Statistics of energy dissipation and stress relaxation in a crumpling network of randomly folded aluminum foils

We study stress relaxation in hand folded aluminum foils subjected to the uniaxial compression force F(λ). We found that once the compression ratio is fixed (λ=const) the compression force decreases in time as Fâ̂F₀P(t), where P(t) is the survival probability time distribution belonging to the domain of attraction of max-stable distribution of the Fréchet type. This finding provides a general physical picture of energy dissipation in the crumpling network of a crushed elastoplastic foil. The difference between energy dissipation statistics in crushed viscoelastic papers and elastoplastic foils is outlined. Specifically, we argue that the dissipation of elastic energy in crushed aluminum foils is ruled by a multiplicative Poisson process governed by the maximum waiting time distribution. The mapping of this process into the problem of transient random walk on a fractal crumpling network is suggested.