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Publications Influence

A finite element method for crack growth without remeshing

- N. Moës, J. Dolbow, T. Belytschko
- Mathematics
- 10 September 1999

SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both… Expand

4,804 292- PDF

Element‐free Galerkin methods

- T. Belytschko, Y. Lu, L. Gu
- Mathematics
- 30 January 1994

An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares… Expand

4,754 290

Elastic crack growth in finite elements with minimal remeshing

- T. Belytschko, T. Black
- Mathematics
- 20 June 1999

A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.… Expand

3,439 246

Nonlinear Finite Elements for Continua and Structures

- T. Belytschko, W. Liu, B. Moran
- Mathematics
- 12 September 2000

Preface. List of Boxes. Introduction. Lagrangian and Eulerian Finite Elements in One Dimension. Continuum Mechanics. Lagrangian Meshes. Constitutive Models Solution Methods and Stability. Arbitrary… Expand

3,189 182- PDF

Meshless methods: An overview and recent developments

- T. Belytschko, Y. Krongauz, D. Organ, Mark A. Fleming, P. Krysl
- Mathematics
- 15 December 1996

Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that… Expand

2,872 106- PDF

Extended finite element method for cohesive crack growth

- N. Moës, T. Belytschko
- Materials Science
- 1 May 2002

The extended finite element method allows one to model displacement discontinuities which do not conform to interelement surfaces. This method is applied to modeling growth of arbitrary cohesive… Expand

1,128 61

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

- T. Fries, T. Belytschko
- Mathematics
- 15 October 2010

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve… Expand

930 59- PDF

Atomistic simulations of nanotube fracture

- T. Belytschko, S. Xiao, G. Schatz, R. Ruoff
- Physics
- 15 June 2002

The fracture of carbon nanotubes is studied by molecular mechanics simulations. The fracture behavior is found to be almost independent of the separation energy and to depend primarily on the… Expand

850 57- PDF

Arbitrary discontinuities in finite elements

- T. Belytschko, N. Moës, S. Usui, C. Parimi
- Mathematics
- 10 February 2001

A technique for modelling arbitrary discontinuities in finite elements is presented. Both discontinuities in the function and its derivatives are considered. Methods for intersecting and branching… Expand

988 49

MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD

- N. Sukumar, D. Chopp, N. Moës, T. Belytschko
- Mathematics
- 14 September 2001

A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (S. Osher, J.A.… Expand

994 46- PDF