A consistent characteristic length for smeared cracking models

A consistent characteristic length for smeared cracking models A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two‐dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

A consistent characteristic length for smeared cracking models

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 1989 John Wiley & Sons, Ltd
ISSN
0029-5981
eISSN
1097-0207
D.O.I.
10.1002/nme.1620280214
Publisher site
See Article on Publisher Site

Abstract

A numerical scheme for crack modelling by means of continuous displacement fields is presented. In two‐dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Feb 1, 1989

References

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