In this approach, the plastic part of the deformation field, traditionally described by regular mappings, is interpreted as localized yielding along flow surfaces, with a kinematics analogous to that of crack formation. The resulting deformation is structured, being composed of a bulk and a surface part, respectively due to the elastic distortion of massive material portions and to localized yielding. There is an energetic competition between these two contributions in the energy functional, whose minimization is sought under irreversibility conditions for the inelastic phenomena. Numerical experiments are performed with a regularized variational approach. Paradigmatic examples show that plastic strain concentrates in coarse bands, but the bands may coalesce to form a plastic region, depending upon the shape and size of the body, the presence of pre-existing defects (voids, holes, notches) and the values of the governing parameters.
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Recall that the model of  is symmetric in tension-compression, so that it does not rule out overlapping of crack lips.
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The authors gratefully acknowledge the Research Fund for Coal and Steel for support under grant RFSR-CT-2012-00026 (“S+G” research project).
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Freddi, F., Royer-Carfagni, G. Plastic Flow as an Energy Minimization Problem. Numerical Experiments. J Elast 116, 53–74 (2014). https://doi.org/10.1007/s10659-013-9457-y
- Variational approach
- Flow lines
Mathematics Subject Classification