Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes

By Dae-Jin Kim, J. Pereira, Carlos Armando Duarte. 2010

137 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4ddc22158f60c597fe6dd55925ed7fde787093ee

How researchers see this paper

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

In Computational Mechanics

1. Carlos Armando Duarte
2. Dae-Jin Kim
3. J. Pereira
4. P. Gupta
5. J. Kim
6. Xiangmin Jiao
7. J. Plews
8. Varun Gupta

In Mechanics of Materials

1. Carlos Armando Duarte
2. Dae-Jin Kim
3. J. Pereira
4. J. Kim
5. J. Plews
6. P. Gupta
7. Xiangmin Jiao
8. T. Eason

Citations in the corpus

• Bridging multiple structural scales with a generalized finite element method (2015, methodology): “This condition also allows for enforcement of the boundary condition as temperature (Dirichlet), flux (Neumann), or convection (mixed) [54], because there are no constraints on solution continuity between local problems.”
• Analysis of three-dimensional fracture mechanics problems: A non-intrusive approach using a generalized finite element method (2012, methodology): “Extensive numerical and mathematical analysis presented in [13,28,31] demonstrate that the accuracy of uG is close to that provided by a direct simulation of the problem with cracks discretized in the global problem.”
• A generalized finite element method with global-local enrichment functions for confined plasticity problems (2012, methodology): “The traction vector, t(umax G,lin), that appears in the integral over ∂ ΩL\(∂ ΩL ∩∂ ΩG) can be computed as presented in [17], t (umax G,lin) = n̂ ·σ (u nmax G,lin) = n̂ · (C : ε (u nmax G,lin)), (14) where n̂ is the outward unit normal vector to ∂ ΩL.”
• Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, methodology): “This methodology was successfully applied in conjunction with the GFEM in [14,15,31, 32 ,50,51 ]a s well as the element-free Galerkin method [33].”
• A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “They are nested in the global mesh to facilitate numerical integration at the coarse scale [40, 43].”
• A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “Other types of boundary conditions such as spring or traction boundary conditions can also be applied on ∂ Ω k L \ (∂ Ω k L ∩ ∂ Ω) [30] .”
• Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM (2012, background): “Some few examples are [5, 6] for threedimensional cracks, [7–9] for cohesive crack growth, [10,11] for considering dynamic fracture, and [12–15] for treating the blending and integration issues.”
• Meshfree Methods: Progress Made after 20 Years (2017, unknown): “This method has been applied to fracture modeling (Kim et al. 2010; Kim and Duarte 2015; Pereira et al. 2012).”
• Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics (2015, background): “Numerically generated global-local enrichment functions [17, 26] provide an alternative to analytical vector singular enrichments to obtain a well-conditioned system of equations.”