A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coeff...A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method.A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted.The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions.Based on the verified theoretical models,the influences of axial static stress on longitudinal velocity,space and time attenuation coefficients and response frequency are investigated by detailed parametric studies.The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock.The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage.Moreover,the initial porosity,initial elastic modulus of the rock voids and skeleton,viscous coefficient and vibration frequency have significant effects on the P-wave velocity,attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.展开更多
A series of coupled static-dynamic loading tests is carried out in this study to understand the effect of slightly dynamic disturbance on the rocks under high static stress.The acoustic emission(AE)and digital image c...A series of coupled static-dynamic loading tests is carried out in this study to understand the effect of slightly dynamic disturbance on the rocks under high static stress.The acoustic emission(AE)and digital image correlation(DIC)techniques are combined to quantitatively characterize the damage and fracturing behaviors of rocks.The effects of three influencing factors,i.e.initial static stress,disturbance amplitude,and disturbance frequency,on the damage and fracturing evolution are analyzed.The experimental results reveal the great differences in AE characteristics and fracturing behaviors of rocks under static loads and coupled static-dynamic loads.Both the Kaiser effect and Felicity effect are observed during the disturbance loading process.The crack initiation,stable and unstable propagation in the highly-stressed rocks can be triggered by cyclic disturbance loads,and more local tensile splitting cracks are found in the rocks subjected to coupled static-dynamic loads.The damage and fracturing evolution of rocks during cyclic disturbances can be divided into two stages,i.e.steady and accelerated stages,and the increase rate and proportion of each stage are greatly affected by these influencing factors.High initial static stress,low disturbance frequency,and high disturbance amplitude are considered to be adverse factors to the stability of the rocks,which would induce a high increase rate of the steady stage and a high proportion of the accelerated stage within the whole disturbance period.Based on the two-stage damage evolution trend,a linear-exponential damage model is employed to predict the instability of the rocks under coupled static-dynamic loads.展开更多
The electromagnetic emission(EME) induced from the rock containing piezoelectric materials was investigated under both static stress and exploding stress wave in the view of piezoelectric effect. The results show that...The electromagnetic emission(EME) induced from the rock containing piezoelectric materials was investigated under both static stress and exploding stress wave in the view of piezoelectric effect. The results show that the intensity of the EME induced from the rock under static stress increases with increasing stress level and loading rate; the relationship between the amplitude of the EME from the rock under different modes of stress wave and elastic parameters and propagation distance was presented. The intensity of the EME relates not only to the strength and elastic moduli of rock masses,but also to the initial damage of the rock. The intensity of EME induced by stress wave reaches the highest at the explosion-center and attenuates with the propagation distance. The intensity of EME increases with increasing the elastic modulus and decreases with increasing initial damage. The results are in good agreement with the experimental results.展开更多
Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress...Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress.Methods:By means of computer simulation, acetabular three dimensional model was input into three dimensional finite element analysis software ANSYS7.0. The acetabular mechanical behavior was calculated and the main stress value, stress distribution and acetabular unit displacement in the direction of main stress were analyzed when anterior wall of acetabulum and acetabular crest were loaded by 1 000 N static stress. Results:When acetabular anterior wall loaded by X direction and Z direction composition force, the stress passed along 4 directions: (1)from acetabular anterior wall to pubic symphysis along superior branch of pubis firstly, (2)from acetabular anterior wall to cacroiliac joint along pelvic ring,(3)in the acetabulum,(4)from the suffered point to ischium. When acetabular crest loaded by X direction and Y direction composition force, the stress transmitted to 4 directions: (1)from acetabular crest to ilium firstly, (2)from suffered point to cacroiliac joint along pelvic ring,(3) in the acetabulum ,(4)along the pubic branch,but no stress transmitted to the ischium branch.Conclusion:Analyzing the stress distribution of acetabulum and units displacement when static stress loaded can provide internal fixation point for acetabular fracture treatment and help understand the stress distribution of acetabulum.展开更多
