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Numerical Representation of Crack Propagation within the Framework of Finite Element Method Using Cohesive Zone Model

Zhang, Wenlong
http://rave.ohiolink.edu/etdc/view?acc_num=ucin155325213759381

Abstract Details

2019, PhD, University of Cincinnati, Engineering and Applied Science: Civil Engineering.
Accurate prediction of crack propagation is of great importance in both academy and industry. Among various theoretical models and numerical techniques, the cohesive zone model and its related methods have been extensively employed to fracture problems due to its efficiency. Although well recognized, it still has its limitations. This dissertation starts with tackling a critical discontinuity issue of the exponential cohesive law in cyclic loading scenarios. A new formulation is proposed to correct that error. The cohesive zone model has also been combined with the fatigue crack growth rate to simulate composite delamination, and this method is improved by incorporating the damage accumulation in the ascending part of the cohesive law. The improved method is implemented into LS-DYNA and used to predict the fatigue life of adhesive joints. Another problem of the cohesive zone model is the artificial compliance issue when zero-thickness cohesive elements are inserted between every element boundary. A comprehensive study is done about the relationship between artificial compliance and the initial stiffness in the cohesive zone model. The study can serve as a guideline of whether to choose the bilinear cohesive law or exponential cohesive law in different scenarios. A mesh-independent cohesive element approach is invented for arbitrary crack propagation. This method adopts the cohesive zone enlargement method and is programmed as a user-defined cohesive material subroutine in LS-DYNA. It successfully predicts the crack shape of two benchmark examples. Diving deeper into the mathematical formulation of the cohesive element method, we found out that the Symmetric Interior Penalty Galerkin method can better constraint the elements’ boundaries. A comprehensive comparison is conducted between these two formulations on both their convergence and artificial compliance properties. Furthermore, an algorithm is invented and implemented into LS-DYNA to enable the transition from the SIPG method to cohesive element method to enable element separation. The implementation is verified through several numerical simulations, especially the concrete plate impact problem. Other applications using the cohesive element method in Civil Engineering are also explored. Last but not least, a regularized damage approach to represent the cohesive zone model using the phase field method is explored. A numerical approach to solve the length-scale independent phase field method is invented and is programmed into LS-DYNA. Several simulations are presented to verify the new numerical scheme. Apart from the length-scale independent phase field approach, a local-domain based energy minimization approach is also proposed to reduce the computational cost. It is argued in this dissertation that it is only a small area near the crack tip that the damage value is dominant. Thus instead of solving the minimization problem over the whole domain, which can be cost ineffective in many cases, we can approximate a local domain where the damage values are dominant and only solve the phase field variable within that domain. The principal stress value is used as a criterion to determine whether an element should be included in the local domain, and two simulations are used to demonstrate the feasibility of this method.
Bahram Shahrooz, Ph.D. (Committee Chair)
Donald French, Ph.D. (Committee Member)
Gian Andrea Rassati, Ph.D. (Committee Member)
Ala Tabiei, Ph.D. (Committee Member)
203 p.
Engineering
Cohesive zone model; Crack propagation; Cohesive element method; Phase field method; Discontinuous Galerkin method; Fatigue

Recommended Citations

Citations

  • Zhang, W. (2019). Numerical Representation of Crack Propagation within the Framework of Finite Element Method Using Cohesive Zone Model [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin155325213759381

    APA Style (7th edition)

  • Zhang, Wenlong. Numerical Representation of Crack Propagation within the Framework of Finite Element Method Using Cohesive Zone Model. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin155325213759381.

    MLA Style (8th edition)

  • Zhang, Wenlong. "Numerical Representation of Crack Propagation within the Framework of Finite Element Method Using Cohesive Zone Model." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin155325213759381

    Chicago Manual of Style (17th edition)

ucin155325213759381
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© 2019, some rights reserved.Creative Commons License Numerical Representation of Crack Propagation within the Framework of Finite Element Method Using Cohesive Zone Model by Wenlong Zhang is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.