheng ◽  
Awei Mabi ◽  
Xigen Lu
Keyword(s):  
Acoustic Emission ◽  
Cyclic Loading ◽  
Energy Density ◽  
Damage Variable ◽  
Dissipated Energy ◽  
Peak Strain ◽  
Rock Damage ◽  
Cyclic Loading And Unloading ◽  
Relative Strain ◽  
Loading And Unloading

The triaxial cyclic loading and unloading test was carried out on a TAW-2000 rock mechanics to study the permeability characteristics of deep-buried sandstone. This paper analyzed the evolution laws of permeability, elastic modulus, rock damage, dissipated energy, and acoustic emission events of sandstone under different confining pressures. It also introduced the concept of relative strain and further discussed the relationship between relative strain and permeability. The test results showed that the permeability of sandstone under cyclic loading and unloading obviously experienced three stages. At a low strain level, the damage degree of sandstone was low. As a result, both the number of acoustic emission events and the proportion of the dissipated energy density were small. In this stage, with increasing the stress, the permeability decreased. With the increase of the relative strain, the propagation of fissure increased through rock interior and the damage of rock was accumulated. Consequently, the number of acoustic emission events grew slowly, and the proportion of dissipated energy density and the damage variable (D) increased gradually. In this stage, the permeability increases. As the axial strain reached the peak strain, the fissures developed into cracks and the rock failure happened. The number of acoustic emission events increased rapidly; both the proportion of the dissipated energy density and the damage variable (D) obtain the maximum value. In this stage, the permeability increased greatly. In this study, the point of fissure propagation of rock specimens was used as the point of demarcation. Before the fissures propagated, the permeability increased slowly and it was in accordance with a linear function. After the fissures propagated, the degree of rock damage increased, and the permeability increased in the form of an exponential function. The larger the confining pressure was, the smaller the relative strain corresponding to the point of fissure propagation was.

scholarly journals Analysis of Energy Dissipation Characteristics of Damaged Sandstone under Impact Load

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Feng Wang ◽  
Haibo Wang ◽  
Ying Xu ◽  
Bing Cheng ◽  
Qianqian Wang
Keyword(s):  
Rock Mass ◽  
Energy Dissipation ◽  
Cyclic Loading ◽  
Dynamic Load ◽  
Impact Load ◽  
Peak Strain ◽  
Dissipation Energy ◽  
Cyclic Loading And Unloading ◽  
Damage Degree ◽  
Loading And Unloading

Before rock burst, coal, and gas outburst dynamic load, rock mass in geotechnical engineering has been an indifferent degree of damage. The dissipation energy of rock mass under dynamic load reflects the difficulty of rock breaking. In view of the energy dissipation of damaged rock mass under dynamic load, the cyclic loading and unloading test is carried out to make sandstone in different damage states, and the damage degree of sandstone is characterized by the change of longitudinal wave velocity before and after cyclic loading and unloading. Then, the rock with different damage degrees is tested by adopting the split Hopkinson pressure bar (SHPB). Finally, the energy dissipation characteristics of damaged rock under impact load are analyzed. The results show that the damage factor of sandstone increases with the increase of the upper limit of stress after cyclic static loading. The dynamic strength and peak strain of damaged sandstone increase with the increase of impact pressure and decrease with the increase of damage degree. With the increase of damage degree of sandstone, the reflection energy and dissipation energy of sandstone increase, while the transmission energy decreases.

scholarly journals Energy Evolution and Mechanical Features of Granite Subjected to Triaxial Loading-Unloading Cycles

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Feng Pei ◽  
Hongguang Ji ◽  
Tongzhao Zhang
Keyword(s):  
Energy Storage ◽  
Energy Dissipation ◽  
Confining Pressure ◽  
Mechanical Parameters ◽  
Energy Evolution ◽  
Dissipation Energy ◽  
Cyclic Loading And Unloading ◽  
Storage Limit ◽  
Loading And Unloading ◽  
Storage Energy

Energy evolution varies during the whole process of rock deformation, and mechanical parameters are markedly altered under cyclic loading and unloading. In order to investigate the effects of confining pressure on energy evolution and mechanical parameters, cyclic loading and unloading experiments were performed for granite under six different confining pressures. The experiment revealed the confining pressure effect on variation and allocation pattern of energy and mechanical characteristics. Four characteristic energy parameters, namely, storage energy rock, storage energy limit, energy storage ratio, and energy dissipation ratio, were proposed to describe energy storage and dissipation properties of rock. Elastic modulus and dissipation ratio presented a downward “U” and “U”-shaped trends, respectively, with loading and unloading cycles, while Poisson’s ratio increased linearly at the same time. Elastic energy was accumulated mainly before peak stress, while the energy dissipation and release were dominant after the peak strength. As the confining pressure increased, efficiency of energy accumulation and storage limit improved. An exponential function was proposed to express the relationship between the energy storage limit and confining pressure. Dissipation energy increased nonlinearly with the strain, and the volume dilatancy point defined the turning point from a relatively slow growth to an accelerated growth of dissipation energy. The dilatancy point can be used as an important indication for the rapid development of dissipation energy.

scholarly journals Acoustic Emission Characteristics and Energy Evolution of Red Sandstone Samples under Cyclic Loading and Unloading

