Twinning is an important deformation mechanism in crystalline materials. Twins nucleate, then grow, forming a discrete pattern of deformation bands with a certain thickness. The mechanism for twin growth is not completely understood. We present a simple phase field model which captures the physics of twin growth and reproduces the details observed during in situ electron backscatter diffraction experiments on α-uranium. The interaction between residual dislocations at twin interfaces and mobile dislocations in untwinned regions increases the stress needed for twin growth. This is described by a nonlocal term in the proposed constitutive equations: the nucleation stress of a twin increases proportionally to the twin phase field in a neighborhood. Competition between slip and twinning favors the nucleation of a new twin rather than the growth of a preexisting twin. The phase field model is coupled with a crystal plasticity finite element solver that includes the plastic deformation due to twinning. Simulations are able to reproduce the number of twins and their thicknesses as a function of the strain observed during in situ electron backscatter diffraction experiments. The stress-strain curve is also reproduced. This comparison allows the values of the nucleation stress and the interaction strength between residual and mobile dislocations to be found. It also gives an estimation of the density of residual dislocations that is consistent with the observed twin thickness. This model can be applied to understand microstructural effects in materials using twinning as a strengthening mechanism.