Cohesive-traction embedded damage-like constitutive law based on non-local approach and its numerical implementation improved by Petrov-Galerkin method

The objective of this study is to propose cohesive-traction embedded damage-like constitutive law based on non-local approach and its numerical implementation using Petrov-Galerkin method to improve dependence of directional mesh bias in crack propagation problem. The extension from local approach t...

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Bibliographic Details
Published inTransactions of the Japan Society for Computational Engineering and Science Vol. 2021; p. 20210008
Main Authors KANEZAWA, Ryohei, SHINTAKU, Yuichi, TERADA, Kenjiro
Format Journal Article
LanguageJapanese
Published JAPAN SOCIETY FOR COMPUTATIONAL ENGINEERING AND SCIENCE 22.04.2021
Subjects
Cohesive Zone Model
Crack Propagation Analysis
Damage Model
Dependence of Directional Mesh Bias
Mesh Sensitivity
Non-local Approach
Petrov-Galerkin Method
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Summary:The objective of this study is to propose cohesive-traction embedded damage-like constitutive law based on non-local approach and its numerical implementation using Petrov-Galerkin method to improve dependence of directional mesh bias in crack propagation problem. The extension from local approach to non-local approach is made by the introduction of weak formulation of balance equations between principal stresses and cohesive traction vectors. In addition, Petrov-Galerkin method is employed for numerical implementation that allows us to obtain proper crack propagation without dependence of directional mesh bias caused by C0 continuity of shape functions. To represent propagation of crack surface between finite elements, the weighting function of the balance equations is shifted from conventional one, which is the first derivative of a test function, to the same order function as test function, which is obtained by finite difference approximation. After verifying the equivalence of the proposed non-local approach to conventional one, we investigate the sensitivity of an additional numerical parameter to shift the weighting function. Finally, the capability of the proposed method is demonstrated by comparing the numerical results of the crack propagation problem obtained by finite element method and isogeometric analysis between two different meshes.
ISSN:1347-8826
DOI:10.11421/jsces.2021.20210008