Dynamic extended finite element method (XFEM) analysis of discontinuous media

• Main Author: Toolabi, Milad
• Other Authors: Louca, Luke
• Published: Imperial College London 2015
• Subjects: 620.001
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.705794

The extended finite element method (XFEM) is found promising in approximating solutions to locally non-smooth features such as jumps, kinks, high gradients, inclusions, or cracks in solid mechanics problems. The XFEM uses the properties of the partition of unity finite element method (PUFEM) to represent the discontinuities without the corresponding finite element mesh requirements. In the present thesis numerical simulations of statically and dynamically loaded heterogeneous beams, heterogeneous plates and two-dimensional cracked media of isotropic and orthotropic constitutive behaviour are performed using XFEM. The examples are chosen such that they represent strong and weak discontinuities, static and dynamic loading conditions, anisotropy and isotropy and strain-rate dependent and independent behaviours. At first, the Timoshenko beam element is studied by adopting the Hellinger-Reissner (HR) functional with the out-of-plane displacement and through-thickness shear strain as degrees of freedom. Heterogeneous beams are considered and the mixed formulation has been combined with XFEM thus mixed enrichment functions are used. The results from the proposed mixed formulation of XFEM correlate well with analytical solutions and Finite Element Method (FEM) and show higher rates of convergence. Thus the proposed method is shear-locking free and computationally more efficient compared to its conventional counterparts. The study is then extended to a heterogeneous Mindlin-Reissner plate with out-of-plane shear assumed constant through length of the element and with a quadratic distribution through the thickness. In all cases the zero shear on traction-free surfaces at the top and bottom are satisfied. These cases involve weak discontinuity. Then a two-dimensional orthotropic medium with an edge crack is considered and the static and dynamic J-integrals and stress intensity factors (SIF's) are calculated. This is achieved by fully (reproducing elements) or partially (blending elements) enriching the elements in the vicinity of the crack tip or body. The enrichment type is restricted to extrinsic mesh-based topological local enrichment in the current work. A constitutive model for strain-rate dependent moduli and Poisson ratios (viscoelasticity) is formulated. The same problem is studied using the viscoelastic constitutive material model implemented in ABAQUS through an implicit user defined material subroutine (UMAT). The results from XFEM correlate well with those of the finite element method (FEM). It is shown that there is an increase in the value of maximum J-integral when the material exhibits strain rate sensitivity.