Abstract

The occurrence of material instabilities in continuum solids is closely associated with the loss of ellipticity in the governing equations. The stability of a material relies on the requirement that the wave speed remains a strictly positive real number for all wave directions. Failure to meet this condition can lead to various types of material instabilities, such as strain localization in the form of shear bands and dynamic instabilities like flutter instability. In this seminar, we explore material instabilities by providing a micromechanical interpretation through the homogenization of prestressed periodic beam lattices. Through homogenization, we can analyze the static and dynamic regimes and unravel the profound connection between the microstructure and the emergence of macroscopic instabilities. Our approach is validated by comparing the response of the discrete lattice, simulated using finite elements, with the response of the equivalent continuum described by the exact Green’s function.