Part II of Professor Christensen's paper on failure mechanics is published in JAM

Failure Mechanics—Part II: The Central and Decisive Role

of Graphene in Defining the Elastic and Failure Properties

for all Isotropic Materials

Continuing from Part I (Christensen, 2014, “Failure Mechanics—Part I: The Coordination

Between Elasticity Theory and Failure Theory for all Isotropic Materials,” ASME J.

Appl. Mech., 81(8), p. 081001), the relationship between elastic energy and failure specification

is further developed. Part I established the coordination of failure theory with

elasticity theory, but subject to one overriding assumption: that the values of the involved

Poisson’s ratios always be non-negative. The present work derives the physical proof

that, contrary to fairly common belief, Poisson’s ratio must always be non-negative. It

can never be negative for homogeneous and isotropic materials. This is accomplished by

first probing the reduced two-dimensional (2D) elasticity problem appropriate to graphene,

then generalizing to three-dimensional (3D) conditions. The nanomechanics analysis

of graphene provides the key to the entire development. Other aspects of failure

theory are also examined and concluded positively. Failure theory as unified with

elasticity theory is thus completed, finalized, and fundamentally validated.

[DOI: 10.1115/1.4028407]

Both Parts I and II are attached.