International Journal for Numerical Methods in Engineering

Fredriksson, Magnus; Ottosen, Niels Saabye

doi: 10.1002/nme.2026pmid: N/A

Based on the assumed strain method, an eight‐node hexahedral element is proposed. Consistent choice of the fundamental element stiffness guarantees convergence and fulfillment of the patch test a priori. In conjunction with a γ‐projection operator, the higher order strain field becomes orthogonal to rigid body and linear displacement fields. The higher order strain field in question is carefully selected to preserve correct rank for the element stiffness matrix, also for distorted elements. Volumetric locking is also removed effectively. By considerations of the bending energy, improved accuracy is obtained even for coarse element meshes. The choice of local co‐ordinate system aligned with the principal axes of inertia makes it possible to improve the performance even for distorted elements. The strain‐driven format obtained is well suited for materials with non‐linear stress–strain relations. Several numerical examples are presented where the excellent performance of the proposed eight‐node hexahedral is verified. Copyright © 2007 John Wiley & Sons, Ltd.

Areias, Pedro M. A.; Belytschko, Ted

doi: 10.1002/nme.2028pmid: N/A

A method for the analysis of shear bands using local partition of unity is developed in the framework of the extended finite element method (XFEM). Enrichments are introduced for both the displacement field and the thermal field. The shear band width is determined by minimizing the plastic work. A coupled finite strain thermo‐elastoplastic constitutive law is used. The enrichment is injected into the mesh when the material law becomes unstable. The criterion based on a complete stability analysis for materials in the finite strain regime including heat conduction, strain hardening, strain rate hardening and thermal softening is presented. A mixed continuous quadrilateral element is employed. The method is applied to the Nesterenko experiments, which exhibit multiple propagating shear bands and other problems. Copyright © 2007 John Wiley & Sons, Ltd.

Kim, Ki‐Seok; Lee, Hae Sung

doi: 10.1002/nme.2031pmid: N/A

This paper presents a new incremental formulation for predicting the curved growth paths of two‐dimensional fatigue cracks. The displacement and traction boundary integral equations (BIEs) are employed to calculate responses of a linear elastic cracked body. The Paris law and the principle of local symmetry are adopted for defining the growth rate and direction of a fatigue crack, respectively. The three governing equations, i.e. the BIEs, the Paris law and the local symmetry condition, are non‐linear with respect to the crack growth path and unknowns on the boundary. Iterative forms of three governing equations are derived to solve problems of the fatigue crack growth by the Newton–Raphson method. The incremental crack path is modelled as a parabola defined by the crack‐tip position, and the trapezoidal rule is employed to integrate the Paris law. The validity of the proposed method is demonstrated by two numerical examples of plates with an edge crack. Copyright © 2007 John Wiley & Sons, Ltd.

Salvadori, Alberto

doi: 10.1002/nme.2041pmid: N/A

The present work deals with the application of the traction hypersingular boundary integral equation to approximate the stress tensor along the boundary, by making use of unit vectors that differ from the normal at the boundary. It is proved that special care is required in the evaluation of the free terms, in order to avoid insidious and unexpected errors. Copyright © 2007 John Wiley & Sons, Ltd.

Liu, Jianfei; Chen, Bin; Chen, Yongqiang

doi: 10.1002/nme.2044pmid: N/A

In this paper, we investigate boundary recovery, the problem that has troubled researchers ever since Delaunay‐based methods were applied to generate mesh. There are a number of algorithms for boundary recovery already and most of them depend heavily on adding extra nodes. In this paper, we make an effort to seek a method to recover boundaries without using extra nodes.