# A path-independent integral and the approximate analysis of strain

@inproceedings{Rice1968API, title={A path-independent integral and the approximate analysis of strain}, author={John R. Rice}, year={1968} }

Abstract : 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. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in…

## 7,287 Citations

### An integral associated with the state of a crack tip in a non-elastic material

- Materials Science
- 1977

An integral has been proposed for a non-elastic material whose value is determined by the magnitude of the singularities at the tip of a crack but which may be evaluated mainly far away from the…

### Non-linear analysis of shallow cracks in smooth and notched plates Part 1: Analytical evaluation

- Engineering
- 2005

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The…

### Computation of the J‐integral for large strains

- Engineering
- 2007

The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all…

### Use of the J Contour Integral in Elastic-Plastic Fracture Studies by Finite-Element Methods:

- Physics
- 1976

In Part 1, a brief summary of the justification and advantages of the use of the J contour integral in elastic-plastic finite-element analysis is given. A more detailed appraisal is then made of its…

### The J-contour integral in peridynamics via displacements

- PhysicsInternational Journal of Fracture
- 2019

Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding…

### On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material

- Physics
- 2011

The path-dependence of the J-integral is investigated numerically via the finite-element method, for a range of loadings, Poisson’s ratios, and hardening exponents within the context of J2-flow…

## References

SHOWING 1-10 OF 28 REFERENCES

### The determination of the elastic field of an ellipsoidal inclusion, and related problems

- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1957

It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation.…

### Contained plastic deformation near cracks and notches under longitudinal shear

- Materials Science
- 1966

An exact linear elastic-perfectly plastic solution is presented for the problem of a sharp notch (or, when the notch angle is zero, a crack) in a plane of finite width subjected to anti-plane…

### Representation of plasticity at notches by linear dislocation arrays

- Materials ScienceProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1965

Further work is reported on the use of linear dislocation arrays to represent plastic relaxation round notches. In previous papers the relaxation in an infinite medium by arrays collinear with the…

### On the Stress Distribution at the Base of a Stationary Crack

- Engineering, Physics
- 1956

In an earlier paper it was suggested that a knowledge of
the elastic-stress variation in the neighborhood of an
angular corner of an infinite plate would perhaps be of
value in analyzing the…

### ELASTIC-PLASTIC DEFORMATION OF A SINGLE GROOVED FLAT PLATE UNDER LONGITUDINAL SHEAR

- Engineering, Materials Science
- 1963

Abstract : The development of the plastic strain in a V-grooved flat plate under longitudinal shear was followed from the elastic through the partially plastic to the fully plastic condition for a…

### EXPERIMENTAL DETERMINATION OF PLASTIC CONSTRAINT AHEAD OF A SHARP CRACK UNDER PLANE-STRAIN CONDITIONS.

- Engineering
- 1966

Abstract : An experimental method of indentifying the plastic constraint ahead of a sharp crack loaded under plane-strain conditions is proposed. The method is based on the idea that the cleavage…

### Rupture of rubber. II. The strain concentration at an incision

- Engineering
- 1955

The strain distribution around the tip of an incision in a thin test-piece of highly elastic material is considered. Using the results of a previous paper, relations between this strain distribution…

### Effects of root radius, stress, crack growth and rate on fracture instability

- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1965

Of various criteria for fracture at the root of a notch, the energy, local stress, and displacement criteria have limited validity. More appropriate is the history of both stress and strain over a…