Temperature-related Cauchy–Born rule for multiscale modeling of crystalline solids

Xiao, Shaoping; Yang, Weixuan

doi:10.1016/j.commatsci.2005.09.007

Cited by 46 publications

(26 citation statements)

References 24 publications

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“…Here it needs to be stressed that the adopted CauchyBorn rule is limited, but it can be overcome if we employ the modified Cauchy-Born hypothesis [24][25][26][27][28][29] , such as the integral mean value based [24] and high-order [26] Cauchy-Born hypothesis, which have succeeded in describing inhomogeneous deformation in quasicontinuum model, such as dislocation dynamics, plastic slip and nano-indentation [19,20] . The exponent Cauchy-Born hypothesis [29] has been used in shape-distortion of the thin-wall carbon nanotubes.…”

Section: Cam's Parameter Calibratingmentioning

confidence: 99%

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The elasto-damage theory of the components assembling model

Deng

Liang

Hai-xing

2009

Sci. China Ser. G-Phys. Mech. Astron.

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Section: Cam's Parameter Calibratingmentioning

confidence: 99%

“…Cauchy-Born hypothesis [14][15][16][24][25][26][27][28][29] builds a bridge between microscopic movements and macroscopic deformations. The hypothesis asserts that the lattice has been subjected to homogeneous deformation locally, as illustrates in Figures 1 and 2.…”

Section: Devivation Of Cammentioning

confidence: 99%

The elasto-damage theory of the components assembling model

Deng

Liang

Hai-xing

2009

Sci. China Ser. G-Phys. Mech. Astron.

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“…However, it is applicable at 0 K, and researchers are trying to extend this method to finite temperatures [8,10,11] or to take the temperature effect into account in a dynamic and multi-spatial scale scheme yet with reduced computational cost [12,13]. Alternatively, Hu et al and Wang et al proposed the molecular statistical thermodynamics (MST)/cluster statistical thermodynamics (CST) as well as the hybrid MST and CST (HMCST) computational frameworks [14,15].…”

Section: Introductionmentioning

confidence: 99%

Molecular statistical thermodynamics – A distinct and efficient numerical approach to quasi-static analysis of nanomaterials at finite temperature

Xiao

Wang

Fang

et al. 2012

Composites Part B: Engineering

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a b s t r a c tThis paper briefly reviews a distinct and efficient numerical approach to quasi-static analysis of nanomaterials at finite temperature: molecular statistical thermodynamics (MST), especially its various applications and efficiency. Different from molecular dynamics (MD) based on Newton equations, MST is a halfanalytical numerical method based on the minimization of Helmholtz free energy. The applications of MST to compression of nanorods, nanoindentations and tension of nanowires show that MST is capable of characterizing the nucleation, propagation and interaction of dislocations as well as phase transformations involved in quasi-static deformations. Not only the mechanical responses and properties calculated with MST are in agreement with MD simulations, but the size effect of Young's modulus of zinc oxide nanowires calculated with MST are also in good consistency with experimental results. All these results justify the reliability of MST. Furthermore, the efficiency analysis indicates that MST is dramatically faster than MD for quasi-static processes and is expected to be capable of simulating nanomaterials at larger scales with high efficiency.

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“…The CBR is usually used to develop the quasi-continuum model in simulating the overall mechanical behavior for discrete systems, which is based on the early work of Born and Huang [19] and then is further developed by Ericksen et al [20] , etc.. Based on the CBR, Park and Liu [21] presented a multiple-scale method to couple atomistic simulation to continuum simulation, which needed a much smaller computational cost than that of atomistic simulation. By proposing a temperature-related Cauchy-Born rule implemented in nanoscale continuum approximations, Xiao and Yang [22] studied temperature dependent physical phenomena of crystalline solids. Steinmann et al [23] investigated the validity of the CBR by direct comparison of continuum with atomistic simulation.…”

Section: Introductionmentioning

confidence: 99%

Size effects of elastic modulus of fcc metals based on the Cauchy-Born rule and nanoplate models

Liu

Song

Wei

2014

Acta Mechanica Solida Sinica

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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.

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Temperature-related Cauchy–Born rule for multiscale modeling of crystalline solids

Cited by 46 publications

References 24 publications

The elasto-damage theory of the components assembling model

The elasto-damage theory of the components assembling model

Molecular statistical thermodynamics – A distinct and efficient numerical approach to quasi-static analysis of nanomaterials at finite temperature

Size effects of elastic modulus of fcc metals based on the Cauchy-Born rule and nanoplate models

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