Chris Timbrell, Angelo Maligno, Zentech International Ltd.
David Stevens, BLOS International

NAFEMS World Congress 2013, Austria, 9-12 June 2013

Abstract:
An improved numerical technique for complex shaped non-planar three-dimensional crack growth simulations is proposed. This technique couples the adaptive re-meshing method used during crack growth simulation in the FE- based fracture mechanics code Zencrack with mesh relaxation using radial basis functions. This allows the uninterrupted simulation of crack propagation in engineering structures where the component geometries and local loading conditions may develop complex 3D crack configurations. Collocation with radial basis functions (RBFs) is an effective methodology for the interpolation of arbitrary scalar and vector fields defined over scattered datasets. By defining a mesh displacement field over a volumetric domain, the RBF collocation approach may be used to smoothly map a user-defined displacement of elements onto the entire domain, thereby "relaxing" the mesh around the imposed displacements. This mesh deformation leads, in most cases, to significantly improved element quality in comparison to traditional mesh-relaxation approaches such as Laplacian relaxation. In particular, elements that lie close to the source of a large displacement can be expected to exhibit significantly improved characteristics (such as aspect ratio and skew) in comparison to traditional approaches. The application of RBF deformation to fracture-tracking problems introduces many additional complexities that require novel and creative solutions. The most significant of these is the large difference in length scales between the imposed deformations - which are of element scale, and the constraints at the domain boundaries - which are of problem-scale. These differences in length scales make the problem unsuitable for use with compactly supported collocation methods. To retain a computationally efficient interpolation which is scalable to large problem sizes, a new method for RBF collocation has been developed which is based on large numbers of overlapping local collocation systems, using the underlying elemental structure as a framework. By linking together these overlapping local collocation systems a sparse global matrix may be formed, which can be solved to obtain the displacement at each node within the relaxation domain. For crack propagation simulation it is desirable to allow the mesh to move freely within the domain, as defined by the imposed displacements around the crack-tip, and to constrain the motion of surface and edge nodes such that they remain within their pre-existing geometric surfaces. In this work we describe surface-constraint methods which are suitable for use with complex 3D geometries where the mesh relaxation is performed using globally or locally supported RBF collocation systems.