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Cosserat continuum models are motivated by modeling size effects in materials with micro-structure. While elastic Cosserat continuum models can reproduce size effects in deformation stiffness, inelastic models are often used to capture localization and post failure behavior of materials. In application of inelastic Cosserat models, parameter determination is a difficult issue not fully addressed. The purpose of this paper is to discuss parameter-related characteristic lengths in Cosserat continuum modeling of granular materials.

Based on a Cosserat continuum extension of a hypoplastic model for granular media, interpretation of additional parameters are sought through analysis of simple one-dimensional shear. Governing equations are obtained, respectively, for small strain shear formation and for stead flow state in localized zone.

Two characteristic lengths are obtained analytically for granular materials: one governs the size effect near boundaries in shear deformation, the other scales the thickness of shear band in failure. While both characteristic lengths are proportional to the micro-structure length (the mean grain diameter), the former is related to the micro-stiffness parameter, and the latter depends on the micro-strength parameter. The results reveal a connection between size effects, the micro-structure length and the material properties. The work also provides a new perspective to inelastic Cosserat continuum models, as well as a possible way for determination micro-deformation and strength parameters.

The results reveal a connection between size effects, the micro-structure length and the material properties. The work provides a new perspective and an interpretation to the micro-deformation and strength parameters of inelastic Cosserat continuum models, as well as a possible way for determination of these parameters.

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.

The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.

The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.