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The theory of the boundary eigenvalue problem in the cohesive crack model and its application

Authors
Journal
Journal of the Mechanics and Physics of Solids
0022-5096
Publisher
Elsevier
Publication Date
Volume
41
Issue
2
Identifiers
DOI: 10.1016/0022-5096(93)90011-4

Abstract

Abstract T he conceptual differences between the conventional cohesive crack model and the cohesive crack model discussed in this paper are briefly reviewed. Based on the potential energy principle and the assumption of a linear softening law, a boundary eigenvalue problem is introduced. Under the critical condition, that is, when the smallest eigenvalue is one, the corresponding eigenfunction represents the non-unique part of the displacement solution, and the critical load can be determined via the eigenfunction. Based on this formulation and using a singular integral equation technique, the boundary eigenvalue problem is established for an infinite plane with a central cut under transverse tension. It is found that the obtained solution approaches Griffith theory in the large size limit. The implication of this result is discussed in comparison with the concept of the R-curve approach.

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