Variation Of Elastic Energy Research Articles

Phase-field modeling of thermal shock fracture in functionally graded materials

In this paper, the thermo-elastic fracture problems of functionally graded materials (FGMs) are thoroughly investigated based on a modified phase field model. In this model, the material constants and fracture toughness vary along a specified direction, the thermal conductivity and stiffness constants in the damaged regions are degraded by the phase-field variable, and the crack evolution is driven by the variation of elastic energy induced by the thermo-mechanical loading. Therefore, the temperature, mechanical and damage fields are coupled with each other. The validation of the present approach has been checked by comparing the present results with the analytical, numerical, and experimental results in literature. The examples of thermo-elastic tensile fracture and thermal shock cracking of FGMs are performed to investigate the influence of material heterogeneity and external thermal loading. Furthermore, the experimental phenomenon of crack deflection in FGMs has been captured by the present simulations. The present study provides a guidance for understanding the fracture mechanism, material design and safety assessment of FGM structures in engineering practice.

Development of the variation-of-elastic-energy-based virtual fields method for parameter identification of incompressible and compressible hyperelastic materials

The virtual fields method (VFM) has played a pivotal role in parameter identification of hyperelastic materials, spanning from rubbers to soft tissues. A key challenge in VFM lies in calculating the internal virtual work, which necessitates the computation of the stress and its conjugate virtual strain. In this study, we introduce a novel theoretical framework for VFM, which directly computes the internal virtual work based on the variation of elastic energy (VEE). The proposed method, namely VEE-VFM, eliminates the calculation of stress and virtual strain, making it remarkably user-friendly compared with the conventional approach. We extend VEE-VFM to both incompressible and compressible hyperelastic materials, including invariant-based and principal stretch-based models. In the end, we demonstrate the accuracy of VEE-VFM and its robustness against noise with numerical experiments.

Experimental study on mechanical properties of sprayed ECC under quasi-static and cyclic loading

The tunnel lining will be subjected to the cyclic action of high ground stress during service. However, there is a lack of research on the damage evolution mechanism of sprayed engineered cementitious composites (ECC) under cyclic loading. Herein, we studied the strain rate effect and fatigue damage evolution mechanism of sprayed ECC by conducting compression and bending tests at different quasi-static strain rates and high-stress cyclic loading-unloading compression and bending tests. The results show that with the increase of strain rate, the compressive peak stress and bending strength of sprayed ECC show an upward trend, as well as the increase of the change rate. At 8.3 × 10−3 s−1, the compressive SGF is 1.52, with an energy storage limit density of 0.501MJ/m3. At 2.1 × 10−2 s−1, the bending SGF is 1.52, with a peak fracture energy of 49.29 J. In addition, under the compression test, the tensile shear failure of specimens develops from finer double shear planes to coarser multiple shear planes. Under the bending test, the position of the main crack of specimen is gradually transferred from the mid-span to both sides. Under high stress cycle test, the input energy and dissipation energy of the two tests have the similar trend, showing “U” type. The variation of elastic energy and dissipation energy conversion rate exhibits a “U” type with different directions. At the last loading, the dissipation energy conversion rate of compression test is 46.8%, while that of bending test is 70.4%. The damage variable of specimen increases significantly with the increase of the number of cycles, accompanied by an increase in the degree of breakage. In addition, the damage variables based on deformation characteristics are higher than those based on energy characteristics.

Energy and Infrared Radiation Characteristics of the Sandstone Damage Evolution Process.

