Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.
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de Borst, R. Numerical modelling of bifurcation and localisation in cohesive-frictional materials. PAGEOPH 137, 367–390 (1991). https://doi.org/10.1007/BF00879040
- Strain localisation
- finite-element analysis
- micro-polar continua
- strain softening
- non-associated plasticity