Orthotropic materials such as composites have been increasingly applied in many engineering applications e.g. aerospace, automobile and marine structures because of their high strength and stiffness to weight ratios. Fracture analysis of such media has been the centre of attention for many researchers in recent decades. As the analytical methods cannot be simply employed for complex problems which are common in structural engineering, numerical methods provide better alternatives.

The complexity of engineering problems and the enormous growth in computer technology has led to the development of several numerical methods. Among them, the extended finite element method (XFEM) has proved to be a promising powerful tool in modelling fracture problems because it enables improved approximations of non-smooth solutions such as those including jumps and singularities. In this approach, to crack modelling, the classical finite element approximation is enriched by a discontinuous function and asymptotic crack-tip displacement fields using the framework of partition of unity (PU). In the XFEM, the finite element mesh is not required to conform to the crack boundaries, and hence a single mesh suffices for modelling the crack stability and capturing its evolution.

On the other hand, isogeometric analysis (IGA) is a promising computational scheme that takes advantage of using non-uniform rational B-splines (NURBS) for both the geometric description and the solution field approximation to: exactly represent complex geometries; to increase the order of continuities between elements; to simplify the refinement process; and to improve solution accuracy. Isogeometric analysis has been effectively applied to a large variety of problems.

The two powerful approaches of XFEM and IGA have recently been combined to include the benefits of both [1]. This method which is also called extended isogeometric analysis (XIGA) has been successfully applied for simulation of stationary and propagating cracks in 2D linear-elastic isotropic media.

In this contribution, XIGA is further extended for fracture analysis of cracked linear-elastic orthotropic materials. For this purpose, the orthotropic enrichment functions applied in XFEM are adopted. The Lagrange multiplier method is utilized to impose essential boundary conditions. The Gauss quadrature rule is applied for integration alongside the "sub-triangles approach" and the "almost polar technique" for split and crack tip elements, respectively [1]. In order to compare the results with those obtained by other semi-analytical and numerical methods, mixed mode stress intensity factors are calculated by adopting the interaction integral technique. Finally, several numerical examples are analysed to demonstrate the accuracy and efficiency of the proposed approach.

1

S.Sh. Ghorashi, N. Valizadeh, S. Mohammadi, "Extended isogeometric analysis (XIGA) for simulation of stationary and propagating cracks", International Journal for Numerical Methods in Engineering, 89, 1069-1101, 2012. doi:10.1002/nme.3277

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £50 +P&P)