CRITICAL WAVE LENGTHS AND INSTABILITIES IN GRADIENT-ENRICHED CONTINUUM THEORIES

ABSTRACT: Continuum material models can be enriched with additional gradients in order to model phenomena that are driven by processes at lower levels of observation. For instance, higher-order gradients of strains or inertia can be included in the equations of elasticity in order to model wave dispersion that occurs in heterogeneous media. These higher-order gradients may be obtained by homogenisation or continualisation procedures applied to heterogeneous micro-structured media. For a systematic comparison of various gradient-enriched continua, dispersion analysis may be used. In this contribution, we will explore the occurence of critical wave lengths and its implications for the material stability. In particular, we will present a unifying theorem that permits to assess the stability of elastic, hardening and softening gradient-enriched continua by means of a critical wave length analysis, whereby the upper or lower bound nature of the critical wave length indicates whether the model is stable or unstable