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s speed saturates as it approaches the transverse speed of sound can be satisfied in a number of ways. On one hand, one can simply fit experimental or atomistic simulations data to mathematical functions that phenomenologically describe the speed of the dislocation as τ varies;

hereafter, the resulting mobility laws are called phenomenological mobility laws. On the other hand, one can attempt to produce physically insightful models that attempt to capture, partially at least, the physical effects that fast moving dislocations encounter;

the resulting laws, here termed inertial mobility laws, typically involve an inertia-like force. This section?will review a number of phenomenological and inertial models that have been suggested in the past;

table?1 summarises the models to be studied. This work does not intend to be an exhaustive account of all the mobility laws that have been proposed in the past. Rather, it intends to showcase the most characteristic features of those that are deemed of relevance to shock physics simulations, where dislocations are often expected to move at ? significant fractions of the transverse speed of sound. 2.1.? Phenomenological laws Phenomenological laws are fits to experimental or atomistic simulations data. They attempt to reproduce the observed relationship between the applied resolved shear stress, τ, and the glissile velocity of the dislocation, v, via a best fit equation. Most draw their data from exper? imental observations of dislocation mobility [9] or, more recently, from molecular dynamics simulations of the mobility of dislocations [22, 23]. They tend to describe only the terminal motion of dislocations, i.e. the stationary speed a dislocation reaches under the application of a constant resolved shear stress;

any possible transient effect in the motion of the dislocation is generally missed. 2.1.1.?Taylor'

s model.? Gillis et?al [16] found that the empirically observed relativistic behav- iour of dislocations in many metals could be best described by modifying the linear drag coefficient in equation?(2). The model, apparently originally due to JW Taylor (vid. [11]), prescribes a drag coefficient of the form / = ? d d v c

1 t

0 2

2 (3) where d0 is the low speed drag coefficient and ct the transverse speed of ........