Coarse-grained flux density profiles in type-II superconductors with nonparallel vortex configurations are obtained by a proposed phenomenological least action principle. We introduce a functional C[ H] which is minimized under a constraint of the kind J ∈ ∆( H, x), where ∆ is a bounded set.In particular, we choose the isotropic case | J | ≤ J c (H), for which the field penetration profiles H( x, t) are derived when a changing external excitation is applied. Faraday's law, and the principle of minimum entropy production rate for stationary thermodynamic processes dictate the evolution of the system.Calculations based on the model can reproduce the physical phenomena of flux transport and consumption, and the striking effect of magnetization collapse in crossed field measurements. PACS number(s): 41.20. Gz,74.60.Jg, 74.60.Ge, 02.30.Xx Typeset using REVT E X 1