Stability of Cohesive Crack Model: Part I—Energy Principles

1995 ◽  
Vol 62 (4) ◽  
pp. 959-964 ◽  
Author(s):  
Z. P. Bazˇant ◽  
Yuan-Neng Li
Keyword(s):  
Potential Energy ◽  
Crack Length ◽  
Crack Opening ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Equilibrium Equations ◽  
Complementary Energy ◽  
Maximum Displacement ◽  
Derivatives Of

The paper deals with a cohesive crack model in which the cohesive (crack-bridging) stress is a specified decreasing function of the crack-opening displacement. Under the assumption that no part of the crack undergoes unloading, the complementary energy and potential energy of an elastic structure which has a cohesive crack and is loaded by a flexible elastic frame is formulated using continuous influence functions representing compliances or stiffnesses relating various points along the crack. By variational analysis, in which the derivatives of the compliance or stiffness functions with respect to the crack length are related to the crack-tip stress intensity factors due to various unit loads, it is shown that the minimizing conditions reduce to the usual compatibility or equilibrium equations for the cohesive cracks. The variational equations obtained can be used as a basis for approximate solutions. Furthermore, the conditions of stability loss of a structure with a growing cohesive crack are obtained from the condition of vanishing of the second variation of the complementary energy or the potential energy. They have the form of a homogeneous Fredholm integral equation for the derivatives of the cohesive stresses or crack opening displacements with respect to the crack length. Loadings with displacement control, load control, or through a flexible loading frame are considered. Extension to the analysis of size effect on the maximum load or maximum displacement are left to a subsequent companion paper.

A Comparison of Cohesive Crack Model and Crack Band Model in Concrete Fracture

2012 ◽  
Vol 170-173 ◽  
pp. 3375-3380
Author(s):  
Liang Wu ◽  
Ze Li ◽  
Shang Huang
Keyword(s):  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Crack Opening ◽  
Cohesive Crack ◽  
Band Model ◽  
Crack Model ◽  
Concrete Fracture ◽  
Cohesive Crack Model ◽  
Crack Band

The cohesive crack model and the crack band model are two convenient approaches in concrete fracture analysis. They can describe in full the fracture process by the different manner: The entire fracture process zone is lumped into the crack line and is characterized in the form of a stress-displacement law which exhibits softening; or the inelastic deformations in the fracture process zone are smeared over a band of a certain width, imagined to exist in front of the main crack. The correlation of the two models is developed based on a characteristic width of crack band. The analysis shows that they can yield about the same results if the crack opening displacement in the cohesive crack model is taken as the fracturing strain that is accumulated over the width of the crack band model. Some basic problems are also discussed in finite element analysis.

scholarly journals A Particle-Based Cohesive Crack Model for Brittle Fracture Problems

Materials ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 3573
Author(s):  
Hu Chen ◽  
Y. X. Zhang ◽  
Linpei Zhu ◽  
Fei Xiong ◽  
Jing Liu ◽  
...  
Keyword(s):  
Fracture Process ◽  
Cohesive Crack ◽  
Contact Model ◽  
Experimental Result ◽  
Crack Model ◽  
Mixed Mode Fracture ◽  
Cohesive Crack Model ◽  
Zone Method ◽  
The Impact ◽  
Linear Softening

Numerical simulations of the fracture process are challenging, and the discrete element (DE) method is an effective means to model fracture problems. The DE model comprises the DE connective model and DE contact model, where the former is used for the representation of isotropic solids before cracks initiate, while the latter is employed to represent particulate materials after cracks propagate. In this paper, a DE particle-based cohesive crack model is developed to model the mixed-mode fracture process of brittle materials, aiming to simulate the material transition from a solid phase to a particulate phase. Because of the particle characteristics of the DE connective model, the cohesive crack model is constructed at inter-particle bonds in the connective stage of the model at a microscale. A potential formulation is adopted by the cohesive zone method, and a linear softening relation is employed by the traction–separation law upon fracture initiation. This particle-based cohesive crack model bridges the microscopic gap between the connective model and the contact model and, thus, is suitable to describe the material separation process from solids to particulates. The proposed model is validated by a number of standard fracture tests, and numerical results are found to be in good agreement with the analytical solutions. A notched concrete beam subjected to an impact loading is modeled, and the impact force obtained from the numerical modeling agrees better with the experimental result than that obtained from the finite element method.

State-of-the-Art Review on Concrete Softening Curve

2010 ◽  
Vol 168-170 ◽  
pp. 669-673
Author(s):  
Zhi Fang Zhao ◽  
Zhi Gang Zhao ◽  
Xiao Jie Feng ◽  
Ming Li
Keyword(s):  
Constitutive Law ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Direct Tension ◽  
Tension Softening ◽  
Nonlinear Form ◽  
Determination Methods ◽  
Relationship Of ◽  
Inverse Analysis Method

The cohesive crack model is widely employed to the fracture analysis of concrete for mode I crack. The tension softening relationship is a very important constitutive law in the cohesive crack model. The determination methods of tension softening relationship of concrete are introduced in this paper which are direct tension methods, J-integral method and inverse analysis method. Meanwhile, those simplified softening curves including linear form and nonlinear form are summarized.

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