For many engineering problems it can be assumed that the damaged material elastic response at a fixed damage state is linear and hyperelastic. With this assumption, a systematic and rigorous approach for formulating damaged elastic stress-strain relations is presented. The approach is based on the Fourier series representations of two naturally defined damage orientation distribution functions and on a theorem on elasticity tensors, and developed resorting neither to the notion of effective stress (strain) nor to the hypothesis of strain (stress) equivalence nor to that of elastic energy equivalence. The proposed approach is finally illustrated by applying it to Light Grey Blue lake Nike Free 4.0 V2 Men
initially isotropic materials and to unidirectional fiber-reinforced composites.
The behavior of physical complexity and mutual information function of the outcome of a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game is studied. The first magnitude is a measure rooted in the Kolmogorov–Chaitin theory and the second a measure related to Shannon's information entropy. Extensive computer simulations were done, as a result
of which, is proposed an ansatz for physical complexity of the type C(l)=lα and the dependence of the Nike Free 5.0 V4 Women Light Gray Blue exponent α from the parameters of the model is established. The accuracy of our results and the relationship with the behavior of mutual information function as a measure of time correlation of agents choice are discussed.