Background: Women are thought to be more susceptible to stress than men in a stressful society, and reducing stress is crucial for women to maintain their health. Static stretching (SST) is applied in various fields t...Background: Women are thought to be more susceptible to stress than men in a stressful society, and reducing stress is crucial for women to maintain their health. Static stretching (SST) is applied in various fields to not only increase muscle flexibility but also reduce stress. Additionally, conscious slower breathing (CSB) predominates parasympathetic activity, causing a relaxing effect. These results indicate that combining SST and CSB may be more useful in reducing stress. However, to the best of our knowledge, the effect of this combination remains unclear. Objective: This study aimed to elucidate the effects of the combination of SST and CSB on autonomic activity and stress in adult women. Methods: Eleven healthy Japanese adult female participants performed SST with nonconscious natural breathing for 20 min. The same participants performed SST in combination with CSB (2 s inspiratory and 4 s expiratory) for 20 min on another day. Salivary cortisol and chromogranin A levels were measured before and after stretching as stress markers of the hypothalamic-pituitary-adrenal axis and sympathetic nervous system. The coefficient of variation of the R-R interval (CVR-R) and high-frequency component (HF), which reflect parasympathetic nerve activity, and heart rate and low-frequency component (LF)/HF ratio, which reflect sympathetic nerve activity, were measured before, during, and after stretching. Results: SST decreased cortisol levels but with no significant changes in chromogranin A, heart rate, CVR-R, HF, or LF/HF ratio. The combination of SST and CSB increased CVR-R and HF levels in addition to decreasing cortisol levels but with no significant changes in chromogranin A, heart rate, or LF/HF levels. Conclusion: These results indicate that the combination of SST and CSB may increase parasympathetic activity and reduce stress. However, future randomized controlled trials with larger sample sizes should support this conclusion.展开更多
In this article, firstly, we calculated and analyzed the patterns of Coulomb stress changes induced by a sequence of strong earthquakes that occurred in Songpan (松藩), Sichuan (四川) Province in 1973 and 1976, an...In this article, firstly, we calculated and analyzed the patterns of Coulomb stress changes induced by a sequence of strong earthquakes that occurred in Songpan (松藩), Sichuan (四川) Province in 1973 and 1976, and discovered that the Ms8.0 Wenchuan (汶川) earthquake of 2008 was epicentered in a relevant Coulomb stress triggering zone. This suggests that the Coulomb stress on the middle and southern segments of the Longmenshan (龙门山) fault zone increased after the Songpan sequence of strong earthquakes, and the stress increment might cause the 2008 Wenchuan earthquake having al- ready occurred somewhat ahead of time. Further, we calculated and analyzed Coulomb stress changes coinduced by both the Songpan sequence and the Ms8.0 Wenchuan mainshock. The result shows that the Ms6.4 Qingchuan (青川) earthquake of May 25, 2008 on the northeastern segment of the Longmenshan fault zone was triggered by the Wenchuan mainshock, and that the southwestern segment of the fault zone is also in the stress triggering zone. Besides, the Maoxian (茂县)-Wenchuan fault (i.e., the back-range fault of the Longmenshan fault zone), which extends parallel to the seismogenic fault of the Wenchuan earthquake, is in a shadow zone of the Coulomb stress changes, and therefore, its potential hazard for producing a strong or large earthquake in the near future could be reduced relatively.展开更多
The main objective of this research was to examine the suitability of aluminium alloy to design a piston of an internal combustion engine for improvement in weight and cost reduction. The piston was modelled using Aut...The main objective of this research was to examine the suitability of aluminium alloy to design a piston of an internal combustion engine for improvement in weight and cost reduction. The piston was modelled using Autodesk Inventor 2017 software. The modelled piston was then imported into Ansys for further analysis. Static structural and thermal analysis were carried out on the pistons of the four different materials namely: Al 413 alloy, Al 384 alloy, Al 390 alloy and Al332 alloy to determine the total deformation, equivalent Von Mises stress, maximum shear stress, and the safety factor. The results of the study revealed that, aluminium 332 alloy piston deformed less compared to the deformations of aluminium 390 alloy piston, aluminium 384 alloy piston and aluminium 413 alloy piston. The induced Von Mises stresses in the pistons of the four different materials were found to be far lower than the yield strengths of all the materials. Hence, all the selected materials including the implementing material have equal properties to withstand the maximum gas load. All the selected materials were observed to have high thermal conductivity enough to be able to withstand the operating temperature in the engine cylinders.展开更多
