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Date of Publication:2022-10-04

Journal:固体力学学报

Volume:38

Issue:2

Page Number:157-164

ISSN No.:0254-7805

Abstract:The cohesive zone model is widely used in fracture mechanics. When the
   fracture process zone (FPZ) in front of the crack tip is too large to be
   neglected,the nonlinear behavior must be considered. That is to say,in
   this circumstance the linear fracture mechanics is no longer valid. In
   order to take into account the nonlinear behavior in FPZ,many fracture
   models have been proposed,among which,the cohesive zone model (CZM)
   might be one of the simplest and has been widely used. However,there
   still remain some problems in the existing numerical methods; for
   instance,length of the fracture process zone cannot be obtained
   accurately; dense meshes are required,etc. In order to get over these
   difficulties,a new analytical singular element is proposed in the
   present study and further extended into the cohesive zone model for
   crack propagation problems. In this singular element,the cohesive
   traction is approximately expressed in the form of polynomial expanding
   though Lagrange interpolation. The special solution corresponding to
   each expanding term is specified analytically. Each special solution
   strictly satisfies the requirements of both differential equations of
   interior domain and the corresponding traction expanding terms. The real
   cohesive traction acting on the cohesive crack surface is thus expressed
   in a natural and strict way. Then the special solution can be
   transformed into nodal forces of the present singular element.
   Assembling the stiffness matrix and nodal force into the global FEM
   system,the cohesive crack problem can be analyzed. An efficient
   iteration procedure is also proposed to solve the nonlinear problem.
   Finally, the cohesive crack propagation under arbitrary external loading
   can be simulated,and the length of FPZ, crack tip opening displacement
   (CTOD) and other parameters in the cohesive crack problem can be
   obtained simultaneously. The validity of the present method is
   illustrated by numerical examples.

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