  We investigate the effect of uniaxial heterostrain on the interacting phase
diagram of magic-angle twisted bilayer graphene. Using both self-consistent
Hartree-Fock and density-matrix renormalization group calculations, we find
that small strain values ($\epsilon \sim 0.1 - 0.2 \%$) drive a
zero-temperature phase transition between the symmetry-broken Kramers
intervalley-coherent insulator and a nematic semi-metal. The critical strain
lies within the range of experimentally observed strain values, and we
therefore predict that strain is at least partly responsible for the
sample-dependent experimental observations.
