Strain Energy Dissipation Research Articles

Energy Evolution Characteristics and Performance Parameter Degradation of Rubber-Mixed Concrete in Sulfate Attack Environment

In order to study the sulfate resistance of rubber concrete (RC), the compressive strength test of RC with different contents (0%, 5%, 10%, and 15%) was carried out, and the proportion of RC with standard curing for 28 days was optimized. Sulfate attack test was carried out on the selected RC and compared with normal concrete (NC). The degradation degree was measured from the effective porosity, relative dynamic elastic modulus, SO42− concentration, and SEM microstructure observation after different attack times. The energy analysis method is used to study the evolution law of total strain energy, elastic strain energy, and dissipated strain energy of NC and RC in the process of deformation and failure after different attack times, and the influence of sulfate attack on concrete is explored from the perspective of energy. The results show that with the progress of sulfate attack, the effective porosity of NC and RC both decreases first and then increases, and the relative dynamic elastic modulus increases first and then decreases. Rubber is beneficial to improve the sulfate resistance of concrete, delay the attack of SO42− on concrete, and improve the ductile deformation of concrete. This study can provide a theoretical reference for the application of RC in practical engineering.

Thermal Damage Constitutive Model and Brittleness Index Based on Energy Dissipation for Deep Rock

In deep underground engineering, rock usually encounters a high temperature problem. The stress–strain relationship of rock under high temperatures is the basis of engineering excavation. Based on the Lemaitre’s equivalent strain hypothesis and energy dissipation theory, the thermal damage constitutive model of rock is established. The results show that the peak stress, ultimate elastic energy and dissipated energy at the peak all decrease with the increase of temperature in a logistic function, which indicates that the increase of temperature aggravates the deterioration of rock’s mechanical properties. Compared with rock’s constitutive model that is established on strength criterion, the thermal damage constitutive model based on energy dissipation better reflects the phenomenon of stress drop after the peak and well describes the whole stress-strain curve of rock failure, which verifies the rationality of the model. The damage model further improves the theoretical system of the rock damage constitutive model and makes up for the defect in that the traditional damage model cannot reasonably explain the nature of rock failure. The brittleness index, defined based on the energy drop coefficient, shows a logistic function with the increase of temperature, which has good physical meaning. Analyzing the phenomenon of the rock stress drop from the perspective of energy is of great significance for deeply understanding the brittle fracture mechanism of rock.

Mechanical Property of Beam-to-Column Connection of Steel Structures With All-Steel Buckling-Restrained Braces

To avoid brittle fracture and plastic yielding of steel beam-to-column connections under earthquakes, a new beam-to-column connection of steel structures with all-steel buckling restrained braces (BRBs) is proposed. The all-steel BRB is connected to the steel beam and column members through pins to form a new connection system. Taking the T-shaped beam-to-column connection steel structure as the research object, two structural types with an all-steel BRB installed on one side (S-type) and two sides (D-type) are considered. Theoretical equations of the connection system’s initial stiffness and yield load are derived through the mechanical models. The yield load, main strain distribution, energy dissipation, and stiffness of the connection system are investigated through quasi-static tests to verify the connection system’s seismic performance. The tests revealed that the proposed new connection system is capable of achieving a stable hysteresis behavior. At the end of loading, the beam and column members are not damaged, and the plastic deformation is concentrated in the plastic energy dissipating replaceable BRB, and the beam and column basically remain elastic. The proposed equations approximately estimated the load response of the proposed connection system. The results show that the damage mode of this new connection system under seismic loading is BRB yielding, with an elastic response from the beam-column members.

Damage characteristics of semi-infinite aluminium targets subjected to normal and oblique projectile impact

The present study investigates the ballistic performance of 50 mm thick 7075-T651 aluminum target against 7.62 API projectile. The focus of this study is to understand the dissipation of total energy engendered by the projectile in impacting the plate target at 0 (normal), 30° and 60° obliquities. Further, the penetration mechanisms and local as well as global plastic deformations developed in the target and projectile were explored. The ballistic experiments on the targets were performed by employing a universal gun and the depth of penetration of the projectile in the target was observed. Three-dimensional computational modelling of projectile and target was carried out in ABAQUS/Explicit module. The material response of both projectile and target was described by the Johnson-Cook strength and damage model. The influence of projectile deformation on the impact resistance of targets was also studied. The plastic strain energy dissipation in the target as well as projectile was evaluated using the validated numerical results and discussed in terms of the damage evolution and local as well as global deformation modes developed in the target and projectile during the impact process.

