Book ChapterDOI
Computational fracture mechanics
James R. Rice,D.M. Tracey +1 more
- pp 585-623
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TLDR
In this article, a finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained, and the three-dimensional aspects of flawed structures and numerical methods of treating them are studied.Abstract:
Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.read more
Citations
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Journal ArticleDOI
An analysis of a new class of integration algorithms for elastoplastic constitutive relations
Michael Ortiz,Juan C. Simo +1 more
TL;DR: In this article, an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations was carried out, where attention was confined to infinitesimal deformations.
Journal ArticleDOI
A stiffness derivative finite element technique for determination of crack tip stress intensity factors
TL;DR: In this article, a finite element technique for determination of elastic crack tip stress intensity factors is presented, based on the energy release rate, and the solution for only a single crack length is required, where the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis.
Journal ArticleDOI
Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory
TL;DR: In this paper, a formulation and algorithmic treatment of static and dynamic plasticity at finite strains based on the multiplicative decomposition is presented which inherits all the features of the classical models of infinitesimal plasticity.
Journal ArticleDOI
Finite element formulations for problems of large elastic-plastic deformation
TL;DR: In this article, an Eulerian finite element formulation for large elastic-plastic flow is presented, based on Hill's variational principle for incremental deformations, and is suited to isotropically hardening Prandtl-Reuss materials.
Journal ArticleDOI
A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
Juan C. Simo,Michael Ortiz +1 more
TL;DR: By assuming from the outset hyperelastic constitutive behavior, an alternative approach to finite deformation plasticity and viscoplasticity is proposed whereby the need for integration of spatial rate constitutive equations is entirely bypassed.
References
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Journal ArticleDOI
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Journal ArticleDOI
On the ductile enlargement of voids in triaxial stress fields
James R. Rice,D.M. Tracey +1 more
TL;DR: In this article, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material.
Journal ArticleDOI
Plane strain deformation near a crack tip in a power-law hardening material
James R. Rice,G. F. Rosengren +1 more
TL;DR: In this paper, the authors investigated the C rack-tip strain singularities with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory).
Journal ArticleDOI
Singular behaviour at the end of a tensile crack in a hardening material
TL;DR: In this paper, a total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used to determine the dominant singularity at the tip of a crack in a tension field.
Related Papers (5)
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
Plane strain deformation near a crack tip in a power-law hardening material
James R. Rice,G. F. Rosengren +1 more