With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever before.This paper is focused ...With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever before.This paper is focused on the prediction methods of effective Young's modulus for periodical cellular materials.Based on comprehensive studies of the existing homogenization method(HM),the G-A meso-mechanics method(G-A MMM) and the stretching energy method(SEM) that are unable to reflect the size effect,we propose the bending energy method(BEM) for the first time,and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM method.Meanwhile,the underlying characteristics of each method and their relations are clarified.To do this,the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four methods.Stretch and bending models of periodical cellular materials are taken into account,respectively for the comparison of stretch and flexural displacements resulting from the above methods.We conclude that the BEM has the strong ability of both predicting the effective Young's modulus and revealing the size effect.Such a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal cell.On the contrary,other three methods can only predict the limited results whenever the cell size tends to be infinitely small.展开更多
A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of ...A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).展开更多
In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the stra...In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 50775184)the National Basic Research Program of China (Grant No. 2006CB601-205)+2 种基金the Aeronautical Science Foundation (Grant No. 2008ZA53007)the Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX200610)the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University (Grant No. 30715003)
文摘With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever before.This paper is focused on the prediction methods of effective Young's modulus for periodical cellular materials.Based on comprehensive studies of the existing homogenization method(HM),the G-A meso-mechanics method(G-A MMM) and the stretching energy method(SEM) that are unable to reflect the size effect,we propose the bending energy method(BEM) for the first time,and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM method.Meanwhile,the underlying characteristics of each method and their relations are clarified.To do this,the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four methods.Stretch and bending models of periodical cellular materials are taken into account,respectively for the comparison of stretch and flexural displacements resulting from the above methods.We conclude that the BEM has the strong ability of both predicting the effective Young's modulus and revealing the size effect.Such a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal cell.On the contrary,other three methods can only predict the limited results whenever the cell size tends to be infinitely small.
文摘A differential geometrical method is for the first time used to calculate the effective moduli of a two-phase elastic composite materials with imperfect interface which the inclusions are assumed to be ellipsoidal of revolutions. All of the interface integral items participating in forming the potential and complementary energy functionals of the composite materials are expressed in terms of intrinsic quantities of the ellipsoidal of revolutions. Based on this, the upper and the lower bound for the effective elastic moduli of the composite materials with inclusions described above have been derived. Under three limiting conditions of sphere, disk and needle shaped inclusions, the results of this paper will return to the bounds obtained by Hashin([6]) (1992).
基金Project supported by the National Natural Science Foundation of China(Nos.11021262,10932011 and 91216108)the National Basic Research Program of China(2012CB937500)
文摘In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.
