Abstract
In this work, the authors discuss a systematic method of characterizing the damage process in graphene. The mathematical formulation is limited to the elastic range. In the elastic constitutive equation for graphene, both the second-order and third-order elastic stiffnesses are considered. The formulation is performed within the framework of Continuum Damage Mechanics. Thus, both the hypotheses of elastic strain equivalence and elastic energy equivalence are utilized. In addition to the classical damage variable that is defined in terms of the cross-sectional area, a new damage variable is introduced and defined in terms of the surface area. This particular damage variable is suited for general nanomaterials, especially graphene. Both the scalar and tensorial formulations are presented. The special case of plane stress in graphene is illustrated as an example using the derived general equations and some interesting results are obtained.
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