The spatiotemporal evolution patterns of complete Coulomb stress changes caused by 1988 Ms7.6 earthquake in Lancang-Gengma, Yunnan, are calculated and studied. And the triggering problems of Ms7.2 Gengma shock occurri...The spatiotemporal evolution patterns of complete Coulomb stress changes caused by 1988 Ms7.6 earthquake in Lancang-Gengma, Yunnan, are calculated and studied. And the triggering problems of Ms7.2 Gengma shock occurring 13 minutes after the main shock and of Ms5.0―6.9 aftershocks within 24 days after the main shock are discussed. The results show that the spatial distribution patterns of complete Coulomb stress changes of the Ms7.6 main shock are strongly asymmetric. The areas of positive dynamic and static Coulomb stress are both coincident well with the strong aftershocks' loca-tions. The Ms7.2 Gengma shock and most of strong aftershocks are subjected to the triggering effect of dynamic and static Coulomb stresses induced by the Ms7.6 Lancang earthquake.展开更多
To quantitatively estimate the workability of cement-based grouting material,from the perspective of rheology,the result of the static yield stress evaluated using the rate-controlled and stress-controlled modes,respe...To quantitatively estimate the workability of cement-based grouting material,from the perspective of rheology,the result of the static yield stress evaluated using the rate-controlled and stress-controlled modes,respectively,was compared using the Rheowin rheometer.Also,the correlation of workability and solid concentration of slurry with static yield stress was studied.Results show that the static yield stress of cement-based grouting slurry relates to the established slurry structure,and is the shear stress corresponding to the transformation of elastics to plastics;In rate-controlled mode,the static yield stress of the slurry is related to the shear rate.The higher the shear rate,the greater the yield stress of the slurry.For the stress-controlled mode,the result is more accurate and suitable for testing static yield stress under different water-cement ratios.Since the water-cement ratio has a good correspondence with the static yield stress and the static yield stress has a good correspondence with the slump flow of the slurry,the static yield stress is the minimum stress to be overcome when the slurry begins to flow and it reflects the yield behavior and structural stability of the cement.展开更多
Residual stresses and deformation of static bonding multi-layer Pyrex7740 glass and aluminum have important effects on performances of bonding parts. The stress and strain finite element analysis of anodic bonding can...Residual stresses and deformation of static bonding multi-layer Pyrex7740 glass and aluminum have important effects on performances of bonding parts. The stress and strain finite element analysis of anodic bonding can optimize the structure and process design, reduce the workload of the experiments, shorten the production cycle, improve the bonding quality, and reduce the process costs. In this paper, residual stresses and deformation in the static bonding two-layer (glass/aluminum), three-layer (glass/aluminum/ glass),five-layer(glass/aluminum/glass/aluminum/glass)and seven-layer (glass/aluminum/glass/aluminum/glass/ aluminum/glass) samples have been analyzed using nonlinear finite element simulation software MARC. The simulation results show that the shear stress distribution and deformation distribution in different multi-layer glass and aluminum samples are similar. The stress distribution along thickness at different typical positions in all multi-layer samples has characteristics of pulse pattern, which has pulse peak at the position of transition layers and then decreases abruptly to the minimum value at the positions of glass and aluminum. The maximum shear stress is located in the outside surface area in the transition layer between the top unconstrained glass layer and aluminum layer. The displacement distribution along thickness in all multi-layer samples increases gradually fi'om the constrained bottom glass layer to the top unconstrained glass layer with abrupt step increase in the aluminum layers, The maximum deformations occur in aluminum layers. It is found that the minimum deformation distortion and the minimum shear stress occur in the three-layer static bonding sample.展开更多
基金Projects(51664017,51964015)supported by the National Natural Science Foundation of ChinaProject(JXUSTQJBJ2017007)supported by the Program of Qingjiang Excellent Young Talents of Jiangxi University of Science and Technology,ChinaProjects(GJJ160616,GJJ171490)supported by Science and Technology Project of Jiangxi Provincial Department of Education,China
文摘A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model.The analytical formulas of longitudinal velocity,space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method.A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted.The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions.Based on the verified theoretical models,the influences of axial static stress on longitudinal velocity,space and time attenuation coefficients and response frequency are investigated by detailed parametric studies.The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock.The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage.Moreover,the initial porosity,initial elastic modulus of the rock voids and skeleton,viscous coefficient and vibration frequency have significant effects on the P-wave velocity,attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.
