On the hyperelastic softening and elastic instabilities in graphene

Abstract

Elastic material instabilities are precursors to failure in defect-free graphene single crystals. Elastic instabilities originate from softening in the material response (decay of tangent moduli) induced by dilatant mechanical deformation. Here, we characterize the softening in the constitutive response of graphene within the framework of hyperelasticity based on symmetry-invariants of the two-dimensional logarithmic strain tensor E (0) . The use of symmetry-invariants provides significant functional simplification in representation of the strain energy function of graphene; ab initio calculations of deformation energy are well-fit using half the number of elastic constants of previous formulations. For a set of large homogeneous deformations comprising uniaxial stretch/stress along the armchair and the zigzag directions, and equi-biaxial tension, stress values predicted by the model compare well with those directly calculated from ab initio solutions. Using acoustic tensor analysis, we show that the constitutive model accurately captures elastic stability limits for a number of biaxial deformation modes, providing results that compare well with independent phonon calculations carried out using linear response density functional perturbation theory. In the case of equi-biaxial deformation, an elastic shearing instability is identified which occurs prior to the configuration of maximum true stress. Potential implications of the present results on the interpretation of limiting deformations achieved in nanoindentation experiments are briefly noted.

Hyperelastic material modeling of graphene based on density functional calculations

“…As shown in Fig. 2, our DFT results for surface tension in pure dilatation match with the results of [1] and there is a difference in the continuum results for J 1 > 0.4. A comparison of the stresses in the stretch direction and perpendicular direction for uniaxial tension in the armchair and zigzag directions is illustrated in Fig.…”

“…1 presents the variation of the material behavior with J 1 . The pure dilatation energy matches perfectly with the model of [1], however there are minor differences in µ and η. As shown in Fig.…”

“…2 Hyperelastic membrane material model [1] propose an anisotropic hyperelastic membrane material model for graphene and use DFT data to calibrate this model. This model is used by [3] to simulate indentation of graphene sheets.…”

“…[6] propose an efficient FE implementation and use it to model carbon nanocones. The material model of [1] is developed based on a set of invariants. These invariants are obtained from the symmetry group of graphene [7] and the logarithmic strain.…”

“…1. [1] use a pure dilatation test and a set of pure shear tests combined with initial pure dilatation. Different experiments can be the reason for slight differences in the constants.…”