TY - GEN
T1 - Localization of Adiabatic Deformations in Thermoviscoplastic Materials
AU - Lee, Min-Gi
AU - Katsaounis, Theodoros
AU - Tzavaras, Athanasios
N1 - KAUST Repository Item: Exported on 2021-09-14
Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST).
PY - 2018/6/27
Y1 - 2018/6/27
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/628076
UR - https://link.springer.com/chapter/10.1007%2F978-3-319-91548-7_21
UR - http://www.scopus.com/inward/record.url?scp=85049438780&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-91548-7_21
DO - 10.1007/978-3-319-91548-7_21
M3 - Conference contribution
AN - SCOPUS:85049438780
SN - 9783319915470
SP - 269
EP - 280
BT - Theory, Numerics and Applications of Hyperbolic Problems II
PB - Springer Nature
ER -