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. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.

Elastic crack growth in finite elements with minimal remeshing

Meshless methods: An overview and recent developments

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.

Non-Linear Finite Element Analysis of Solids and Structures: de Borst/Non-Linear Finite Element Analysis of Solids and Structures

This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.

As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

The C programming language

On August 24, 2006, the Standard Performance Evaluation Corporation (SPEC) announced CPU2006 [2], which replaces CPU2000. The SPEC CPU benchmarks are widely used in both industry and academia [3].

https://www.spec.org/cpu2006/publications/CPU2006benchmarks.pdf

SPEC CPU2006 benchmark descriptions

Preface. List of Boxes. Introduction. Lagrangian and Eulerian Finite Elements in One Dimension. Continuum Mechanics. Lagrangian Meshes. Constitutive Models Solution Methods and Stability. Arbitrary Lagrangian Eulerian Formulations. Element Technology. Beams and Shells. Contact--Impact. Appendix 1: Voigt Notation. Appendix 2: Norms. Appendix 3: Element Shape Functions. Glossary. References. Index.

/pdf/nonlinear-finite-elements-for-continua-and-structures-1qwp4eb2pg.pdf

Nonlinear Finite Elements for Continua and Structures

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

/pdf/extended-finite-element-method-for-three-dimensional-crack-1fm01px0sf.pdf

Extended finite element method for three-dimensional crack modelling

Based on a line-integral expression for the energy release rate in terms of crack tip fields, which is valid for general material response, a (area/volume) domain integral expression for the energetic force in a thermally stressed body is derived. The general three-dimensional finite domain integral expression and the two-dimensional and axisymmetric specializations for the energy release rate are given. The domain expression is naturally compatible with the finite element formulation of the field equations. As such it is ideally suited for efficient and accurate calculation of the pointwise values of the energy release rate along a three-dimensional crack front. The finite element implementation of the domain integral corresponds to the virtual crack extension technique. Procedures for calculating the energy release rate using the numerically determined field solutions are discussed. For illustrative purposes several numerical examples are presented.

Energy release rate along a three-dimensional crack front in a thermally stressed body

The application of the Natural Element Method (NEM) 1; 2 to boundary value problems in two-dimensional small displacement elastostatics is presented. The discrete model of the domain consists of a set of distinct nodes N, and a polygonal description of the boundary @. In the Natural Element Method, the trial and test functions are constructed using natural neighbour interpolants. These interpolants are based on the Voronoi tessellation of the set of nodes N. The interpolants are smooth (C 1 ) everywhere, except at the nodes where they are C 0 . In one-dimension, NEM is identical to linear nite elements. The NEM interpolant is strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates imposition of essential boundary conditions. A methodology to model material discontinuities and non-convex bodies (cracks) using NEM is also described. A standard displacement-based Galerkin procedure is used to obtain the discrete system of linear equations. Application of NEM to various problems in solid mechanics, which include, the patch test, gradient problems, bimaterial interface, and a static crack problem are presented. Excellent agreement with exact (analytical) solutions is obtained, which exemplies the accuracy and robustness of NEM and suggests its potential application in the context of other classes of problems|crack growth, plates, and large deformations to name a few. ? 1998 John Wiley & Sons, Ltd.

/pdf/the-natural-element-method-in-solid-mechanics-3x5o8vclau.pdf

The natural element method in solid mechanics

SUMMARY The Element-Free Galerkin (EFG) method is a meshless method for solving partial di⁄erential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom. ( 1997 by John Wiley & Sons, Ltd.

Brian Moran

Papers

Nonlinear Finite Elements for Continua and Structures

Extended finite element method for three-dimensional crack modelling

Energy release rate along a three-dimensional crack front in a thermally stressed body

The natural element method in solid mechanics

Enriched element-free galerkin methods for crack tip fields