基金the State Key Research Development Program of China(Grant No.2017YFC0804203)National Natural Science Foundation of China(Grant No.51621006)the Open Fund of the State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z018001).
文摘A series of coupled static-dynamic loading tests is carried out in this study to understand the effect of slightly dynamic disturbance on the rocks under high static stress.The acoustic emission(AE)and digital image correlation(DIC)techniques are combined to quantitatively characterize the damage and fracturing behaviors of rocks.The effects of three influencing factors,i.e.initial static stress,disturbance amplitude,and disturbance frequency,on the damage and fracturing evolution are analyzed.The experimental results reveal the great differences in AE characteristics and fracturing behaviors of rocks under static loads and coupled static-dynamic loads.Both the Kaiser effect and Felicity effect are observed during the disturbance loading process.The crack initiation,stable and unstable propagation in the highly-stressed rocks can be triggered by cyclic disturbance loads,and more local tensile splitting cracks are found in the rocks subjected to coupled static-dynamic loads.The damage and fracturing evolution of rocks during cyclic disturbances can be divided into two stages,i.e.steady and accelerated stages,and the increase rate and proportion of each stage are greatly affected by these influencing factors.High initial static stress,low disturbance frequency,and high disturbance amplitude are considered to be adverse factors to the stability of the rocks,which would induce a high increase rate of the steady stage and a high proportion of the accelerated stage within the whole disturbance period.Based on the two-stage damage evolution trend,a linear-exponential damage model is employed to predict the instability of the rocks under coupled static-dynamic loads.
基金Project(50490274) supported by National Natural Science Foundation of China
文摘The electromagnetic emission(EME) induced from the rock containing piezoelectric materials was investigated under both static stress and exploding stress wave in the view of piezoelectric effect. The results show that the intensity of the EME induced from the rock under static stress increases with increasing stress level and loading rate; the relationship between the amplitude of the EME from the rock under different modes of stress wave and elastic parameters and propagation distance was presented. The intensity of the EME relates not only to the strength and elastic moduli of rock masses,but also to the initial damage of the rock. The intensity of EME induced by stress wave reaches the highest at the explosion-center and attenuates with the propagation distance. The intensity of EME increases with increasing the elastic modulus and decreases with increasing initial damage. The results are in good agreement with the experimental results.
文摘Objective:To explore the mechanical behavior of acetabulum loaded by static stress and provide the mechanical basis for clinical analysis and judgement on acetabular mechanical distribution and effect of static stress.Methods:By means of computer simulation, acetabular three dimensional model was input into three dimensional finite element analysis software ANSYS7.0. The acetabular mechanical behavior was calculated and the main stress value, stress distribution and acetabular unit displacement in the direction of main stress were analyzed when anterior wall of acetabulum and acetabular crest were loaded by 1 000 N static stress. Results:When acetabular anterior wall loaded by X direction and Z direction composition force, the stress passed along 4 directions: (1)from acetabular anterior wall to pubic symphysis along superior branch of pubis firstly, (2)from acetabular anterior wall to cacroiliac joint along pelvic ring,(3)in the acetabulum,(4)from the suffered point to ischium. When acetabular crest loaded by X direction and Y direction composition force, the stress transmitted to 4 directions: (1)from acetabular crest to ilium firstly, (2)from suffered point to cacroiliac joint along pelvic ring,(3) in the acetabulum ,(4)along the pubic branch,but no stress transmitted to the ischium branch.Conclusion:Analyzing the stress distribution of acetabulum and units displacement when static stress loaded can provide internal fixation point for acetabular fracture treatment and help understand the stress distribution of acetabulum.
