2021-04-162019-01-010013794418737315WOS;000483383200018SCOPUS;2-s2.0-85070621827http://hdl.handle.net/10784/29221A “local” hypercomplex-variable finite element method, L-ZFEM, is proposed for the computation of the energy release rate (ERR) using the stiffness derivative equation. This approach is analogous to the stiffness derivative method proposed by Parks and Hellen but has superior numerical accuracy. In addition, this method is significantly more efficient than the previously published “global” hypercomplex-variable finite element method, ZFEM, in that the global hypercomplex system of FE equations is not assembled nor solved. Instead, the displacement field is computed using a traditional, real-valued finite element method, and the numerical derivative of the stiffness matrix at the element level is only computed for a group of local, surrounding elements to the crack tip by using a Taylor series expansion based on complex numbers or dual numbers. The ERR is then determined as a sum of the element contributions. Derivatives of the ERR with respect to an arbitrary model parameter such as a crack extension, material property, or geometric feature are also available using a combination of the global and local methods, GL-ZFEM. Both L-ZFEM and GL-ZFEM were implemented into the commercial finite element software Abaqus through user defined element subroutines. Numerical results show that the ERR obtained by L-ZFEM has the same accuracy as that estimated through the global ZFEM or the J-integral methods but exhibits superior computational efficiency. © 2019 Elsevier Ltdenghttps://v2.sherpa.ac.uk/id/publication/issn/0013-7944info:eu-repo/semantics/articleABAQUSComputational efficiencyCrack tipsEnergy release rateNumerical methodsStiffnessStiffness matrixSubroutinesTaylor seriesComplex taylor series expansionsComplex variable finite elementsDerivative methodHypercomplexJ integralFinite element method2021-04-16Aguirre-Mesa A.M.Ramirez-Tamayo D.Garcia M.J.Montoya A.Millwater H.10.1016/j.engfracmech.2019.106581