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We present the results from an extensive atomistic molecular dynamics simulation study of poly(ethylene oxide) (PEO) doped with various amounts of lithium-bis(trifluoromethane)sulfonimide (LiTFSI) salt under the influence of external electric field strengths up to $1\,$V/nm. The motivation stems from recent experimental reports on the nonlinear response of mobilities to the application of an electric field in such electrolyte systems and arising speculations on field-induced alignment of the polymer chains, creating channel-like structures that facilitate ion passage. Hence, we systematically examine the electric field impact on the lithium coordination environment, polymer structure as well as ionic transport properties and further present a procedure to quantify the susceptibility of both structural and dynamical observables to the external field. Our investigation reveals indeed a coiled-to-stretched transformation of the PEO strands along with a concurrent nonlinear behavior of the dynamic properties. However, from studying the temporal response of the unperturbed electrolyte system to field application we are able to exclude a structurally conditioned enhancement of ion transport and surprisingly observe a slowing down. A microscopic understanding is supplied.