Constitutive Equations for Graphene Based on Anisotropic Theory
The constitutive equations, describing the relations between stresses and strains in the single layer graphene, were obtained based on the anisotropic theory. The equations showed that (1) there are 3 nonzero stress components in graphene for it is in the plane stress state; (2) there are 4 elastic constants independent in the constitutive equations describing the material properties of graphene; and (3) the normal stress merely results in normal strains if graphene in simple tension in primary directions but generates the normal strains and shear strains if in non-primary directions. In addition, the Hamilton method determining the 4 elastic constants in constitutive equations of graphene was introduced.
S. H. Ban et al., "Constitutive Equations for Graphene Based on Anisotropic Theory", Advanced Materials Research, Vols. 314-316, pp. 1268-1272, 2011