  This work revolves around the rigorous asymptotic analysis of models in
nonlocal hyperelasticity. The corresponding variational problems involve
integral functionals depending on nonlocal gradients with a finite interaction
range $\delta$, called the horizon. After an isotropic scaling of the
associated kernel functions, we prove convergence results in the two critical
limit regimes of vanishing and diverging horizon. While the nonlocal gradients
localize to the classical gradient as $\delta\to 0$, we recover the Riesz
fractional gradient as $\delta\to \infty$, irrespective of the nonlocal
gradient we started with. Besides rigorous convergence statements for the
nonlocal gradients, our analysis in both cases requires compact embeddings
uniformly in $\delta$ as a crucial ingredient. These tools enable us to derive
the $\Gamma$-convergence of quasiconvex integral functionals with varying
horizon to their local and fractional counterparts, respectively.
