STABILITY OF COHESIVE CRACK MODEL .1. ENERGY PRINCIPLES

Authors
Citation
Zp. Bazant et Yn. Li, STABILITY OF COHESIVE CRACK MODEL .1. ENERGY PRINCIPLES, Journal of applied mechanics, 62(4), 1995, pp. 959-964
Citations number
23
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanics
Journal title
ISSN journal
0021-8936
Volume
62
Issue
4
Year of publication
1995
Pages
959 - 964
Database
ISI
SICI code
0021-8936(1995)62:4<959:SOCCM.>2.0.ZU;2-W
Abstract
The paper deals with a cohesive crack model in which the cohesive (cra ck-bridging) stress is a specified decreasing function of the crack-op ening displacement. Under the assumption that no part of the crack und ergoes unloading, the complementary energy and potential energy of an elastic structure which has a cohesive crack and is loaded by a flexib le elastic frame is formulated using continuous influence functions re presenting compliances or stiffnesses relating various points along th e crack. By variational analysis, in which the derivatives of the comp liance or stiffness functions with respect to the crack length are rel ated to the crack-tip stress intensity factors due to various unit loa ds, it is shown that the minimizing conditions reduce to the usual com patibility or equilibrium equations for the cohesive cracks. The varia tional equations obtained can be used as a basis for approximate solut ions. Furthermore, the conditions of stability loss of a structure wit h a growing cohesive crack are obtained from the condition of vanishin g of the second variation of the complementary energy or the potential energy. They have the form of a homogeneous Fredholm integral equatio n for the derivatives of the cohesive stresses or crack opening displa cements with respect to the crack length Loadings with displacement co ntrol, load control, or through a flexible loading frame are considere d. Extension to the analysis of size effect on the maximum load or max imum displacement are left to a subsequent companion paper.