Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics


Localization in inelastic rate dependent shearing deformations

Th. Katsaounis, M-G. Lee, A. Tzavaras, Localization in inelastic rate dependent shearing deformations​, Journal of Mechanics and Physics of Solids, 98(1):106-125, 2017
Theodoros Katsaounis, Min-Gi Lee, Athanasios Tzavaras
shear bands, Hadamard instability, shear localization
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, in- dicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing struc- ture and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions​.