We consider rate-independent models which are defined via two functionals: the time-dependent energy-storage functional I : [0, T ]×X → [0,∞] and the dissipation distance D : X × X → [0,∞]. A function z : [0, T ] → X is called a solution of the energetic model, if for all 0 ≤ s < t ≤ T we have stability: I(t, z(t)) ≤ I(t, z̃) +D(z(t), z̃) for all z̃ ∈ X; energy inequality: I(t, z(t))+DissD(z, [s, ...