A novel SAM/X-FEM coupling approach for the simulation of 3D fatigue crack growth under rolling contact loading

A Computational Framework for Crack Propagation Along Contact Interfaces and Surfaces Under Load

“…where M m ∈ H 1 ( h σ ) is a vector of n mat basis functions for approximating material positions. The integration domain in (57) is represented by a single layer of triangular elements adjacent to the trace of the crack front ∂ h cr on the traction surface h σ . Moreover, the assembly is performed only to the algebraic entry of the system associated with the single node corresponding to ∂ h cr ∩ h σ , see Fig.…”

“…In this section, we verify the implementation of the virtual work of surface traction in the material domain, i.e. of the term T mat in (44) (see (57) for the discretised setting), which contributes to configurational forces driving crack propagation. The verification is based on comparison of the crack energy release rate computed in simulation and from an analytical solution for the stress state around the crack tip in an infinite body under plane strain conditions [98], see Fig.…”

“…In particular, crack propagation has been modelled considering frictional and adhesive contact between crack surfaces [49][50][51][52][53][54]. Some of the most popular methods for such problems are X-FEM [55][56][57], cohesive elements [49], phase-field [58] and short crack correction models [59]. These models are often employed to investigate the influence of fretting fatigue on the nucleation of a crack on one side of the contact interface and its propagation towards the interior of the body.…”

“…These models are often employed to investigate the influence of fretting fatigue on the nucleation of a crack on one side of the contact interface and its propagation towards the interior of the body. This class of problem is of great importance for the railway industry [57,[60][61][62][63], as well as for the aviation industry to assess the safety of turbine blades assembly [64][65][66].…”

A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

“…In an iterative process, a part of the global model is replaced by the more detailed local model exactly and non-invasively: the global model is never modified; only interface displacements and reaction forces are exchanged. This strategy along with its concept of non-invasiveness have been successfully applied in FEM and are still gathering a considerable interest in the community (see [19] for local plasticity, [20,21,22,23] for crack propagation, [24,25,26] for fracture modeling with the phase-field approach, [27,28] for domain decomposition solvers, [29] for multi-contact problems, [30] for real aeronautical structures, and [31] for multiscale periodic heterogeneous materials, to name a few). In this work where we consider the coupling of a global IG model with a local FE model, the non-invasive global/local framework appears even more relevant [32]: (i) it naturally avoids costly spline re-parametrization procedures, which may have been necessary otherwise to incorporate a truly-independent local region within the initial IG model, (ii) the global IG stiffness operator can be assembled and factorized only once and the IG system to be solved remains well-conditioned regardless of the shape of the local region, and (iii) it offers the opportunity to simply couple an IG code with any existing robust FE code suitable for the modelling of complex local behaviors.…”