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Research Papers

Failure Mechanics—Part II: The Central and Decisive Role of Graphene in Defining the Elastic and Failure Properties for all Isotropic Materials

[+] Author and Article Information
Richard M. Christensen

Professor Research Emeritus
Aeronautics and Astronautics Department,
Stanford University,
Stanford, CA 94305
e-mail: christensen@stanford.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 14, 2014; final manuscript received August 18, 2014; accepted manuscript posted August 27, 2014; published online September 17, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(11), 111001 (Sep 17, 2014) (10 pages) Paper No: JAM-14-1370; doi: 10.1115/1.4028407 History: Received August 14, 2014; Revised August 18, 2014; Accepted August 27, 2014

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.

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References

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Figures

Grahic Jump Location
Fig. 1

Hexagonal symmetry for graphene

Grahic Jump Location
Fig. 2

Effective elastic member connecting carbon atoms

Grahic Jump Location
Fig. 3

2D ν2D* versus κ, Table 1

Grahic Jump Location
Fig. 4

3D ν* versus κ, Table 2

Grahic Jump Location
Fig. 5

Biaxial failure data for fused graphite, Ely [18]

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