Modelling of Cohesive-Frictional Materials, Proc. CDM-2004, ed. by P.A.Vermeer et al., A.A.Balkema Publishers, Leiden, The Netherlands, pp. 323-337


   Milan Jirásek
Czech Technical University in Prague, Czech Republic
Peter Grassl
Swiss Federal Institute of Technology at Lausanne, Switzerland


Two classes of nonlocal models for softening materials with nonassociated plastic flow  are described and their localization properties are analyzed. Models of the first class are based on standard plasticity and use a hardening-softening law dependent on both local and nonlocal cumulative plastic strain. Models of the second class are based on combination of plasticity and damage mechanics and use a damage evolution law dependent again on local and nonlocal cumulative plastic strain. Conditions for continuous and discontinuous bifurcations from a uniform state in an infinite medium are derived, and the evolution of localized plastic zone is illustrated by simple one- and two-dimensional examples.


We have shown that there is a close relationship between the critical plastic modulus obtained by classical localization analysis based on the acoustic tensor of a local model and  the conditions of bifurcation from a uniform state for the nonlocal extension of that model based on nonlocal hardening law or nonlocal damage evolution law. The results serve as a basis for the development of a regularized model for concrete that can capture both tensile and compressive failure modes.

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CVUT / 19 November 2004 /