A virtual crack extension method to compute energy release rates using a complex variable finite element method. (August 2016)

• Record Type: Journal Article
• Authors: Millwater, H.; Wagner, D.; Baines, A.; Montoya, A.
• Is Part Of: Engineering fracture mechanics. Volume 162(2016)
• Page Start: 95
• Page End: 111
• Publication Date: 2016-08
• Subjects: Strain energy release rate -- Virtual crack extension method -- Stiffness derivative method -- Complex variable finite element method -- Complex Taylor series expansion method; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2016.04.002
• Languages: English
• ISSNs: 0013-7944

Abstract

Abstract: 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.