The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich str...The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.展开更多
A complex rubber foam under quasi-static compression is simulated using the finite element method （FEM）, The present work sets up the phenomenological constitutive model for the silicon rubber, The computerized tomo...A complex rubber foam under quasi-static compression is simulated using the finite element method （FEM）, The present work sets up the phenomenological constitutive model for the silicon rubber, The computerized tomography （CT） technique is utilized to reconstruct the real complex foam geometries, The quasi-static uniaxial compression on the foam is simulated in ABAQUS. The present work obtains the stress response as the nominal strain nearly reaches 80% and the foam exhibits hyper-elastic behavior, The FEM results achieve good agreements with the data obtained from the multi-scale simulation and the tests as the nominal strain is less than 60%.展开更多
Based on the rigid plastic theory; the load-deflection functions with and without considering the effect of strain hardening are respectively derived for an elliptical tube under quasi-static compression by two parall...Based on the rigid plastic theory; the load-deflection functions with and without considering the effect of strain hardening are respectively derived for an elliptical tube under quasi-static compression by two parallel rigid plates. The non-dimensional load-deflection responses predicted by the present theory and the finite element simula- tions are compared, and the favorable agreement is found. The results show that strain hardening may have a noticeable influence on the load-deflection curves of an elliptical tube under quasi-static compression. Compared with the circular counterpart, the ellip- tical tube exhibits different energy absorption behavior due to the difference between the major axis and the minor axis. When loaded along the major axis of a slightly oval tube, a relative even and long plateau region of the load-deflection curve is achieved, which is especially desirable for the design of energy absorbers.展开更多
Compression waves propagating through molten metals are contributed to degassing, accelerating reaction rate,removing exclusions from molten metals and refining solidification structures during metallurgical processin...Compression waves propagating through molten metals are contributed to degassing, accelerating reaction rate,removing exclusions from molten metals and refining solidification structures during metallurgical processing of materials. In the present study, two electromagnetic methods are proposed to generate intense compression wavesdirectly in liquid metals. One is the simultaneous imposition of a high frequency electrical current field and a staticmagnetic field; the other is that of a high frequency magnetic field and a static magnetic field. A mathematical modelbased on compressible fluid dynamics and electromagnetic fields theory has been developed to derive pressure distributions of the generated waves in a metal. It shows that the intensity of compression waves is proportional to thatof the high frequency electromagnetic force. And the frequency is the same as that of the imposed electromagneticforce. On the basis of theoretical analyses, pressure change in liquid gallium was examined by a pressure transducerunder various conditions. The observed results approximately agreed with the predictions derived from the theoreticalanalyses and calculations. Moreover, the effect of the generated waves on improvement of solidification structureswas also examined. It shows that the generated compression waves can refine solidification structures when they wereapplied to solidification process of Sn-Pb alloy. This study indicates a new method to generate compression wavesby imposing high frequency electromagnetic force locally on molten metals and this kind of compression waves canprobably overcome the difficulties when waves are excited by mechanical vibration in high temperature environments.展开更多
基金supported by the Natural Science Foundation of Tianjin Munici-pality[21YDTPJC00480]the Science and Technology Project of Tianjin[20YDTPJC00830].
文摘The sandwich structure of cushioning packaging has an important influence on the cushioning performance.Mathematical fractal theory is an important graphic expression.Based on Hilbert fractal theory,a new sandwich structure was designed.The generation mechanism and recurrence formula of theHilbert fractal were expressed by Lin’s language,and the second-orderHilbert sandwich structure was constructed fromthermoplastic polyurethane.The constitutive model of the hyperelastic body was established by using the finite element method.With the unit mass energy absorption as the optimization goal,the fractal sandwich structure was optimized,and the best result was obtained when the order was 2.5 and the unit layer thickness was 0.75 mm.TheHilbert sandwich structure was compared with the rice-shaped sandwich structure commonly used in industry,and the Hilbert fractal structure had better energy absorption.This has practical significance for the development and application of newcushioning packaging structures.
基金supported by the National Natural Science Foundation of China(No.11272300)the NSAF(No.U1530259)
文摘A complex rubber foam under quasi-static compression is simulated using the finite element method （FEM）, The present work sets up the phenomenological constitutive model for the silicon rubber, The computerized tomography （CT） technique is utilized to reconstruct the real complex foam geometries, The quasi-static uniaxial compression on the foam is simulated in ABAQUS. The present work obtains the stress response as the nominal strain nearly reaches 80% and the foam exhibits hyper-elastic behavior, The FEM results achieve good agreements with the data obtained from the multi-scale simulation and the tests as the nominal strain is less than 60%.
基金Project supported by the National Natural Science Foundation of China(No.11472035)
文摘Based on the rigid plastic theory; the load-deflection functions with and without considering the effect of strain hardening are respectively derived for an elliptical tube under quasi-static compression by two parallel rigid plates. The non-dimensional load-deflection responses predicted by the present theory and the finite element simula- tions are compared, and the favorable agreement is found. The results show that strain hardening may have a noticeable influence on the load-deflection curves of an elliptical tube under quasi-static compression. Compared with the circular counterpart, the ellip- tical tube exhibits different energy absorption behavior due to the difference between the major axis and the minor axis. When loaded along the major axis of a slightly oval tube, a relative even and long plateau region of the load-deflection curve is achieved, which is especially desirable for the design of energy absorbers.
基金This work has been partially performed under the financial supports from the National Natural Science Foundation of China (Grant No.50204004)the National Fundamental Research Project - new generation steel research project of China (Grant No.G1998061
文摘Compression waves propagating through molten metals are contributed to degassing, accelerating reaction rate,removing exclusions from molten metals and refining solidification structures during metallurgical processing of materials. In the present study, two electromagnetic methods are proposed to generate intense compression wavesdirectly in liquid metals. One is the simultaneous imposition of a high frequency electrical current field and a staticmagnetic field; the other is that of a high frequency magnetic field and a static magnetic field. A mathematical modelbased on compressible fluid dynamics and electromagnetic fields theory has been developed to derive pressure distributions of the generated waves in a metal. It shows that the intensity of compression waves is proportional to thatof the high frequency electromagnetic force. And the frequency is the same as that of the imposed electromagneticforce. On the basis of theoretical analyses, pressure change in liquid gallium was examined by a pressure transducerunder various conditions. The observed results approximately agreed with the predictions derived from the theoreticalanalyses and calculations. Moreover, the effect of the generated waves on improvement of solidification structureswas also examined. It shows that the generated compression waves can refine solidification structures when they wereapplied to solidification process of Sn-Pb alloy. This study indicates a new method to generate compression wavesby imposing high frequency electromagnetic force locally on molten metals and this kind of compression waves canprobably overcome the difficulties when waves are excited by mechanical vibration in high temperature environments.