Strain characteristics and energy dissipation laws of gas-bearing coal during impact fracture process

To reveal fracture mechanism of gas-bearing coal subjected to complex geology environment, the impact dynamics experiments were conducted to study energy characteristics based on split Hopkinson pressure bar (SHPB) system. The incident, reflected and transmission strain were collected to calculate various energy. It was found reflected strain was always larger than transmission strain. Therefore, the reflected energy was generally higher than transmission energy under different loading conditions, but they were smaller than incident energy. With time evolution, both elastic deformation and dissipative energy experienced slow increase, rapid increase, peak point and decrease stage regardless of loading conditions. Before macro failure, micro-meso fractures had changed drasticly, which also involved intense energy conversion. So dissipative energy peak was earlier than that of elastic deformation energy. Due to pre-damage of static load and weakening effects of gas, the dissipative energy decreased with their increases (static load from 2.00 to 9.00 MPa and gas pressure from 0.25 to 1.50 MPa) during impact fracture process. However, at high confining pressure and dynamic load environment, the impact failure of gas-bearing coal exhausted massive energy. These energy characteristics will provide guidances to prevent and control disaster during coal mining and coal seam gas (CSG) exploitation in deep area.

Linear energy storage and dissipation laws of concrete under uniaxial compression at different ages

To investigate the influence of age on energy storage and dissipation laws, uniaxial compression (UC) and single–cyclic loading–unloading uniaxial compression (SCLUC) tests were conducted on C35 concrete specimens with ages of 3 d, 7 d, 15 d, 28 d. The experimental results showed that the input strain energy (ISE), elastic strain energy (ESE), and dissipated strain energy (DSE) increased nonlinearly with the stress level during the pre-peak loading stage. Analyzing the relationship between the three strain energies, both ESE and DSE increase linearly with the increase of ISE in the pre-peak loading stage at different ages, namely, linear energy storage and dissipation laws exist in every ages. Based on the linear energy storage and dissipation laws, a novel method was proposed to calculate the DSE and ESE at the ultimate strength point of the concrete at different ages. In addition, we found that the DSE was greater than the ESE of concrete in the loading stage, because the energy was mainly dissipated in forming cracks, grain dislocation, and producing plastic displacement during compression. The value of compression energy storage coefficient represents the capacity of the concrete to store ESE, whereas energy dissipation coefficient represents the strain energy dissipation capacity of concrete. In the future, based on the linear energy storage and dissipation laws of concrete, the new method for calculating the damage variable may be proposed.

Loading-unloading behavior of a clayey rock under thermo-hydro-mechanical conditions

Various investigations have been carried out on the hydro-mechanical behavior of geomaterials, but those of clayey rock are still limited. Among these existing studies, very few data are available related to the thermal effects, particularly the loading-unloading behavior of clayey rock at high temperatures. In this paper, undrained loading-unloading triaxial tests on undisturbed specimens of Boom Clay extracted from Mol, Belgium, were carried out with the aim to study (1) the influence of temperature and load path on the thermo-hydro-mechanical behavior of clayey rock, and (2) the formation mechanism of loading-unloading stress-strain hysteresis loops. The test results first revealed the stress paths–dependent stress-strain behavior of Boom Clay. The increase of initial mean effective stress p0′ has a positive effect on the mechanical behavior of Boom Clay. Secondly, temperature elevation induced the strength weakening of Boom Clay even under loading-unloading conditions. Thirdly, the p0′ and temperature had a bearing on the loading-unloading elastic modulus (defined as the peak-to-peak secant modulus of a hysteresis loop). Strain energy dissipation during the loading-unloading is then discussed from the perspective of thermodynamics. Finally, the study concludes that the stress-strain hysteresis loops for Boom Clay may be closely related to its high content of adsorbed water, and it may be driven by the combined effect of “friction resistance” and “viscous resistance.”