The mechanical characteristics and mechanisms of rock failure involve complex rock mass mechanics problems involving parameters such as energy concentration, storage, dissipation, and release. Therefore, it is important to select appropriate monitoring technologies to carry out relevant research. Fortunately, infrared thermal imaging monitoring technology has obvious advantages in the experimental study of rock failure processes and energy dissipation and release characteristics under load damage. Therefore, it is necessary to establish the theoretical relationship between the strain energy and infrared radiation information of sandstone and to reveal its fracture energy dissipation and disaster mechanism. In this study, an MTS electro-hydraulic servo press was used to carry out uniaxial loading experiments on sandstone. The characteristics of dissipated energy, elastic energy, and infrared radiation during the damage process of sandstone were studied using infrared thermal imaging technology. The results show that (1) the transition of sandstone loading from one stable state to another occurs in the form of an abrupt change. This sudden change is characterized by the simultaneous occurrence of elastic energy release, dissipative energy surging, and infrared radiation count (IRC) surging, and it has the characteristics of a short duration and large amplitude variation. (2) With the increase in the elastic energy variation, the surge in the IRC of sandstone samples presents three different development stages, namely fluctuation (stage Ⅰ), steady rise (stage Ⅱ), and rapid rise (stage Ⅲ). (3) The more obvious the surge in the IRC, the greater the degree of local damage of the sandstone and the greater the range of the corresponding elastic energy change (or dissipation energy change). (4) A method of sandstone microcrack location and propagation pattern recognition based on infrared thermal imaging technology is proposed. This method can dynamically generate the distribution nephograph of tension-shear microcracks of the bearing rock and accurately evaluate the real-time process of rock damage evolution. Finally, this study can provide a theoretical basis for rock stability, safety monitoring, and early warning.

Study on mechanical properties and energy evolution of coal under liquid nitrogen freezing

To investigate coal’s mechanical properties and energy evolution laws under different liquid nitrogen (LN2) freezing conditions, uniaxial compression experiments were carried out on frozen coal samples, with water saturation and LN2 freezing time as variables. Based on the experimental results, the mechanical properties, acoustic emission characteristics, and energy release laws of coal were analyzed, and the mechanism of mechanical strength enhancement of coal frozen by LN2 was also discussed. The results prove the positive role of LN2 freezing in enhancing coal’s mechanical strength, that is, under the action of LN2 freezing, both the uniaxial compressive strength and elastic modulus of coal increase with the increase in water saturation and LN2 freezing time. Besides, the longer the LN2 freezing time, the longer the time the loaded coal maintains the elastic stage. At the compaction stage, acoustic emission events with large amplitude frequently occur due to the sliding friction between ice particles and the coal matrix. Under the action of LN2 freezing, the water in coal pores turns into the ice with an expanded volume and then fill the pores, which weakens the stress concentration effect at the crack tip and further prevents the crack extension of the loaded coal. With the increase in water saturation and LN2 freezing time, two peak points gradually appear on the curve of elastic energy variation of frozen coal with strain, indicating that LN2 freezing enables water-containing coal to withstand deformation even after the initial load damage. The formation of pore ice has three positive effects on coal’s mechanical strength enhancement, i.e., pore ice bears a certain mechanical strength, plays a cementing role, and reduces the stress concentration at the crack tip.

Reformulation of the Virtual Fields Method Based on the Variation of Elastic Energy for Hyperelastic Materials

Reformulation of the Virtual Fields Method Based on the Variation of Elastic Energy for Hyperelastic Materials

Phase-field modeling of hydro-thermally induced fracture in thermo-poroelastic media

This paper develops a phase-field approach to model hydro-thermally induced crack propagation in thermo-poroelastic media. Both thermal conduction and convection, and the fully thermo-poroelastic coupled effect are taken into consideration in the phase-field model. The fluid content is influenced by the volumetric strain, temperature, and pressure. The heat flux is susceptible to temperature change and fluid flux. The injection fluid pressure and thermal loading trigger the variation of elastic energy, and then drive crack propagation, which is captured by the phase-field variable. A segregated solution scheme and the finite element implementation details are provided here for solving the nonlinear thermo-poroelastic problem. Several examples are tested to verify the present approach and to show its ability to simulate hydro-thermally induced crack propagation in the application of cold fluid injection in a cracked reservoir. The numerical results indicate that the development of the thermal effect on crack propagation is slow when compared with that of the fluid pressure. The present approach can serve as a convenient simulation tool for crack propagation in geothermal and oil/gas reservoir developments.

