Proc. of the International Conference on Computational Plasticity,
Barcelona, 11-14 September 2000. (CD-ROM)
CONDITIONS OF UNIQUENESS FOR FINITE ELEMENTS WITH EMBEDDED CRACKS
Milan Jirásek
Swiss Federal Institute of Technology
LSC -DGC,
EPFL,
1015 Lausanne,
Switzerland
Abstract
The recently emerged idea of incorporating strain or displacement discontinuities
into standard finite element interpolations has triggered the development
of powerful techniques that allow efficient modeling of regions with highly
localized strains, e.g., of fracture process zones in concrete or shear
bands in metals or soils. The present paper addresses the fundamental issue
of uniqueness of such enriched formulations, which has important implications
for the robustness of the corresponding numerical algorithms. For a linear
triangular element with an embedded strong discontinuity described by traction-separation
law formulated within the framework of damage or plasticity, explicit conditions
that guarantee uniqueness on the element level are derived, and the resulting
restrictions limiting the size of the element are discussed.
Conclusions
This paper has presented a detailed analysis of the basic equations describing
linear triangular finite elements with embedded displacement discontinuities
that represent highly localized cracks. It has been shown that these equations
have a unique solution only if the element size does not exceed a critical
value that is affected by the characteristic length of the material, shape
of the element, Poisson's ratio, and type of problem (plane stress or plane
strain). If uniqueness is lost on the level of a single finite element,
numerical problems resulting into the loss of convergence can be expected
on the global level. The derived conditions permit the design of finite
element meshes for which such problems do not occur.
The complete paper can be downloaded in PostScript
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EPFL / 27 March 2000 / milan.jirasek@epfl.ch