Proc. of the International Conference on Computational Plasticity,
Barcelona, 11-14 September 2000. (CD-ROM)


Milan Jirásek
Swiss Federal Institute of Technology
LSC -DGC, EPFL, 1015 Lausanne, Switzerland


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.


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 format (470 kB) or in PDF format (165 kB).

EPFL / 27 March 2000 /