On the Numerical Implementation of a Multi-Mechanism Cyclic Plasticity Model Associated to a Dilation Second Gradient Model Aiming Strain Localization Mitigation

Abstract

This paper deals with numerical simulations of granular soils, idealized by a cyclic multi-mechanism anisotropic non-associated plasticity constitutive model (Aubry et al. 1982; Hujeux 1985) coupled to a dilation second gradient model (Fernandes et al. 2008), under a finite elements method framework. This constitutive model is integrated through an implicit scheme into the Finite Element software Code_Aster(Foucault 2009). The use of this constitutive model, in case of strain localization, exhibits mesh sensitivity as for any strain-softening model. First we verify the ability of the dilation second gradient model to (1) circumvent the problem of mesh sensitivity with this model and to (2) describe the post-peak behaviour of the studied loading process. We studied a biaxial laboratory test, on Hostun sand, under drained conditions and monotonic loading. Second we develop a methodology to determine the values of the second gradient parameter – i.e. characteristic length – for different sets of soil model parameters. We have adapted a 1-D theoretical approach proposed by Chambon et al. (2001), applied to our constitutive model, whose comparison with our numerical results provides a characteristic length. To check the ability of the dilation second gradient model to ensure objective results with this soil constitutive model, we performed an extensive validation on a bearing capacity case with excavation.