Pumping Patterns and Work Done During Peristalsis in Finite-Length Elastic Tubes.

Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities, and pressure variations is presented. This simplified model is compared with detailed fluid-structure three-dimensional (3D) immersed boundary (IB) simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our one-dimensional (1D) model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of work done during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

Misorientation dependence of the grain boundary migration rate: role of elastic anisotropy

ABSTRACT In this work, numerical computations of image forces and stored energy during the growth of a strain free grain within a recovered matrix containing an array of identical dislocations are performed. A decrease of the stored energy is observed when image forces are attractive and an increase when image forces are repulsive. The variation of elastic energy depends closely on the material elastic anisotropy, the number of dislocations in the array and its initial distance to grain boundary. For an array of 20 edge dislocations and the motion of a planar grain boundary over approximately 180 atomic spacing, the magnitude of the energy variation is on the order of one dislocation line energy for Al and six for Cu, which is significant in both cases. Furthermore, by sweeping the whole orientation space for FCC crystals, it is shown that grain boundaries near a misorientation are among those that can display the highest attractive forces on edge dislocations. Since grain boundary migration is driven by the reduction of stored energy, the results are analysed in light of experimental recrystallization data in FCC metals which show that the fastest moving boundaries are often characterised by misorientation axis around and misorientation angle close to .

Shale Brittleness Index Based on the Energy Evolution Theory and Evaluation with Logging Data: A Case Study of the Guandong Block.

Shale brittleness is a key index that indicates the shale fracability, provides a basis for selecting wells and intervals to be fractured, and guarantees the good fracturing effect. The available models are not accurate in evaluating the shale brittleness when considering the confining pressure, and it is necessary to establish a new shale brittleness model under the geo-stress. In this study, the variation of elastic energy, fracture energy, and residual elastic energy in the whole process of rock compression and failure is analyzed based on the stress–strain curve in the experiments, and a shale brittleness index reflecting the energy evolution characteristics during rock failure under different confining pressures is established; a method of directly evaluating the shale brittleness with logging data by combining the rock mechanic experiment results with logging interpretation results is proposed. The calculation results show that the brittleness decreases as the confining pressure increases. When the confining pressure of the Kong-2 member shale of the Guandong block is less than 25 MPa, the brittleness index decreases significantly as the confining pressure increases, and when the confining pressure is greater than 25 MPa, the brittleness index decreases slightly. It is shown that the shale brittleness index is more sensitive to the confining pressure within a certain range and less sensitive to the confining pressure above a certain value.

Variation of Elastic Energy Shows Reliable Signal of Upcoming Catastrophic Failure

We consider the Equal-Load-Sharing Fiber Bundle Model as a model for composite materials under stress and derive elastic energy and damage energy as a function of strain. With gradual increase of stress (or strain) the bundle approaches a catastrophic failure point where the elastic energy is always larger than the damage energy. We observe that elastic energy has a maximum that appears after the catastrophic failure point is passed, i.e., in the unstable phase of the system. However, the slope of elastic energy {\it vs.\/} strain curve has a maximum which always appears before the catastrophic failure point and therefore this can be used as a reliable signal of upcoming catastrophic failure. We study this behavior analytically for power-law type and Weibull type distributions of fiber thresholds and compare the results with numerical simulations on a single bundle with large number of fibers.

Investigation of feet functions of large ruminants with a decoupled model of equivalent mechanism.