Damping of rubberized recycled aggregate concrete and damping estimation of its elements by finite element analysis

Concrete structures inevitably suffer from dynamic loadings, causing damage and uncomfortable vibration. Improving the damping of concrete to passively absorb the vibration energy is beneficial to mitigate the hazards and improve comfort. However, at least two challenges must be completed before applying this strategy, namely, preparing effective energy dissipating concrete and estimating the damping parameter of its elements and structures. In this study, rubberized recycled aggregate concrete (RRAC), prepared with coarse recycled concrete aggregate (RCA) and recycled rubber aggregate (RRA) instead of natural aggregate, is experimentally validated to show higher damping. Besides, a universal function of energy dissipation over strain amplitude is established for concrete containing natural aggregate, RCA, and RRA. Based on the found strain–energy dissipation function and finite element analysis, an iterative method of estimating the inner damping ratio of RRAC elements from the material damping is proposed and validated. Through the proposed method, the effects of loading amplitude, loading frequency, and stress history on the nonlinear damping behaviors of RRAC beams are numerically analyzed. The experiment result and the proposed damping determination method can encourage the application of recycled building materials in structural engineering, especially in projects with requirements of vibration control.

Seismic performance of a novel partial precast RC shear wall with reserved cast-in-place base and wall edges

Precast reinforced concrete (RC) shear walls have attracted significant research efforts due to advantages over the conventional construction methods such as better quality control, shorter construction time and less environmental impact. Research efforts have been dedicated to exploring alternative methods for the connections of precast shear walls. In this paper, a novel partial precast shear wall is proposed, which is made of a precast shear wall with double-legs at the base, and reserved cast-in-place base zone and wall edges. To begin, the design concept of the proposed precast shear wall is described. A comprehensive experiment program is then presented, in which two groups of identical full-scale shear walls were designed, constructed and tested in a cyclic pseudo-static manner in order to investigate the seismic performance of the proposed wall. Each group consisted of three specimens, one cast-in-place and two proposed walls. These two groups of specimens were tested under a high axial load index of 0.3 and 0.4, respectively. The test results indicate that the failure modes of the proposed partial precast walls were similar with those constructed with cast-in-place method. For both axial load indices, the precast walls had comparable seismic performance with the cast-in-place walls in terms of lateral load capacity, stiffness degradation, steel strain behavior, energy dissipation, and residual displacement but better deformability and ductility. In addition, higher axial load indices resulted in decrease in ductility and increase in residual displacements. Moreover, the same precast walls in the same group had similar performance, providing confidence in the repeatability of the test results and stable performance of the proposed walls. It can come to the conclusion that the proposed partial precast shear walls can have comparable and stable seismic performance with the conventional cast-in-place method and hence can be taken as an alternative in practice.

Capturing Dynamic Behaviors of a Rate Sensitive, Elastomer with Strain Energy Absorptions and Dissipation Effects

A strain-rate-sensitive polyurethane elastomer is numerically investigated to reveal impact behaviors and analyze the inputted strain energy dissipation features with concerned rate dependencies. In view of the amorphous structure of elastomers, a thermo-mechanical model is developed via relating the macro-mechanical behaviors to micro-structural changes through molecular transitions and two distinct flow activations with each possessing a unique activation energy. Under large straining, detangling of molecular chains and networks through sliding is found to produce serious frictional effects resulting in instantaneous heat generation and temperature rise. To incorporate these heat-effected issues, an instantaneous temperature rise is calculated at each macro-level material point to ascertain the localized changes in the associated mechanical response. The overall perspectives of the dynamic mechanical behavior including visco-elastic large deformation, rate dependent yielding, thermal softening, flow at plateau stress, and strain hardening are found well captured. Investigations are extended for the material recoverability and accordingly, strain energy absorptions are clarified. Finally, a power law function is proposed for designing the energy absorption relation to the applied loading rate.

