Mixed-mode stress intensity factors computation in functionally graded materials using a hypercomplex-variable finite element formulation

The hypercomplex-variable finite element method, ZFEM, is extended to compute the mode I and mode II energy release rates (ERR) for functionally graded materials. The ERR is computed using an efficient local stiffness derivative approach, L-ZFEM, that computes the derivative of the stiffness matrix...

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Vydáno v:International journal of fracture Ročník 226; číslo 2; s. 219 - 232
Hlavní autoři: Ramirez-Tamayo, Daniel, Balcer, Matthew, Montoya, Arturo, Millwater, Harry
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2020
Springer Nature B.V
Springer
Témata:
Automotive Engineering
Characterization and Evaluation of Materials
Chemistry and Materials Science
Civil Engineering
Classical Mechanics
Complex variables
Computation
Crack tips
Derivatives
Energy release rate
Exact solutions
Finite element method
Fracture mechanics
Functionally gradient materials
J integral
Material properties
Materials Science
Mechanical Engineering
Mechanics
Original Paper
Perturbation
Self-similarity
Stiffness matrix
Stress intensity factors
User elements
Non-homogeneous materials
Virtual crack extension method
Complex variable finite element method
J-integral
Strain energy release rate
ISSN:0376-9429, 1573-2673
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Popis
Shrnutí:The hypercomplex-variable finite element method, ZFEM, is extended to compute the mode I and mode II energy release rates (ERR) for functionally graded materials. The ERR is computed using an efficient local stiffness derivative approach, L-ZFEM, that computes the derivative of the stiffness matrix at the element level using the highly accurate complex-variable sensitivity method. Mode I and II values are computed using the appropriate perturbation of the surrounding crack tip elements, i.e., perturbations in the self-similar (mode I) and perpendicular (mode II) directions. The energy release rate values are as accurate as the J -integral results. The advantage of this approach is that the derivatives are only required for a small number of elements surrounding the crack tip and no energy conservation integrals are required. In addition, derivatives of the ERR with respect to the FGM material properties are computed by combining the local stiffness derivative approach with a global complex variable formulation, G-ZFEM. This methodology was implemented into the commercial finite element software Abaqus through a combination of Abaqus intrinsic elements and a complex variable user element subroutine (UEL). Numerical results are compared against analytical solutions and other numerical approaches and demonstrate excellent accuracy.
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content type line 14
NA0003948
USDOE National Nuclear Security Administration (NNSA)
ISSN:0376-9429
1573-2673
DOI:10.1007/s10704-020-00489-5