Solving thermal and phase change problems with the eXtended finite element method

By R. Merle, John Dolbow. 2002

154 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/449fa51db48aa34bc0e183955b9fdbd1b9c60a2b

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “(2001), a computational model for rigid particles in Stokes flow was proposed, whereas moving phase boundary problems have been modeled using the coupled extended finite element and level set methods (Merle and Dolbow, 2002; Ji et al., 2002; Chessa et al., 2002).”
The extended finite element method in thermoelastic fracture mechanics (2008, methodology): “Though XFEM was applied to thermal problems in [16] and to shear band problems with thermal effects in [17], it is applied to steady-state thermoelastic fracture mechanics for the first time in this paper.”
An Extended Finite Element Method for Two-Phase Fluids (2003, methodology): “Wagner et al. [37] solve problems involving particulate Stokes ow. Chessa et al. [6], Dolbow and Merle [10] and Renaud and Dolbow [ 25 ] applied XFEM to solidication problems.”
Imposing Dirichlet boundary conditions in the extended finite element method (2006, methodology): “Another tempting approach is to enrich the material interface with a discontinuous Heaviside function (as if it were a crack) and then saw together both sides with Lagrange multipliers, following the idea initiated by Merle and Dolbow [15].”
Reengineering Aircraft Structural Life Prediction Using a Digital Twin (2011, methodology): “GFEM has been applied to fracture mechanics [12], thermal analysis [3, 9], and CFD [13] problems.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “In [59, 121] the LATIN method [109] is used for enforcing constraints.”
A hybrid extended finite element/level set method for modeling phase transformations (2002, methodology): “We brie�y describe the two-dimensional analog to the weak formulation =time stepping algorithm presented in Reference [ 24 ].”
A combined extended finite element and level set method for biofilm growth (2008, methodology): “crack growth and solidification in [29,30,31,32,33,34,35] and was recently used for industrial damage tolerance analyses [36].”
A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels (2005, background): “The basic concepts were later adapted to the simulation of evolving phase interfaces by Merle and Dolbow (2002), Ji et al. (2002), and Chessa et al. (2002).”