Localisation of deformation as a local quasi-static/dynamic transition

The problem of modeling the strain localization in elasto-visco-nonlinear materials and structures submitted to so-called quasi-static loadings is considered. Unlike the usual approaches, which assume that the localization band remains in (quasi-)static equilibrium, it is here assumed that localization is essentially a dynamic phenomenon, even if the external loadings are 'quasi-static'. This means that the localization criterion proposed is also a 'local loss of the (quasi-)staticity' criterion. As soon as the criterion is verified, the dynamic problem is treated (at least locally) instead of the (quasi-)static one. (Author)