Investigation on Pore-Fracture of Coal and Its Influence Mechanism on Tensile Failure Behavior of Coals with Bursting Proneness

Both computed tomography (CT) and notched semicircular bend (NSCB) tests are performed for coals with high and medium bursting proneness to extract the scientific expression of pore-fracture and its influence mechanism on the tensile failure behavior. The acoustic emission (AE) parameters in the sample during loading and failure are monitored, and the influence mechanism of pore-fracture on tensile failure behavior of coal is analyzed. The result illustrates that the spatial distribution feature of the pore-fracture in coals with high and medium bursting proneness is extremely different. The deformation and failure mode of the coals are affected by many factors, loading mode, notch depth and width, mechanical properties of matrix and minal, spatial distribution feature of pore-fracture, etc. The influence of primary pore-fracture in the coal on the extension and penetration of the secondary fracture could be divided into two types: bifurcation and promotion, which would cause different local damage in the sample and affect the final failure mode. The feature of acoustic emission parameters indicates that the deformation and failure process of a sample under loading could be divided into four stages: compaction stage, elastic deformation stage, displacement plastic growth stage, and post peak failure stage, which is the result of comprehensive action of many factors. The evolution process of secondary fracture is accompanied by the dissipation of elastic strain energy and the intensification of internal damage of coal, which reflects the failure process of coal.

Theoretical damage characterisation and damage evolution process of intact rocks based on linear energy dissipation law under uniaxial compression

The investigation of rock damage behaviour is an important requirement for ensuring stability control and safety prediction in rock engineering. In this study, based on the linear energy dissipation law and energy dissipation coefficient, a theoretical method is introduced for characterising the damage of intact rocks under uniaxial compression conditions. The existing uniaxial compression test data of 14 kinds of rock materials (including 6 types of granite , 4 types of sandstone , 2 types of marble, 1 type of slate, and 1 type of limestone) were used to verify the effectiveness of the damage characterization method. The results indicate that the damage evolution process of rocks under uniaxial compression can be fully expressed by the proposed theoretical damage characterisation method, and the damage variable exhibits a quadratic functional relationship with the loading stress level. Moreover, with the linear energy storage law serving as a theoretical basis, the peak dissipated strain energy in a rock damage expression under uniaxial compression can be accurately calculated. The new theoretical damage characterisation method overcomes the shortcomings of conventional damage characterisation methods (e.g. estimating the peak dissipated strain energy through a hypothesis), and provides a new means for analysing rock damage from an energy viewpoint.

Experimental investigation on the strain energy evolution mechanism of granite specimens with a single flaw

Damage and fracture of rocks is a comprehensive result of strain energy dissipation and release. In order to study the energy evolution mechanism of hard brittle rock masses during failure process, uniaxial compression tests on the granite specimens with a single pre-existing flaw are carried out with digital image correlation method (DIC). The results indicate that: (1) The stress fluctuation before structural failure corresponds to the sudden increase of the dissipated energy, the essence is that rock masses occur obviously damage and cracking. (2) For medium flaw dip angles, the stress fluctuation occurs repeatedly in stages, whose strain energy is dissipated gradually; for large or small dip angles, the stress fluctuation is almost not appeared, and the energy dissipation is insignificant. (3) With the increase of flaw dip angles, the dissipated energy ratio at the peak stress first increases and then decreases showing an inverted U-shaped, resulting in a similar law of rock damage but a contrary law of strength; the corresponding elastic energy ratio is U-shaped of decreasing first and then increasing, causing the structural failure changes from dynamic to static and then to dynamic again. The results can provide theoretical references for the formation mechanism and prevention method of dynamic disasters of rock underground engineering.

