CRITICAL EIGENMODES AND INTRINSIC MATERIAL LENGTH

Abstract

The main aim of the paper is to study how the inclusion of nonlocality (gradient dependent terms) into the constitutive equations changes the mathematical description of material instability problems. The motivation comes from the theory of dynamical systems, when the stability analysis can be performed by finding eigenvalues and eigenvectors of certain linear operators. Some of the eigenvectors define critical eigenmodes and the postbifurcation investigation is based on these critical eigenmodes. The results show that by considering the body as a dynamical system the critical eigenmodes can be selected when the constitutive equation contains the second gradient term. The wavelength of the dominant eigenmode can be identified with the intrinsic material length.