Fractional Derivatives and Dynamical Systems in Material Instability

Abstract

Loss of stability is studied extensively in nonlinear investigations, and classified as generic bifurcations. It requires regularity, being connected with non-locality. Such behavior comes from gradient terms in constitutive equations. Most fractional derivatives are non-local, thus by using them in defining strain, a non-local strain appears. In such a way, various versions of non-localities are obtained by using various types of fractional derivatives. The study aims for constitutive modeling via instability phenomena, that is, by observing the way of loss of stability of material, we can be informed about the proper form of its mathematical model.

Editorial for Special Issue “Fractional Behavior in Nature 2019”

“…In [2], Peter Béda studies material instability problems, such as shear band or neck formation, and uses the information gathered to obtain constitutive modeling. The obtained model together with the equations of motion and the kinematic equation, form a system which has generic bifurcation at loss of stability.…”