Simulation of Complex 3D Non-planar Crack Propagation Using Robust Adaptive Re-meshing and Radial Basis Functions
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.