Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method

Abstract

Kim, D J.; Duarte, C A.; and Eason, T, "Analysis of three-dimensional fracture mechanics problems: A nonintrusive approach using a generalized finite element method" (2012 (structural) and local (crack) scale problems. In the approach presented here, an initial global scale problem is solved by a commercial finite element analysis software, local problems containing 3-D fractures are solved by an hp-adaptive GFEM software and an enriched global scale problem is solved by a combination of the FEM and GFEM softwares. The interactions between the solvers are limited to the exchange of load and solution vectors and does not require the introduction of user subroutines to existing FEM software. As a results, the user can benefit from built-in features of available commercial grade FEM software while adding the benefits of the GFEM for this class of problems. Several threedimensional fracture mechanics problems aimed at investigating the applicability and accuracy of the proposed two-solver methodology are presented.

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

“…The non-intrusive coupling strategy seems to be well-established nowadays in the FEbased computational mechanics community (see, e.g., [10,[14][15][16][17][18][19][20][21][22][32][33][34]). …”

“…Its construction from CAD data is likely to require important human and computing resources since it may be necessary to make several simplification assumptions to proceed to its meshing. The local model may include any specific local behaviors to allow for a more detailed analysis of the large-scale structure (e.g., local plasticity [10], local fracture [15,16], local uncertainties [17], 3D-shell coupling [18], local contact [20], etc).…”

“…The replacement of part of a global model by a more detailed local model can be carried out exactly and non-intrusively: the global model is never modified; only interface displacements and reaction forces are exchanged. This strategy has been successfully applied in many domains (see, e.g., [15,16] for crack propagation, [17] for taking localized uncertainties into account, [18,19] for non-intrusive plate/3D coupling, [20] for non-linear domain decomposition and [21,22] for transient dynamics analysis). It is of interest to note at this stage that this methodology has some similarities with certain superposition-based multiscale methods that have been proposed long before the concept of non-intrusiveness was introduced (see, e.g, [23] for an overview).…”

Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

“…This feature is the basis of the non-overlapping domain decomposition methods developed for high performance computing on parallel computer architectures (see, e.g., [42][43][44]). In the same idea, such a property enables to build non-intrusive coupling algorithms for the modeling of local behaviors (see, e.g., [14,12,32,[34][35][36]). Several numerical codes can then be coupled in an iterative way with the exchange of only interface data to carry out the global/local simulation.…”

“…An iterative coupling technique is used to perform the substitution in an exact but non-intrusive way: only interface data are transmitted from one model to the other and the global stiffness operator remains unchanged (independently from the shape of the local domain). The performance of such a strategy has been highlighted in many applications (see, e.g., [12,32] for the modeling of crack propagation, [33] for the modeling of localized uncertainties, [34] for 3D-plate coupling and [35] for nonlinear domain decomposition).…”