Strain localization in geomaterials and regularization: rate-dependency, higher order continuum theories and multi-physics

Strain localization is a central topic in geomechanics as it is often related to failure and other important physical phenomena and geological processes.This chapter is addressed to graduate students and researchers interested in an introduction to strain localization analysis. We present fundamental notions that are frequently met in this topic, such as loss of uniqueness, bifurcation, stability, illposedness and mesh dependency.We first show the inherent pathology of classical, Cauchy, rate-independent continua that leads to mesh sensitivity and we present methods for alleviating/regularizing this problem. These methods involve the use of theories that result in the introduction of characteristic time and length scales into the system. We focus mainly on ratedependent constitutive laws, Micromorphic continua and multiphysics.Regularization of strain localization is shown as general as possible using bifurcation and stability analysis and without prescribing exact constitutive relations. Onedimensional examples are then used to illustrate each regularization approach and show in a mathematically simple manner the main results