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The kink we found at $v = 0.1~\mathrm{a.u.}$ can be explained by conservation laws in the effective homogeneous electron gas and general properties of electronic density of states in crystalline $\mathrm{Cu}$.  The minimum energy loss with maximum momentum transfer from an electron to an ion moving with velocity $v$ are respectively $2\hbar k_\text{F}$ and $2\hbar k_\text{F} v$ (plus corrections of order $m_\text{e}/m_\text{p}$).   Due to Pauli exclusion only electrons in the energy range $E_\text{F} \pm 2\hbar k_\text{F} v$ can participate in the stopping process.   Taking into account that DFT band structure predicts that the $\mathrm{d}$-band edge  is $\Delta_\text{DFT} = 1.6~\mathrm{eV}$ below the Fermi energy (see for example, Fig. 3(a) Fig.~3(a)  in Ref.~\cite{Lin_2008}), that electron (band) effective mass are close to $1$for  and $k_\text{F} = 0.72$ for the effective homogeneous electron gas of  $\mathrm{Cu}$ $\mathrm{s}$-electrons \cite{Ashcroft_2003}. \cite{Ashcroft_2003}, we can derive a value of th $v_\text{kink}$.  Based in this DFT ground state density of states plus conservation laws we obtain an estimate of $v_\text{kink} = \Delta/\hbar/k_\text{F} = 0.082~\mathrm{a.u.}$ in qualitative agreement with the TDDFT prediction.  In reality, the $\mathrm{d}$-band is about $\Delta_\text{exp} = 2~\mathrm{eV}$ below the Fermi energy as indicated by ARPES \cite{Knapp_1979}, that means that both the DFT-based estimate and the TDDFT result should be giving an underestimation of 25\% of the kink location.  The second (negative) kink at $v = 0.3~\mathrm{a.u.}$ is more difficult to explain precisely as the qualitative description in terms of $k_\text{F}$ (as in the homogeneous eletron gas) become more ambiguous, but it is related to the point at which the whole conduction band (11 $\mathrm{s} + \mathrm{d}$ electrons) starts participating in the process.