文摘Background: Women are thought to be more susceptible to stress than men in a stressful society, and reducing stress is crucial for women to maintain their health. Static stretching (SST) is applied in various fields to not only increase muscle flexibility but also reduce stress. Additionally, conscious slower breathing (CSB) predominates parasympathetic activity, causing a relaxing effect. These results indicate that combining SST and CSB may be more useful in reducing stress. However, to the best of our knowledge, the effect of this combination remains unclear. Objective: This study aimed to elucidate the effects of the combination of SST and CSB on autonomic activity and stress in adult women. Methods: Eleven healthy Japanese adult female participants performed SST with nonconscious natural breathing for 20 min. The same participants performed SST in combination with CSB (2 s inspiratory and 4 s expiratory) for 20 min on another day. Salivary cortisol and chromogranin A levels were measured before and after stretching as stress markers of the hypothalamic-pituitary-adrenal axis and sympathetic nervous system. The coefficient of variation of the R-R interval (CVR-R) and high-frequency component (HF), which reflect parasympathetic nerve activity, and heart rate and low-frequency component (LF)/HF ratio, which reflect sympathetic nerve activity, were measured before, during, and after stretching. Results: SST decreased cortisol levels but with no significant changes in chromogranin A, heart rate, CVR-R, HF, or LF/HF ratio. The combination of SST and CSB increased CVR-R and HF levels in addition to decreasing cortisol levels but with no significant changes in chromogranin A, heart rate, or LF/HF levels. Conclusion: These results indicate that the combination of SST and CSB may increase parasympathetic activity and reduce stress. However, future randomized controlled trials with larger sample sizes should support this conclusion.
基金supported by the Open Fund Project of State Key Laboratory of Earthquake Dynamics (No. LED2008B01)
文摘In this article, firstly, we calculated and analyzed the patterns of Coulomb stress changes induced by a sequence of strong earthquakes that occurred in Songpan (松藩), Sichuan (四川) Province in 1973 and 1976, and discovered that the Ms8.0 Wenchuan (汶川) earthquake of 2008 was epicentered in a relevant Coulomb stress triggering zone. This suggests that the Coulomb stress on the middle and southern segments of the Longmenshan (龙门山) fault zone increased after the Songpan sequence of strong earthquakes, and the stress increment might cause the 2008 Wenchuan earthquake having al- ready occurred somewhat ahead of time. Further, we calculated and analyzed Coulomb stress changes coinduced by both the Songpan sequence and the Ms8.0 Wenchuan mainshock. The result shows that the Ms6.4 Qingchuan (青川) earthquake of May 25, 2008 on the northeastern segment of the Longmenshan fault zone was triggered by the Wenchuan mainshock, and that the southwestern segment of the fault zone is also in the stress triggering zone. Besides, the Maoxian (茂县)-Wenchuan fault (i.e., the back-range fault of the Longmenshan fault zone), which extends parallel to the seismogenic fault of the Wenchuan earthquake, is in a shadow zone of the Coulomb stress changes, and therefore, its potential hazard for producing a strong or large earthquake in the near future could be reduced relatively.
文摘The main objective of this research was to examine the suitability of aluminium alloy to design a piston of an internal combustion engine for improvement in weight and cost reduction. The piston was modelled using Autodesk Inventor 2017 software. The modelled piston was then imported into Ansys for further analysis. Static structural and thermal analysis were carried out on the pistons of the four different materials namely: Al 413 alloy, Al 384 alloy, Al 390 alloy and Al332 alloy to determine the total deformation, equivalent Von Mises stress, maximum shear stress, and the safety factor. The results of the study revealed that, aluminium 332 alloy piston deformed less compared to the deformations of aluminium 390 alloy piston, aluminium 384 alloy piston and aluminium 413 alloy piston. The induced Von Mises stresses in the pistons of the four different materials were found to be far lower than the yield strengths of all the materials. Hence, all the selected materials including the implementing material have equal properties to withstand the maximum gas load. All the selected materials were observed to have high thermal conductivity enough to be able to withstand the operating temperature in the engine cylinders.
