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We study the onset of localisation of plastic deformation for a class of materials that exhibit both temperature and rate sensitivity. The onset of localisation is determined via an energy bifurcation criterion, defined by the postulate that viscoplastic materials admit a critical (mechanical) energy input above which deformation becomes unstable and plastic localisation ensues. In analogy to the classical concepts of mechanics, the conditions for the onset of localisation in temperature-sensitive viscoplastic materials are reached at a critical stress. However, it is shown that in viscoplastic materials a material bifurcation occurs when the heat supply through mechanical work surpasses the diffusion capabilities of the material. This transition from near-isothermal stable evolution to near-adiabatic thermal runaway is the wellknown concept of shear heating. Here, it is generalised and the correspondence between this runaway instability and the localisation of plastic deformation in solid mechanics is detailed. The obtained phase space controlling the localisation is shown to govern the evolution of the system in the postyield regime. These results suggest that the energy balance essentially drives the evolution of the plastic deformation and therefore constitutes a physics-based hardening law for thermoviscoplastic materials.

Item Type:	Refereed Article
Keywords:	buckling
Research Division:	Mathematical Sciences
Research Group:	Applied Mathematics
Research Field:	Theoretical and Applied Mechanics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
Author:	Bassom, AP (Professor Andrew Bassom)
ID Code:	109812
Year Published:	2016
Web of Science® Times Cited:	5
Deposited By:	Mathematics and Physics
Deposited On:	2016-07-04
Last Modified:	2017-11-08
Downloads:	46 View Download Statistics