Benchmarking Fractional and Prony Memory in Viscoplasticity with Directional Hardening

Fractional memory kernels provide compact descriptions of hereditary deformation, but a good fit does not establish that a continuous spectrum is needed. We construct a synthetic prediction benchmark by comparing local, Caputo-fractional and Prony memory in one associated elasto-viscoplastic host with directional hardening. The memory acts on the cumulative plastic multiplier. A positive spectral representation gives a common dissipation identity and finite-energy bounds. Preparations with matched mechanical variables, rate and memory force still separate during a common hold, for fractional and Prony memory alike. This establishes a role for hidden memory states, not a distinction between kernels. In separate fractional-versus-Prony-2 fit-and-predict tests, the generating family has the smaller error on both withheld histories in 20 of 20 low-noise cases and 16 of 18 high-noise cases. Four- and eight-mode Prony laws fit fractional-generated training data slightly better than the fractional law but predict the longer histories less accurately. The spread between fitted predictions is sensitive to the optimization budget and is not treated as proof of non-identifiability. Finer-grid generation and independently refined scoring reduce the prediction margin and expose discretization bias. These synthetic benchmarks distinguish predictive preference among tested candidates; they do not identify a physical spectrum or validate clay behaviour.