A finite element method for the simulation of strong and weak discontinuities in solid mechanics

By Anita Hansbo, Peter Hansbo. 2004

872 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fa4568c452ca4e569c72f6bea7c0471f48dae064

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Finite strain fracture of 2D problems with injected anisotropic softening elements (2014, background): “Total and partial remeshing approaches [25,32,10,18], versions of local displacement [47,46,41,57,44] (and strain [50,2,58]) enrichments, clique overlaps [38], edges repositioning or edge-based fracture with R-adaptivity [45]; Element erosion [63], smeared procedures [49], viscousregularized techniq”
Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions (2017, methodology): “Therefore, we have employed the phantom node method (Chau-Dinh et al. 2012; Hansbo and Hansbo 2004; Rabczuk et al. 2008; Song et al. 2006; Vu-Bac et al. 2013) in order to model fracture in PNCs.”
Finite strain fracture of plates and shells with configurational forces and edge rotations (2013, background): “Full and localized rezoning and remeshing approaches [5, 10–12], local displacement [13–16] (or strain [17, 18]) enrichments, and clique overlaps [2, 19]; Element erosion [20], smeared band procedures [21], viscous-regularized techniques [22], and gradient and nonlocal continua [23]; Phase-field mod”
Stress-based topology optimization using spatial gradient stabilized XFEM (2017, positive): “Following the work by Terada et al. (2003), Hansbo and Hansbo (2004), and Makhija and Maute (2014), a generalized Heaviside enrichment strategy with multiple enrichment levels is adopted.”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, background): “Hansbo and Hansbo came up with yet another technique to describe strong discontinuities within finite elements [22] whose kinematics was proved equivalent to that of XFEM [5].”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, background): “Note that the Heaviside enriched XFEM/GFEM formulation can also handle problems with weak discontinuities, though enforcing continuity at the interface is required [15].”
A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity (2009, methodology): “In this case there is no stability problem in the pressure, and the results of [6] can be directly applied in the compressible subdomain.”
An augmented finite element method for modeling arbitrary discontinuities in composite materials (2009, methodology): “A very similar procedure was proposed by Hansbo and Hansbo (2002, 2004) , who elucidated their technique through a 3-node linear element and demonstrated its effectiveness through elliptic interface”