A computational approach to handle complex microstructure geometries

By Nicolas Moës, Mathieu Cloirec, P. Cartraud, Jean-François Remacle. 2003

773 citations recorded by the source corpus.

In multiscale analysis of components, there is usually a need to solve microstructures with complex geometries. In this paper, we use the extended finite element method (X-FEM) to solve scales involving complex geometries. The X-FEM allows one to use meshes not necessarily matching the physical surface of the problem while retaining the accuracy of the classical finite element approach. For material interfaces, this is achieved by introducing a new enrichment strategy. Although the mesh does not need to conform to the physical surfaces, it needs to be fine enough to capture the geometry of these surfaces. A simple algorithm is described to adaptively refine the mesh to meet this geometrical requirement. Numerical experiments on the periodic homogenization of two-phase complex cells demonstrate the accuracy and simplicity of the X-FEM. (C) 2003 Elsevier B.V. All rights reserved.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a772b1ecd5e46e3814c01d71422ed50b5a8792e7

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Stability of incompressible formulations enriched with X-FEM (2008, methodology): “The X-FEM method has been used for the simulation of a wide variety of problems such as fracture mechanics problems (2D[18–20], 3D[21–23], plates [24,25], cohesive zone modeling [26,27], dynamic fracture [28], nonlinear fracture mechanics[29–31]), holes [32,33], but also material inclusions [33,34] ”
X-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries (2008, background): “The linear and bilinear weak forms are simply integrated on the matter part of the elements [8,12].”
A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries (2012, methodology): “To address this issue, we employ a scaling factor s as introduced in (4) to avoid excessively large gradients in the enrichment functions [19].”
Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals (2010, methodology): “[15] used an enrichment with a discontinuous derivative to describe the non-smooth behavior of the solution at material interfaces in microstructural geometries.”
Imposing Dirichlet boundary conditions in the extended finite element method (2006, methodology): “The discontinuities may be related to cracks [7, 8], material interfaces [9, 10] or voids [11].”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, background): “Note that in an earlier reference [42] a similar idea was adopted with a different purpose of eliminating the issue of blend elements in the modeling of weak discontinuities.”
Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings (2012, background): “Indeed, level set functions, introduced in Osher and Sethian [26], have been widely used to represent material interfaces or free boundaries in an easy manner [22,18].”
Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties (2004, methodology): “Despite the disadvantages associated with conventional modeling tools like FEM in efficiently model real microstructures, serious and novel attempts are being made to incorporate three dimensional analyses into practice [8, 9, 10, 13, 14, 15, 16].”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “With suitable extensions of the algorithm, quadrature schemes can also be developed for higher-order finite elements and weak discontinuities [76–80].”
A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels (2005, methodology): “Some work along these lines using the X-FEM has been performed by Moës et al. (2003), albeit for stationary material interfaces.”