A two-scale generalized finite element method for fatigue crack propagation simulations utilizing a fixed, coarse hexahedral mesh

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• 作者：P. O’Hara ; J. Hollkamp ; C. A. Duarte ; T. Eason
• 关键词：Generalized finite elements ; Multi ; scale methods ; Partition ; of ; unity methods ; Computational fracture mechanics ; hp ; Methods
• 刊名：Computational Mechanics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：57
• 期：1
• 页码：55-74
• 全文大小：3,258 KB
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• 作者单位：P. O’Hara (1)
  J. Hollkamp (3)
  C. A. Duarte (2)
  T. Eason (3)
  
  1. Universal Technology Corporation, 1270 North Fairfield Rd, Dayton, OH, 45432, USA
  3. Air Force Research Laboratory, Structural Sciences Center, WPAFB, Dayton, OH, 45433, USA
  2. Newmark Laboratory, Department of Civil and Environmental Engineering, University of Illinois, 205 North Mathews Avenue, Urbana, IL, 61801, USA
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Numerical and Computational Methods in Engineering
  Computational Science and Engineering
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0924

文摘

This paper presents a two-scale extension of the generalized finite element method (GFEM) which allows for static fracture analyses as well as fatigue crack propagation simulations on fixed, coarse hexahedral meshes. The approach is based on the use of specifically-tailored enrichment functions computed on-the-fly through the use of a fine-scale boundary value problem (BVP) defined in the neighborhood of existing mechanically-short cracks. The fine-scale BVP utilizes tetrahedral elements, and thus offers the potential for the use of a highly adapted fine-scale mesh in the regions of crack fronts capable of generating accurate enrichment functions for use in the coarse-scale hexahedral model. In this manner, automated \(\textit{hp}\)-adaptivity which can be used for accurate fracture analyses, is now available for use on coarse, uniform hexahedral meshes without the requirements of irregular meshes and constrained approximations. The two-scale GFEM approach is verified and compared against alternative approaches for static fracture analyses, as well as mixed-mode fatigue crack propagation simulations. The numerical examples demonstrate the ability of the proposed approach to deliver accurate results even in scenarios involving multiple discontinuities or sharp kinks within a single computational element. The proposed approach is also applied to a representative panel model similar in design and complexity to that which may be used in the aerospace community. Keywords Generalized finite elements Multi-scale methods Partition-of-unity methods Computational fracture mechanics hp-Methods