Discontinuous modelling of shear bands using adaptive meshfree methods

Rabczuk, Timon; Samaniego, Esteban

doi:10.1016/j.cma.2007.08.027

Cited by 147 publications

(46 citation statements)

References 90 publications

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“…We can quote Gao and Klein (1999) Rabczuk and Samaniego (2008), besides the earlier references Needleman and Tvergaard (1994a,b), Belytschko and Tabbara (1996), and Zhou et al (1996b). The challenge is to accurately capture the experimentally observed failure mode transition from ductile to brittle failure as the impact velocity reduces, as well as the critical value of the impact velocity where this transition occurs.…”

Section: Failure Mode Transition In Ductile Materialsmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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This paper presents the extension of some finite elements with embedded strong discontinuities to the fully transient range with the focus on dynamic fracture. Cracks and shear bands are modeled in this setting as discontinuities of the displacement field, the so-called strong discontinuities, propagating through the continuum. These discontinuities are embedded into the finite elements through the proper enhancement of the discrete strain field of the element. General elements, like displacement or assumed strain based elements, can be considered in this framework, capturing sharply the kinematics of the discontinuity for all these cases. The local character of the enhancement (local in the sense of defined at the element level, independently for each element) allows the static condensation of the different local parameters considered in the definition of the displacement jumps. All these features lead to an efficient formulation for the modeling of fracture in solids, very easily incorporated in an existing general finite element code due to its modularity. We investigate in this paper the use of this finite element formulation for the special challenges that the dynamic range leads to. Specifically, we consider the modeling of failure mode transitions in ductile materials and crack branching in brittle solids. To illustrate the performance of the proposed formulation, we present a series of numerical simulations of these cases with detailed comparisons with experimental and other numerical results reported in the literature. We conclude that these finite element methods handle well these dynamic problems, still maintaining the aforementioned features of computational efficiency and modularity.

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Section: Failure Mode Transition In Ductile Materialsmentioning

confidence: 99%

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

2009

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“…They are particularly well suited for dynamic fracture and large deformations. Moreover, adaptive hrefinement can be easily implemented in a meshfree context [185][186][187]. Though all methods discussed so far are capable of capturing discrete cracks, a certain refinement around the crack front is still needed for accuracy and efficiency reasons [188].…”

Section: Meshfree Methodsmentioning

confidence: 99%

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Rabczuk

2013

ISRN Applied Mathematics

151

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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“…This problem also appears in a number of references e.g. [99,101,102,104,105] and the modelling of problems which are dominated by shear bands are covered using meshless methods in [106][107][108]. The Figure 17(d).…”

Section: Footing Loaded On a Slopementioning

confidence: 99%

Finite deformation elasto-plastic modelling using an adaptive meshless method

Ullah

Augarde

2013

Computers & Structures

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'Finite deformation elasto-plastic modelling using an adaptive meshless method. ', Computers and structures., Further information on publisher's website:http://dx.doi.org/10. 1016/j.compstruc.2012.04.001 Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Computers and structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. A denitive version will be subsequently published in Computers and structures, 2012Computers and structures, , 10.1016Computers and structures, /j.compstruc.2012 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Problems including both material and geometric nonlinearities are of practical engineering importance in many applications. Efficient computational modelling of these problems with minimum computer resources remains challenging. Often these problems are modelled with the finite element method (FEM) with adaptive analysis, in which an error estimation procedure automatically determines regions for coarse and fine discretization. Meshless methods offer the attractive possibility of simpler adaptive procedures involving no remeshing, simply insertion or deletion of nodes. However, as meshless methods are computationally more expensive than the FEM, the use of the minimum possible number and proper distribution of nodes are important issues. In this study an adaptive meshless approach for nonlinear solid mechanics is developed based on the element free Galerkin method. An existing error estimation procedure for linear elasto-static problems, is extended here for nonlinear problems including finite deformation and elasto-plasticity, and a new adaptive procedure is described and demonstrated.

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Discontinuous modelling of shear bands using adaptive meshfree methods

Cited by 147 publications

References 90 publications

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

Finite deformation elasto-plastic modelling using an adaptive meshless method

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