Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test

By John Dolbow, A. Devan. 2004

80 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2cfa9062150e6b2b1b0adba5e125834946746f50

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions (2010, background): “(34) For fatigue life prediction under multi-axial loading, the following equivalent stress intensity factor, 𝐾eqv , is also computed: 𝐾eqv = 𝐾I 2 + 𝐾II 2+(1 − 𝜈2)𝐾III 2 (35) In Eqn (35) 𝜇 and where 𝜅 are defined by 𝜇 = 𝐸 2(1+𝜈) , 𝜅 = 3 − 4𝜈 for the plain-strain assumption or 𝜅 = (3 − ”
Strain smoothing in FEM and XFEM (2010, background): “In particular, the suppression of volumetric locking for incompressible materials [31,50].”
Extended meshfree methods without branch enrichment for cohesive cracks (2007, methodology): “If the cohesive crack is considered and a crack tip is located on an edge of a domain of influence, not inside of any domain of influence at the same time, a successful enrichment can be devised by using only the sign function or the Heaviside step function without other enrichment functions [18,51]”
Stress analysis around crack tips in finite strain problems using the eXtended finite element method (2005, methodology): “It seems that only one paper has been published on this problem: this paper, presented by Dolbow and Devan [14] concerns geometrically nonlinear fracture with the X-FEM.”
Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “A discontinuous patch test [20] for the Laplace crack problem is solved to verify the consistency of the formulation.”
Stability of incompressible formulations enriched with X-FEM (2008, background): “The latest work concerning volumetric incompressibility was proposed by Dolbow and Devan [29].”
The MLS-based numerical manifold method with applications to crack analysis (2014, methodology): “This example was devised by Dolbow and Devan (2004) for the purpose of testing if the sophisticated approximations they developed could pass the discontinuous patch test.”