A virtual crack extension method to compute energy release rates using a complex variable finite element method

The complex-valued finite element method, ZFEM, is proposed as a new virtual crack extension method to compute the energy release rate. The energy release rate is computed as a numerical derivative of the strain energy with respect to a crack extension using the complex Taylor series expansion metho...

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Vydáno v:Engineering fracture mechanics Ročník 162; s. 95 - 111
Hlavní autoři: Millwater, H., Wagner, D., Baines, A., Montoya, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.08.2016
Témata:
Complex Taylor series expansion method
Complex variable finite element method
Computation
Derivatives
Energy release rate
Finite element method
Fracture mechanics
Mathematical analysis
Mathematical models
Self-similarity
Stiffness derivative method
Strain energy release rate
Virtual crack extension method
Virtual crack extension method
Complex Taylor series expansion method
Complex variable finite element method
Strain energy release rate
Stiffness derivative method
ISSN:0013-7944, 1873-7315
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Shrnutí:The complex-valued finite element method, ZFEM, is proposed as a new virtual crack extension method to compute the energy release rate. The energy release rate is computed as a numerical derivative of the strain energy with respect to a crack extension using the complex Taylor series expansion method (CTSE). This is accomplished using a finite element method with complex nodal coordinates and extending the crack by a very small quantity along the imaginary directions of the complex nodal coordinates. The resulting finite element formulation becomes complex valued with the imaginary component of the strain energy containing the energy release rate. This method retains the conceptual simplicity of numerical differentiation but eliminates numerical issues regarding perturbation of the crack size. Both two- and three-dimensional examples are provided. Numerical examples indicate that the energy release rate computed using ZFEM is of the same accuracy as the domain-based J integral formulation. The method is very general and can be applied to self-similar or non-self-similar crack extensions.
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ISSN:0013-7944
1873-7315
DOI:10.1016/j.engfracmech.2016.04.002