基金Supported by the National Natural Science Foundation of China (Grant No. 40364001)the Key Lab. Open Foundation for Earth and Space Environment and Geodesy of the Ministry of Education of China (Grant No. 03-04-07)
文摘The spatiotemporal evolution patterns of complete Coulomb stress changes caused by 1988 Ms7.6 earthquake in Lancang-Gengma, Yunnan, are calculated and studied. And the triggering problems of Ms7.2 Gengma shock occurring 13 minutes after the main shock and of Ms5.0―6.9 aftershocks within 24 days after the main shock are discussed. The results show that the spatial distribution patterns of complete Coulomb stress changes of the Ms7.6 main shock are strongly asymmetric. The areas of positive dynamic and static Coulomb stress are both coincident well with the strong aftershocks' loca-tions. The Ms7.2 Gengma shock and most of strong aftershocks are subjected to the triggering effect of dynamic and static Coulomb stresses induced by the Ms7.6 Lancang earthquake.
基金Funded by Science and Technology Program of Gansu Provincial Department of Housing and Construction (No.JK2021-11)National Natural Science Fundation of China (No.52161007)+1 种基金Science and Technology Project of Gansu Provincial Department of TransportationNatural Science Foundation of Gansu Province (No. 20JR10RA170)。
文摘To quantitatively estimate the workability of cement-based grouting material,from the perspective of rheology,the result of the static yield stress evaluated using the rate-controlled and stress-controlled modes,respectively,was compared using the Rheowin rheometer.Also,the correlation of workability and solid concentration of slurry with static yield stress was studied.Results show that the static yield stress of cement-based grouting slurry relates to the established slurry structure,and is the shear stress corresponding to the transformation of elastics to plastics;In rate-controlled mode,the static yield stress of the slurry is related to the shear rate.The higher the shear rate,the greater the yield stress of the slurry.For the stress-controlled mode,the result is more accurate and suitable for testing static yield stress under different water-cement ratios.Since the water-cement ratio has a good correspondence with the static yield stress and the static yield stress has a good correspondence with the slump flow of the slurry,the static yield stress is the minimum stress to be overcome when the slurry begins to flow and it reflects the yield behavior and structural stability of the cement.
基金Supported by the National Natural Science Foundation of China(No.51275332)Shanxi Graduate Outstanding Innovative Projects(No.20123104)
文摘Residual stresses and deformation of static bonding multi-layer Pyrex7740 glass and aluminum have important effects on performances of bonding parts. The stress and strain finite element analysis of anodic bonding can optimize the structure and process design, reduce the workload of the experiments, shorten the production cycle, improve the bonding quality, and reduce the process costs. In this paper, residual stresses and deformation in the static bonding two-layer (glass/aluminum), three-layer (glass/aluminum/ glass),five-layer(glass/aluminum/glass/aluminum/glass)and seven-layer (glass/aluminum/glass/aluminum/glass/ aluminum/glass) samples have been analyzed using nonlinear finite element simulation software MARC. The simulation results show that the shear stress distribution and deformation distribution in different multi-layer glass and aluminum samples are similar. The stress distribution along thickness at different typical positions in all multi-layer samples has characteristics of pulse pattern, which has pulse peak at the position of transition layers and then decreases abruptly to the minimum value at the positions of glass and aluminum. The maximum shear stress is located in the outside surface area in the transition layer between the top unconstrained glass layer and aluminum layer. The displacement distribution along thickness in all multi-layer samples increases gradually fi'om the constrained bottom glass layer to the top unconstrained glass layer with abrupt step increase in the aluminum layers, The maximum deformations occur in aluminum layers. It is found that the minimum deformation distortion and the minimum shear stress occur in the three-layer static bonding sample.