TY - JOUR
T1 - A two-scale generalized finite element method for fatigue crack propagation simulations utilizing a fixed, coarse hexahedral mesh
AU - O’Hara, P.
AU - Hollkamp, J.
AU - Duarte, C. A.
AU - Eason, T.
N1 - Funding Information:
The financial support of the Air Force Office of Scientific Research through Task No. 09RB07COR (Dr. David Stargel, Program Officer), is gratefully acknowledged.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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 $$\textit{hp}$$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.
AB - 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 $$\textit{hp}$$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.
KW - Computational fracture mechanics
KW - Generalized finite elements
KW - Multi-scale methods
KW - Partition-of-unity methods
KW - hp-Methods
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U2 - 10.1007/s00466-015-1221-7
DO - 10.1007/s00466-015-1221-7
M3 - Article
AN - SCOPUS:84953349213
SN - 0178-7675
VL - 57
SP - 55
EP - 74
JO - Computational Mechanics
JF - Computational Mechanics
IS - 1
ER -