Ebook: On strategies for tracking strong discontinuities in computational failure mechanics

The work deals with the strategies for tracking displacement jumps (strong discontinuities) in
computational failure mechanics in the context of finite elements with embedded discontinuities.
As an alternative to classical strategies, based on the spatial propagation of a selected discon-
tinuity, a new technique is presented. The strategy lies on tracing, at once, the envelope family
of the propagation directions all over the domain and, then, select the one (or the ones) of
interest. The mathematical problem is presented in terms of a heat-conduction like problem,
which facilitates the physical perception of the results and the understanding of the numerical
difficulties. Numerical examples and application to fracture problems are presented.