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A damage plastic constitutive model for metals is proposed in this paper. An anisotropic damage tensor and a damage surface are adopted to describe the degradation of the mechanical properties of metals. The model is developed within the thermodynamic framework and creates an anisotropic damage plastic model with the ability to describe the plastic and damage behavior of iron based materials. According to the principle of strain energy equivalence between the undamaged and damaged materials, the linear elastic constitutive equations for the damaged material expressed a stiffness tensor in the damaged configuration. The damaged material is modeled using the constitutive laws of the undamaged... 

Various experimental and theoretical investigations have been carried out to determine the elastic properties of nanotubes in the axial direction. Their behavior in transverse directions, however, has not been well studied. In this paper, a combination of molecular dynamics (MD) and continuum-based elasticity model is used to predict the transverse-isotropic elastic properties of single-walled carbon nanotubes (SWCNTs). From this modeling study, five independent elastic constants of an SWCNT in transverse directions are obtained by analyzing its deformations under four different loading conditions, namely, axial tension, torsion, uniform and non-uniform radial pressure. To find the elastic...