Low cycle fatigue response of differently aged AA6063 alloy: Statistical analysis and microstructural evolution

Understanding the dynamic structural changes during cyclic deformation of Al-alloys is a discipline of great interest to material technologists. The primary objective of this report is to assess the low cycle fatigue (LCF) behaviour of AA6063 alloy in under-aged (UA), peak-aged (PA) and over-aged (OA) states and to understand the energetic aspects of cyclic plastic behaviour in the background of the nature and density of the dislocations. Two parameters Weibull distribution analyses, for the first time, establish that despite inferior monotonic strength, LCF life of UA alloy is twice compared to PA alloy at higher (≥0.5%) strain amplitudes. This corroborates well with the fact that the cumulative dissipated plastic strain energy density (CPSED) values exhibit reverse variation with applied strain amplitude in the case of UA alloy as compared to PA and OA alloys. TEM analyses confirm that strain-induced vacancy-driven dynamic precipitation causes dramatic cyclic hardening in UA alloy resulting in improved fatigue life. One can also evidence this from the fivefold increase in the plastic strain energy dissipation and 2-times increased of post-fatigue hardness. In contrast, fracture surface analyses and XRD-based dislocation density measurements coupled with TEM examinations reveal that the shearing or by-passing of precipitates by the dislocations in the PA or OA alloys, respectively, lead to strain localization and cyclic softening, and consequently, reduce the plastic strain energy dissipation and lower fatigue life. The study provides important guidelines for the development of high strength Al-alloys with improved fatigue performance.

Virtual multi‐dimensional internal bonds model with fracture energy conservation for three‐dimensional numerical simulation of laboratory scale fluid pressurized fracturing

AbstractStrain‐softening models have proved effective in treating fracturing under mechanical load. However, these models tend to suffer from mesh‐size dependency due to failure in preserving the fracture energy. The Virtual Multi‐Dimensional Internal Bond Model (VMIB) is derived from a particle‐based constitutive law at the micro scale that is implemented in a 3D Finite Element Method (FEM), in which material softening and energy dissipation occur in the “representative elementary volume”. However, according to the classic fracture mechanics theory, energy dissipation is due to the creation of new fracture surfaces instead of homogenized softening within the volume element. Therefore, the dissipated strain energy has to be consistent with the fracture energy during failure process. We present an improved VMIB model to bridge the energy storage in a volume and dissipation over a fracture surface. This is accomplished by developing a 3D virtual bond potential that incorporates the material fracture energy and eliminates the mesh‐size sensitivity. The virtual bond potential considers both the critical fracture energy and element size. The 3D model is calibrated and verified simulations of a group of three‐point‐bend tests. Then, by incorporating the coupled three‐dimensional element partition method, the model is applied to a series of laboratory scale fluid pressurized fracturing experiments. Multiple fracture propagation from closely‐staged cluster from a laboratory test is simulated. The comparisons between numerical and experimental results indicate that the model captures the fractures growth influenced by the stress boundary conditions and the stress shadow. The predicted breakdown pressure reasonably agrees with the experiment data.

Investigation of design and performance improvements on solid resilient tires through numerical simulation

Solid tires are often utilized to bear excessive loads. Therefore, sidewall cracks and internal heat build-up affect their durability more significantly. It is a challenge to minimize these factors and improve tire performance while maintaining the functionality of the solid tire. Moreover, there are no specific standard guidelines for modifying the solid tire design to achieve this objective. This study proposes several design and performance improvements to the solid resilient tire and investigates the performance of these modified designs using the Finite Element (FE) method under static and dynamic conditions. For these FE simulations, suitable hyperelastic models are obtained using curve fitting combined with three standard error measures. The results show that the Mooney-Rivlin, Ogden, and Yeoh material models show good agreement with experimental data for modelling the base, cushion, and tread layers of the tire, respectively. The developed FE models are validated using experimental data obtained from a leading tire manufacturing company in Sri Lanka. The validated model is used to develop and analyse two distinct tire models which have two different cavity geometries (circular and elliptical) in their cushion layers to minimize heat build-up and sidewall cracks. The tire reinforcements are also rearranged to further improve the performance of the models. The introduction of cavities helps to reduce strain energy dissipation and to increase the dissipation of internal heat by convection. Furthermore, the stress intensity on the side walls is also reduced, thereby minimizing sidewall cracks. Numerical experiments show that the modified designs have a lower strain energy density, lower stress concentration, and less material utilization when compared to the basic tire design.

