Adaptive hierarchical refinement of NURBS in cohesive fracture analysis

Lin Chen, Erik Jan Lingen and René de Borst
Int J Numer Meth Engng. 2017;112:2151–2173, DOI: 10.1002/nme.5600


Adaptive hierarchical refinement in isogeometric analysis is developed to model cohesive crack propagation along a prescribed interface. In the analysis, the crack is introduced by knot insertion in the NURBS basis, which yields C−1 continuous basis functions. To capture the stress state smoothly ahead of the crack tip, the hierarchical refinement of the spline basis functions is used starting from a coarse initial mesh. A multilevel mesh is constructed, with a fine mesh used for quantifying the stresses ahead of the crack tip, knot insertion to insert the crack, and coarsening in thewake of the crack tip, since a lower resolution suffices there. This technique can be interpreted as a moving mesh around the crack tip. To ensure compatibility with existing finite element programs, an element-wise point of view is adopted using Bézier extraction. A detailed description is given how the approach can be implemented in a finite element data structure. The accuracy of the approach to cohesive fracture modelling is demonstrated by several numerical examples, including a double cantilever beam, an L-shaped specimen, and a fibre embedded in an epoxy matrix.

A parallel linear solver exploiting the physical properties of the underlying mechanical problem

F.J. Lingen, P.G. Bonnier, R.B.J. Brinkgreve, M.B. Van Gijzen, C. Vuik
Comput Geosci (2014) 18:913–926, DOI 10.1007/s10596-014-9435-x


The iterative solution of large systems of equations may benefit from parallel processing. However, using a straightforward domain decomposition in “layered” geomechanical finite element models with
significantly different stiffnesses may lead to slow or non-converging solutions. Physics-based domain decomposition is the answer to such problems, as explained in this paper and demonstrated on the basis of a few examples. Together with a two-level preconditioner comprising an additive Schwarz preconditioner that operates on the sub-domain level, an algebraic coarse grid preconditioner that operates on the global level, and additional load balancing measures, the described solver provides an efficient and robust solution of large systems of equations. Although the solver has been developed primarily for geomechanical problems, the ideas are applicable to the solution of other physical problems involving large differences in material properties.

Nozzles – on external loads and internal pressure

C.J. Dekker, H.J. Bos
International Journal of Pressure Vessels and Piping, Volume 72, Issue 1, June 1997, Pages 1–18


Close comparison of local load stress calculation methods reveals considerable differences. To investigate we performed many finite element analyses of nozzles on cylinders concentrating not just on the shell stresses but also on the stresses in the nozzle wall. Local load stresses were sometimes found to be much higher in the nozzle than in the shell. This led us to formulate a ‘modified improved shrink ring method’ and to devise multiplication (contour-) charts for deriving local load nozzle stresses from local load shell stresses. Being important for a proper nozzle assessment, pressure induced stresses were investigated too. This resulted in non-dimensional parameter graphs to determine pressure induced stresses at nozzles. © 1997 Elsevier Science Ltd.