Structural Engineering and Mechanics

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Mode I crack propagation analisys using strain energy minimization and shape sensitivity

  • Beatriz Ferreira Souza (Department of Civil Engineering, University of Brasilia (UnB), Campus Darcy Ribeiro) ;
  • Gilberto Gomes (Department of Civil Engineering, University of Brasilia (UnB), Campus Darcy Ribeiro)
  • Received : 2024.04.18
  • Accepted : 2024.09.19
  • Published : 2024.10.10
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Abstract

The crack propagation path can be considered as a boundary problem in which the crack advances towards the interior of the domain. Consequently, this poses an optimization problem wherein the local crack-growth direction angle can be treated as a design variable. The advantage of this approach is that the continuous minimization of strain energy naturally leads to the mode I propagation path. Furthermore, this procedure does not rely on the precise characterization of the stress field at the crack tip and is independent of stress intensity factors. This paper proposes an algorithm based on internal point exploration as well as shape sensitivity optimization and strain energy minimization to determine the crack propagation direction. To implement this methodology, the algorithm utilizes a modeling GUI associated with an academic analysis program based on the Dual Boundary Elements Method and determines the propagation path by exploiting the elastic strain energy at points in the domain that are candidates to be included in the boundary. The sensitivity of the optimal solution is also assessed in the vicinity of the optimum point, ensuring the stability and robustness of the solution. The results obtained demonstrate that the proposed methodology accurately predicts the crack propagation direction in Mode I opening for a single crack (lateral and central). Furthermore, robust optimal solutions were achieved in all cases, indicating that the optimal solution was not highly sensitive to changes in the design variable in the vicinity of the optimal point.

Keywords

Acknowledgement

This study was financed in part by the Coordination for the Improvement of Higher Education Personnel (CAPES) and Graduate Program in Structures and Civil Construction at the University of Brasilia.

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