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.

中文翻译：

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温度敏感粘塑性材料中塑性变形的局部化条件

我们研究了一类具有温度和速率敏感性的材料的塑性变形局部化的开始。局部化的开始是通过能量分叉标准确定的，该标准由粘塑性材料接受临界（机械）能量输入的假设定义，高于该能量输入，变形变得不稳定并随之发生塑性局部化。类似于力学的经典概念，温度敏感粘塑性材料的局部化开始条件是在临界应力下达到的。然而，研究表明，在粘塑性材料中，当通过机械功提供的热量超过材料的扩散能力时，就会发生材料分叉。这种从近等温稳定演化到近绝热热失控的转变是众所周知的剪切加热概念。在这里，它进行了概括，并详细说明了这种失控的不稳定性与固体力学中塑性变形的局部化之间的对应关系。获得的控制定位的相空间被证明可以控制系统在屈服后状态下的演化。这些结果表明，能量平衡本质上推动了塑性变形的演变，因此构成了热粘塑性材料的基于物理学的硬化规律。获得的控制定位的相空间被证明可以控制系统在屈服后状态下的演化。这些结果表明，能量平衡本质上推动了塑性变形的演变，因此构成了热粘塑性材料的基于物理学的硬化规律。获得的控制定位的相空间被证明可以控制系统在屈服后状态下的演化。这些结果表明，能量平衡本质上推动了塑性变形的演变，因此构成了热粘塑性材料的基于物理学的硬化规律。