Generation via variational convergence of Balanced Viscosity solutions to rate-independent systems

In this paper we investigate the origin of the Balanced Viscosity solution concept for rate-independent evolution in the setting of a finite-dimensional space. Namely, given a family of dissipation potentials $(\Psi_n)_n$ with superlinear growth at infinity and a smooth energy functional $\mathcal{E}$, we enucleate sufficient conditions on them ensuring that the associated gradient systems $(\Psi_n,\mathcal{E})$ Evolutionary Gamma-converge to a limiting rate-independent system, understood in the sense of Balanced Viscosity solutions. In particular, our analysis encompasses both the vanishing-viscosity approximation of rate-independent systems and their stochastic derivation.