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Stability and size-dependency of temperature-related Cauchy-Born hypothesis

Khoei, A. R ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.commatsci.2011.01.004
  3. Publisher: 2011
  4. Abstract:
  5. In continuum mechanics, the constitutive models are usually based on the Cauchy-Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this paper is to investigate the temperature effect on the stability and size-dependency of Cauchy-Born hypothesis. Three-dimensional temperature-related Cauchy-Born formulations are developed for crystalline structure and the stability and size-dependency of temperature-related Cauchy-Born hypothesis are investigated by means of direct comparison between atomistic and continuous mediums. In order to control the temperature effect, the Nose-Hoover thermostat is employed. Since the Helmholtz free energy is temperature dependent; the first Piola-Kirchhoff stresses are explicitly computed as the first derivative of the Helmholtz free energy density to the deformation gradient. It is numerically shown that the validity surfaces become smaller at higher temperature, which is significant in larger specimen. It is also presented that the material stability decreases with increasing the ambient temperature
  6. Keywords:
  7. Temperature-related Cauchy-Born ; Ambient temperatures ; Cauchy-Born hypothesis ; Continuous medium ; Crystalline structure ; Deformation gradients ; Dimensional temperatures ; First derivative ; First piola-kirchhoff stress ; Helmholtz free energy ; Higher temperatures ; Intrinsic characteristics ; Material stability ; Nose-Hoover thermostat ; Size effect ; Size-Dependency ; Temperature dependent ; Temperature effects ; Continuum mechanics ; Deformation ; Elasticity ; Free energy ; Stability ; Temperature ; Thermostats ; Molecular dynamics
  8. Source: Computational Materials Science ; Volume 50, Issue 5 , March , 2011 , Pages 1731-1743 ; 09270256 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0927025611000231