ABSTRACTCloven hooves of ruminants adapt to diverse terrain, provide propulsive force and support the whole body during movement in natural environments. To reveal how the feet ensure terrain adaptability by choosing the proper configurations and terrain conditions, we model the feet of ruminants as an equivalent mechanism with flexion-extension and lateral movement decoupled. The upper part of the equivalent mechanism can flex and extend, while the lower part performs the lateral movement. Combination of the two parts can adapt to longitudinal slope (anterior-posterior) and transverse slope (medial-lateral), respectively. When one of two digits closes laterally, the workspace of the other decreases. The distal interdigital ligament between two digits limits their motion by elastic force and stores energy during movement. Differences in elastic energy variation of the ligament on different transverse slopes are characterized based on the configurations of two digits and the elastic energy between them. If the upper one of two symmetric digits is fixed, the foot landing on the grade surface (2°) shows greater capacity for absorbing energy; otherwise, level ground is the best choice for ruminants. As for the asymmetric digits, longer lateral digits enhance the optimal adaptive lateral angle. The asymmetry predisposes the feet to damage on the hard ground, which indicates soft ground is more suitable.

Elastic energy in locomotion: Spring-mass vs. poly-articulated models

The human is often modeled as a Poly-Articulated Model (PAM) with rigid segments while some authors use a Spring Mass Model (SMM) for modeling locomotion. These two models are considered independent, and the objective of this study was to link them in order to enlighten the origin of the elasticity in locomotion.Using the characteristics of the two models, a theoretical relationship demonstrates that the variation of elastic energy of the SMM equals the variation of the internal kinetic energy minus internal forces work of the PAM. This theoretical relationship was experimentally investigated among 19 healthy participants walking and running on a treadmill.The results showed that the equality is verified except during the double support phase at 0.56ms−1, at high walking speeds (1.67 and 2.22ms−1) or during the aerial phase of running.The formal relationship showed that the global stiffness of the SMM is directly related to the work of the internal forces of the PAM, and thus, to the characteristics of the musculoskeletal system. It also showed the relevance of taking into account the participation of each joint in the global stiffness. Finally, the coordination of internal forces work to produce a global stiffness may be considered as a new criterion of movement optimization for clinical purposes or motion planning for humanoid robots.

An energy-based analysis for aggregate size effect on mechanical strength of cement-based materials

In this paper, the mechanical strength of cement-based materials is investigated. The emphasis is put on the aggregate size effect on the mechanical strength in uniaxial and triaxial compression tests. An analytical study based on Griffith’s surface energy criterion is performed. The surface energy for the creation of crack surfaces is related to the variation of elastic energy between the intact and cracked materials. The effective elastic properties of cement-based materials are estimated respectively by Mori–Tanaka scheme for the intact material and Reuss lower bound for the cracked material. The aggregate size effect is taken into account by the fact that the total energy needed for crack surface creation depends on the size of aggregates which are subjected to progressive debonding during the failure process. Further, a series of parametric studies are realized to study the effect of confining stress on the mechanical strength of cement-based materials. Comparisons between analytical results and experimental data are presented.

나노인덴테이션 해석을 통한 Ag/Cu층에서 발생하는 Misfit 전위의 slip 특성에 대한 연구

Ag/Cu층에서 발생하는 misfit 전위를 분석하기 위하여, EAM기법을 활용한 나노인덴테이션 해석을 수행하였다. N<TEX>$\'{o}$</TEX>se-Hoover 서모스텟 조건에 의거하여, 2-5nm 정도의 두께를 갖는 필름층에 구형 인덴터로 압입하였다. 해석결과는 misfit 전위에 대한 상대적인 압입위치가, 4nm이하의 필름에 대하여 영향을 미치는 것으로 나타났다. 전위에 의한 슬립 발생할 때 탄성에너지 변화는 Ag/Cu의 연화의 중요한 변수로 작용하며, 각각의 경우에 대하여 임계필름두께에 대해서도 고찰하였다. The EAM simulation of nanoindentation was performed to investigate misfit dislocation slip in the Ag/Cu. The film layer, whose thickness in the range of 2-5nm, was indented by a spherical indenter with the N<TEX>$\'{o}$</TEX>se-Hoover thermostat condition. The simulation shows that the indentation position relative to misfit dislocation (MFD) has the effect on the dislocation, glide up or cross slip, for Ag film layer thickness less than 4 nm. Elastic energy variation during MFDs slip was revealed to be a key factor for the softening of Ag/Cu. The critical film layer thickness was evaluated for each case of Ag/Cu according to the spline extrapolation technique.

