Post-Critical Plastic Deformation Pattern in Incrementally Nonlinear Materials at Finite Strain
Deformation pattern in a simple, time-independent material with a yield-surface vertex effect are investigated in plane stress and plane strain beyond the critical instant of ellipticity loss under isothermal, quasistatic loading. The energy criterion of path instability applied to a family of post-critical solutions eliminates unstable deformation paths and enforces the return to the elliptic regime or its boundary. In that way an automatic branch switching algorithm for the discretized problem is used to determine the overall deformation pattern, although the solutions remain locally indeterminate due to the absence of an internal length scale. The incipient volume fraction of multiple planar bands has a well-defined value insensitive to the mesh size in finite element calculations. The observed formation of coarse, differently aligned secondary shear bands in isochoric plain strain compression at later stages of the numerical simulation is theoretically supported by the energy criterion.
KeywordsShear Rate Shear Band Localization Zone Critical Instant Deformation Path
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