Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Abstract

Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

Accelerating isogeometric boundary element analysis for 3‐dimensional elastostatics problems through black‐box fast multipole method with proper generalized decomposition

“…Importantly, IGA offers a considerable potential advantage over the conventional BEM in that it can circumvent the meshing procedure and eliminate geometry representation error. The idea of a true integration between CAD and analysis was explored in various areas including elastostatics,() shape optimization,() acoustics,() and fracture mechanics . However, a well‐known drawback of both BEM and IGABEM remains, ie, the dense (and for the collocation form of the BEM, nonsymmetric) matrix for which O ( n 2 ) operations are needed to compute the matrix coefficients and other O ( n 3 ) operations to solve the system using direct solvers ( n being the number of degrees of freedom (DOF)).…”

“…The idea of a true integration between CAD and analysis was explored in various areas including elastostatics, [22][23][24] shape optimization, 25,26 acoustics, 7,8,27 and fracture mechanics. 28 However, a well-known drawback of both BEM and IGABEM remains, ie, the dense (and for the collocation form of the BEM, nonsymmetric) matrix for which O(n 2 ) operations are needed to compute the matrix coefficients and other O(n 3 ) operations to solve the system using direct solvers (n being the number of degrees of freedom (DOF)). We note that symmetric Galerkin formulations 29 are more amenable to mathematical analysis, and optimal preconditioner strategies (ie, operator preconditioning 30 ) are available.…”

What makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences

“…Recourse is always made to some type of mathematical model, usually a set of partial differential equations (PDEs). The resulting problem is solved numerically using a wide variety of discretisation methods including finite element methods [22][23][24][25][26], finite differences, meshfree methods [27], isogeometric approaches [28,29], geometry independent field approximation [30,31], scaled-boundary finite elements [32][33][34][35][36], boundary element approaches [37], enriched boundary elements [38] or combinations thereof [39][40][41].…”

A review of fatigue crack propagation modelling techniques using FEM and XFEM

“…For each step, the crack is advanced a small length, and the number of cycles required for the next crack increment is estimated using one of the crack propagation laws. In order to accomplish this, the computational method needs to perform the following tasks within each step [12,13]…”