Localization of Adiabatic Deformations in Thermoviscoplastic Materials
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2018-06-27
Print Publication Date2018
Permanent link to this recordhttp://hdl.handle.net/10754/628076
MetadataShow full item record
AbstractWe 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.
CitationLee M-G, Katsaounis T, Tzavaras AE (2018) Localization of Adiabatic Deformations in Thermoviscoplastic Materials. Springer Proceedings in Mathematics & Statistics: 269–280. Available: http://dx.doi.org/10.1007/978-3-319-91548-7_21.
SponsorsThis research was supported by King Abdullah University of Science and Technology (KAUST).
Conference/Event name16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016