Computational models for mode I composite fracture failure: the virtual crack closure technique versus the two-step extension method

This paper deals with the numerical determination of the energy release rate under mode I in carbon fibre reinforced composites (CFRC). Two different models are reviewed: the virtual crack closure technique (VCCT) and the Two-step extension method. The Two-step extension method needs two computational steps in order to calculate the energy release rate (G). The VCCT method is able to provide ERR value only from one computational step. Results were compared with empirical data obtained from double cantilever beam (DCB) tests carried out on unidirectional AS4/8552 carbon/epoxy laminates. This study showed that, in a pure mode I state, results obtained via the Two-step extension method were in agreement with a straightforward calculation of the elastic energy variation in the system. As expected, results obtained from VCCT and Two-step extension models converge as element length decreases. Regarding the comparison between experimental and numerical results, the study showed that a correction for testing devices compliance was needed to match both models.

Analysis of the dialectical relation between top coal caving and coal-gas outburst

According to the different engineering mechanical states of top coal caving and normal stoping of gaseous loose thick coal seams, the dialectical relation between this caving method and dynamic disasters was analyzed by simulating the change of stress states in the process of top coal initial caving with different mining and caving ratios based on the ANSYS10.0. The variation of elastic energy and methane expansion energy during first top coal caving was analyzed by first weighting and periodic weighting and combining with coal stress and deformation distribution of top coal normal stoping as well as positive and negative examples in top coal caving of outburst coal seam. The research shows that the outburst risk increases along with the increase of the caving ratio in the initial mining stage. In the period of normal stoping, when the mining and caving ratio is smaller than 1:3 and hard and massive overlying strata do not exist (periodic weighting is not obvious), it is beneficial to control ground stress leading type outburst. Thus, it is unreasonable to prohibit top coal caving in dangerous and outburst prone areas.

Numerical and experimental validation of computational models for mode I composite fracture failure

This work compares the numerical determination of the strain energy release rate in mode I for the interlaminar fracture of composite laminates by means of two different models: the virtual crack closure technique (VCCT) and the two-step extension method. Results were compared with empirical data obtained from double cantilever beam (DCB) tests carried out on unidirectional AS4/8552 carbon/epoxy laminates. The study showed that, in a pure mode I state, results obtained via the two-step method were in agreement with a straightforward calculation of the elastic energy variation in the system. Results from VCCT calculations were slightly lower than those obtained through the two-step method using four node elements in plane strain. As expected, results from both models converge as element length decreases.

Surface instability and delamination of epitaxially stressed bilayers

Abstract The possibility for a localized roughness to develop has been investigated at the intersection of the interface and the free surface of an epitaxially stressed bilayer. After a general derivation of the elastic energy variation due to a localized fluctuation of the surface described by a function h, the stability of the free surface with respect to two particular fluctuations has been characterized as a function of the lattice mismatch between the two layers. The formation of cracks from the localized roughness is finally discussed.

Buckling of Thin Films on Substrates: From Straight-Sided Wrinkles to Both Worm-Like and Varicose Structures

ABSTRACTThe evolution from straight-sided wrinkles to both worm-like and varicose structures has been investigated mainly by atomic force microscopy. The elastic energy variation related to the formation of these two buckling structures has been computed and discussed. It is shown that both transitions are energetically favourable above a longitudinal (along the initial wrinkle axis) critical stress of few GPa in compression, that is of the order of the internal compressive stresses present in the thin films.