We study an instability occurring at high strain-rate deformations, induced by thermal softening properties of metals, and leading to the formation of shear bands. We consider adiabatic shear deformations of thermoviscoplastic materials and establish the existence of a family of focusing self-similar solutions that capture this instability. The self-similar solutions emerge as the net response resulting from the competition between Hadamard instability and viscosity. Their existence is turned into a problem of constructing a heteroclinic orbit for an associated dynamical system, which is achieved with the help of geometric singular perturbation theory.
CITATION STYLE
Lee, M. G., Katsaounis, T., & Tzavaras, A. E. (2018). Localization of adiabatic deformations in thermoviscoplastic materials. In Springer Proceedings in Mathematics and Statistics (Vol. 237, pp. 269–280). Springer New York LLC. https://doi.org/10.1007/978-3-319-91548-7_21
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