  Using calculations from first principles based on density functional theory
we have studied the strain sensitivity of the high-field superconducting magnet
A15 Nb3Sn. The Nb3Sn lattice cell was deformed in the same way as observed
experimentally on multi-filamentary, technological wires subject to loads
applied along their axes. The phonon dispersion curves and electronic band
structures along different high-symmetry directions in the Brillouin zone were
calculated, at different levels of applied strain, {\epsilon}, both on the
compressive and the tensile side. Starting from the calculated averaged phonon
frequencies and electron-phonon coupling, the superconducting characteristic
critical temperature of the material, Tc, has been calculated by means of the
Allen-Dynes modification of the McMillan formula. As a result, the
characteristic bell-shaped Tc vs. {\epsilon} curve, with a maximum at zero
intrinsic strain, and with a slight asymmetry between the tensile and
compressive sides, has been obtained. These first-principle calculations thus
show that the strain sensitivity of Nb3Sn has a microscopic and intrinsic
origin, originating from shifts in the Nb3Sn critical surface. In addition, our
computations show that variations of superconducting properties of this
compound are correlated to stress-induced changes in both the phononic and
electronic properties. Finally, the strain function describing the strain
sensitivity of Nb3Sn has been extracted from the computed Tc({\epsilon}) curve,
and compared to experimental data from multi-filamentary wires. Both curves
show the expected bell-shaped behavior, but the strain sensitivity of the wire
is enhanced with respect to the theoretical predictions of the bulk, perfectly
binary and stoichiometric Nb3Sn. Understanding the origin of this difference
might open potential pathways towards the improvement of the strain tolerance
in such systems.
