The extended finite element method (XFEM) for solidification problems

By J. Chessa, Patrick Smolinski, Ted Belytschko. 2002

340 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9b99d5106724093e6806d9c4027815bb14d7b232

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. John Dolbow
2. H. Ji
3. David L. Chopp
4. Adrian J. Lew
5. Gustavo C. Buscaglia
6. Stéphane P.A. Bordas
7. A. Simone
8. Marc Duflot

In Mechanical Engineering

1. Stéphane P.A. Bordas
2. Ted Belytschko
3. Timon Rabczuk
4. Carlos Armando Duarte
5. Thomas-Peter Fries
6. Marc Duflot
7. R. Gracie
8. John Dolbow

In Mechanics of Materials

1. Stéphane P.A. Bordas
2. Ted Belytschko
3. Timon Rabczuk
4. Carlos Armando Duarte
5. Marc Duflot
6. Charles E. Augarde
7. Xiaoying Zhuang
8. Thomas-Peter Fries

Citations in the corpus

• The extended/generalized finite element method: An overview of the method and its applications (2010, background): “[50], Ji and Dolbow [103], and Liu and Borja [114] in the XFEM.”
• The Discontinuity‐Enriched Finite Element Method (2017, neutral): “Equation (5) yields w1 = −xΓ∕L = −w while Equation (6) yields w2 = 1 + w1 = 1 − w.”
• On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) (2011, background): “This enrichment function is suitable for any problem involving discontinuities in the first derivative of the solution such as diffusion problems arising in solidification [39] or biofilm growth [40].”
• A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006, methodology): “The constraints on essential boundary conditions are enforced by a penalty method [27].”
• On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method (2004, methodology): “Previous efforts have enforced Dirichlet conditions weakly using Lagrange multipliers [8, 9] and penalty methods [10].”
• A review of extended/generalized finite element methods for material modeling (2009, background): “Such applications were first proposed in Chessa and Belytschko [24, 23, 22].”
• The extended finite element method in thermoelastic fracture mechanics (2008, background): “Such functions enrich the displacement field in References [18, 26–29] in order to represent material interfaces.”