Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

Recently, the authors (Xiao and Karihaloo, J Mech Mater Struct 1: 2006) obtained universal asymptotic expansions at a cohesive crack tip, analogous to the Williams (ASME J Appl Mech 24: [109][110][111][112][113][114] 1957) expansions at a traction-free crack tip for any normal cohesion-separation law (i.e. softening law) that can be expressed in a special polynomial. This special form ensures that the radial and angular variations of the asymptotic fields are separable as in the Williams expansions. The coefficients of the expansions of course depend nonlinearly on the softening law and the boundary conditions. They demonstrated that many commonly-used cohesion-separation laws, e.g., rectangular, linear, bilinear and exponential, can indeed be expressed very accurately in this special form. They also obtained universal asymptotic expansions when the cohesive crack faces are subjected to Coulomb friction. The special polynomial involves fractional powers which seem rather contrived. In this paper, we will show that the asymptotic expansions can be obtained in a separable form even when the cohesion-separation law is in a special polynomial form involving only integer powers.

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Section: Implementation Of the Asymptotic Fields In Xfem/gfemmentioning

confidence: 99%

Asymptotic fields at the tip of a cohesive crack

Karihaloo

Xiao

2008

Int J Fract

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“…Karihaloo et al [68,116] studied a neartip enrichment basis that includes higher order terms of the asymptotic expansion of the crack tip field in two dimensions. The enrichments are expressed in terms of the mode I and mode II stress intensity factors, K I and K II , so the solution immediately provides these stress intensity factors.…”

Section: Literature Review On Crackmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

1,199

695

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Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

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“…It is more convenient to use only the leading term of the displacement asymptotic field at the tip of a cohesive crack (which ensures a displacement discontinuity normal to the cohesive crack face) as the enrichment function, as in most implementations of the XFEM in the literature. The complete implementation with several examples can be found in [Xiao et al 2006, in press]. In the following, a typical mode I cohesive cracking problem of quasibrittle materials -a three point bend beam without any initial crack (Figure 9) made of a quasibrittle material with the linear softening law (57) -is analyzed.…”

Section: Implementation Of the Asymptotic Fields In Xfem/gfem And Examentioning

confidence: 99%

Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

Xiao

Karihaloo

2006

JOMMS

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The lack of any work on the asymptotic fields at the tips of cohesive cracks belies the widespread use of cohesive crack models. This study is concerned with the solution of asymptotic fields at cohesive crack tips in quasibrittle materials. Only normal cohesive separation is considered, but the effect of Coulomb friction on the cohesive crack faces is studied. The special case of a pure mode I cohesive crack is fully investigated. The solution is valid for any separation law that can be expressed in a special polynomial form. It is shown that many commonly used separation laws of quasibrittle materials, for example, rectangular, linear, bilinear, and exponential, can be easily expressed in this form. The asymptotic fields obtained can be used as enrichment functions in the extended/generalized finite element method at the tip of long cohesive cracks, as well as short branches/kinks.

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Incremental‐secant modulus iteration scheme and stress recovery for simulating cracking process in quasi‐brittle materials using XFEM

Cited by 34 publications

References 32 publications

Asymptotic fields at the tip of a cohesive crack

Asymptotic fields at the tip of a cohesive crack

The extended/generalized finite element method: An overview of the method and its applications

Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

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