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A theory of undamageable graphene

Voyiadjis G. Z., Kattan P. I.

Engineering Transactions

2018

Vol. 66, iss. 4

461--470

It is the aim of this work to develop and extend the theory of undamageable materials to graphene. An undamageable material is a material where the value of the damage variable remains zero throughout the deformation process. It is anticipated that the constitutive equations for undamageable graphene can be modeled with differential equations for the case of graphene. The equations are solved for three cases: n = 1, n = 2, and the general case of n. It is hoped that undamageable graphene can be achieved in the laboratory in the near future when the manufacturing technology advances so as to produce such materials.

Governing Differential Equations for the Mechanics of Undamageable Materials

Voyiadjis G. Z., Kattan P. I.

Engineering Transactions

2014

Vol. 62, iss. 3

241–-267

In this work the mathematical foundations of the mechanics of elastic undamageable materials are presented. In particular the governing differential equations are derived for both the scalar and tensorial cases. In the isotropic case it is found that the resulting scalar differential equations are simple and easy to solve. However, in the anisotropic case the tensorial differential equations are complicated and unsolvable at this time. The current work presents the solution in the form of explicit nonlinear stress-strain relations for the simple one-dimensional case. However, the general solution of the three-dimensional case remains unattainable at the present time. Only the governing tensorial differential equations are derived for this latter case. It is to be noted that the term “undamageable” is reflected in the context of the material stiffness and not the property of indestructibility due to various loading conditions. Thus, the undamageable material reflects that no microcracks or microvoids occur as well as no plastic yielding in the material. To illustrate this concept, a last section is added on applications.