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Tianzuo Wang ◽  
Chunli Wang ◽  
Fei Xue ◽  
Linxiang Wang ◽  
Beyene Hana Teshome ◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Cyclic Loading ◽  
Uniaxial Compression ◽  
Dissipated Energy ◽  
Strengthening Effect ◽  
Energy Rate ◽  
Red Sandstone ◽  
Rock Samples ◽  
Cyclic Loading And Unloading ◽  
Loading And Unloading

To explore the characteristics of rock deformation and failure under cyclic loading and unloading, the MTS815 rock mechanics test system and acoustic emission (AE) signal acquisition system were used to perform cyclic loading and unloading tests on red sandstone samples. The results showed that, compared with the uniaxial compression test, cyclic loading and unloading had a certain strengthening effect on the strength of the samples. The plastic deformation of the rock samples increased as the number of cycles increased. Based on AE signals, the cracking mode classification was analyzed on the basis of the average frequency and the rise angle of the waveforms. It was observed that the Felicity ratio gradually decreased with the increase in the stress level, which showed a cumulative damage effect. From the perspective of energy, the obvious increase of AE energy rate was mainly concentrated in the early and late stages of uniaxial compression, while the significant increase of dissipated energy rate occurred in the late stage of uniaxial compression. During the cyclic loading and unloading, most of the work done by external forces in the compaction stage and the elastic stage was converted into elastic strain energy, and dissipated energy began to gradually increase in the stage of stable fracture development. In addition, it was found that the damage evolution of the rock samples changed from slow to fast, and the dissipated energy ratio increased when failure was approaching.

Experimental evaluation of fatigue damage in two-stage loading tests based on the energy dissipation

2015 ◽  
Vol 229 (7) ◽  
pp. 1280-1291 ◽  
Author(s):  
Giovanni Meneghetti ◽  
Mauro Ricotta ◽  
Bruno Atzori
Keyword(s):  
Energy Dissipation ◽  
Fatigue Test ◽  
Fatigue Damage ◽  
Stress Amplitude ◽  
Mechanical Energy ◽  
Heat Energy ◽  
Dissipated Energy ◽  
External Loading ◽  
Test Results ◽  
Stored Energy

Heat energy dissipation is a manifestation of damage accumulation in fatigue-loaded components. Once recognized that some mechanical energy has to be expended to fatigue a material, energy partition into heat and stored energy is thought of as a material property in the present testing conditions. However, most of the mechanical input energy is dissipated as heat; therefore, the stored energy is difficult to estimate as difference between the expended and the dissipated energy. In this article heat energy is assumed as an index of fatigue damage. Since it reflects the material response to external loading, heat energy was seen to reduce the scatter of constant amplitude fatigue test results with respect to the use of the stress amplitude. Moreover, two-level fatigue test results could be interpreted with a higher level of accuracy when Miner’s rule was applied in terms of energy rather than stress amplitude.

scholarly journals Reconstruction of the 3D pressure field and energy dissipation of a Taylor droplet from a $$\upmu$$PIV measurement

2021 ◽  
Vol 62 (4) ◽  
Author(s):  
Ulrich Mießner ◽  
Thorben Helmers ◽  
Ralph Lindken ◽  
Jerry Westerweel
Keyword(s):  
Energy Dissipation ◽  
Pressure Gradient ◽  
Pressure Field ◽  
Estimation Method ◽  
Dissipated Energy ◽  
Spatial Integration ◽  
Mean Flow ◽  
Bypass Flow ◽  
Taylor Flow ◽  
Piv Measurement

Abstract In this study, we reconstruct the 3D pressure field and derive the 3D contributions of the energy dissipation from a 3D3C velocity field measurement of Taylor droplets moving in a horizontal microchannel ($$\rm Ca_c=0.0050$$ Ca c = 0.0050 , $$\rm Re_c=0.0519$$ Re c = 0.0519 , $$\rm Bo=0.0043$$ Bo = 0.0043 , $$\lambda =\tfrac{\eta _{d}}{\eta _{c}}=2.625$$ λ = η d η c = 2.625 ). We divide the pressure field in a wall-proximate part and a core-flow to describe the phenomenology. At the wall, the pressure decreases expectedly in downstream direction. In contrast, we find a reversed pressure gradient in the core of the flow that drives the bypass flow of continuous phase through the corners (gutters) and causes the Taylor droplet’s relative velocity between the faster droplet flow and the slower mean flow. Based on the pressure field, we quantify the driving pressure gradient of the bypass flow and verify a simple estimation method: the geometry of the gutter entrances delivers a Laplace pressure difference. As a direct measure for the viscous dissipation, we calculate the 3D distribution of work done on the flow elements, that is necessary to maintain the stationarity of the Taylor flow. The spatial integration of this distribution provides the overall dissipated energy and allows to identify and quantify different contributions from the individual fluid phases, from the wall-proximate layer and from the flow redirection due to presence of the droplet interface. For the first time, we provide deep insight into the 3D pressure field and the distribution of the energy dissipation in the Taylor flow based on experimentally acquired 3D3C velocity data. We provide the 3D pressure field of and the 3D distribution of work as supplementary material to enable a benchmark for CFD and numerical simulations. Graphical abstract

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