A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

AbstractIn this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero‐energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two‐phase stabilization scheme is formulated based on an energy method that incorporates inhomogeneous solid deformation and fluid flow. In this method, the nonlocal formulations of skeleton strain energy and fluid flow dissipation energy equate to their local formulations. The stable coupled nonlocal poromechanics model is solved for dynamic analysis by an implicit time integration scheme. As a new contribution, we validate the coupled stabilization formulation by comparing numerical results with analytical and finite element solutions for one‐dimensional and two‐dimensional dynamic problems in saturated porous media. Numerical examples of dynamic strain localization in saturated porous media are presented to demonstrate the efficacy of the stable coupled poromechanics framework for localized failure under dynamic loads.

Analysis of Mudstone Fracture and Precursory Characteristics after Corrosion of Acidic Solution Based on Dissipative Strain Energy

The deformation and failure of rock materials are closely related to the strain energy characteristics during the loading process. These strain energy characteristics and rock properties are greatly affected when the rock is subjected to the acidic solution. To study the effects of chemical solutions with different pH on the mechanical properties and strain energy mechanism of mudstone, the chemical corrosion mudstone samples are subjected to a uniaxial loading testing machine (CN64 electro-hydraulic servo). The corrosive effects of the acidic solution on the porosity, strain energy characteristics, and failure mode of mudstone samples were thoroughly investigated. The findings of this research indicate that: (1) The rate of change in the porosity and chemical damage coefficient of rock samples after chemical corrosion decreases, which is closely linear with the increase of solution pH; (2) The total strain energy, elastic strain energy, and dissipative strain energy decrease with the increase of pH, and, as a result, it is proposed that the observed turning point of the proportion curve of dissipated strain energy from decline to rise is used as a precursor point of the rock failure; (3) The stress value of the failure precursor point increases and the strain value decreases with the increase in pH value. However, the ratio of the stress value of the failure precursor point to the peak stress hardly changes with pH value, and its value is about 0.883; and (4) Rock samples soaked in a weak acidic chemical solution (pH 7.3 and 5.3) are damaged by tensile crack, while rock samples soaked in a strong acidic chemical solution (pH 3.3 and 1.3) are mainly damaged by the combination of tensile and shear. The findings of this study can be used to provide an experimental and theoretical foundation for monitoring rock engineering disasters such as slope, tunnel, and coal mine failures.

Cracking elements method with a dissipation-based arc-length approach

The dissipated strain energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used to develop an arc-length constraint equation for tracking the energy dissipation path instead of the elastic unloading path of the response of a structure. This was the motivation for the development of a dissipation-based arc-length method, followed by its implementation in the framework of the recently proposed Global Cracking Elements Method (GCEM). The dissipated energy is extracted with the help of the crack openings and tractions, i.e. by means of the displacement jumps and the cohesive forces between the two surfaces of a crack. The stiffness factor of the arc-length constraint equation is obtained in the solution process by means of the Sherman-Morrison formula. Several numerical tests are performed. The results demonstrate the robustness of the proposed method. It captures both global and local peak loads and all snap-back parts of the force-displacement responses of loaded structures with multiple cracks. • The dissipated energy is directly determined by the crack openings and tractions as opposed to indirect determination by forces and displacements. • Path following and crack propagating are treated simultaneously without a special strategy. • The Sherman-Morrison formula is used for implementation of the solution process and the coding efforts are reduced. • The stiffness factor of the arc-length constraint is obtained during, rather than before, the solution process.

Large Amplitude Oscillatory Shear testing for the performance grading of straight and polymer modified asphalt binders

This paper discusses the accuracy of performance grading through Large Amplitude Oscillatory Shear (LAOS) testing of asphalt binders, in comparison to results obtained by well-validated Double-Edge-Notched Tension (DENT) tests. The LAOS test is proposed as both a qualitative and quantitative method of analysing binder performance through Lissajous-Bowditch plots, and repeatable correlations between peak strain energy dissipation and CTOD values. The correlation between LAOS and Critical Crack Tip Opening Displacement (CTOD) in the DENT test is found to be strong. The findings of this preliminary study on a limited set of binders suggest that LAOS tests may provide practical measures of performance in high strain failure.