Revisiting strain localization analysis for elastoplastic constitutive models in geomechanics

The localization of deformations plays a crucial role in the failure of granular materials. Concerning classical continuum constitutive models, the localization of deformations is considered to be connected to the loss of ellipticity of the governing rate equilibrium equations, and entails mesh sensitivity in finite element simulations. While previous studies are often limited to strain localization analyses of individual tests, the focus of the present contribution lies on studying the localization properties in general constitutive states. For this purpose, a staggered optimization algorithm for determining the loss of ellipticity, considering both extreme values, minimum and maximum, of the determinant of the acoustic tensor, is proposed. Part of this algorithm representing a novel application of spherical Fibonacci lattices for discretizing the feasible domain of the associated optimization problem. In the presented localization study of the widely recognized modified Cam-clay model, special attention is paid to determining the influence of the individual model parameters. Specifically, three factors favoring strain localization are found, namely (i) a low value of the ratio of the primary compression index and the recompression index, (ii) a large value of the critical state frictional constant, as well as (iii) a large value of Poisson's ratio. Moreover, a structural finite element study is performed, confirming the results of localization analyses at the constitutive level.