Nonlocal regularization of an anisotropic critical state model for sand

Abstract

Many advanced constitutive models which can capture the strain-softening and state-dependent dilatancy response of sand have been developed. These models can give good prediction of the single soil element behaviour under various loading conditions. But the solution will be highly mesh-dependent when they are used in real boundary value problems due to the strain-softening. They can give mesh-dependent strain localization pattern and bearing capacity of foundations on sand. Nonlocal regularization of an anisotropic critical state sand model is presented. The evolution of void ratio which has a significant influence on strain-softening is assumed to depend on the volumetric strain increment of both the local and neighbouring integration points. The regularization method has been implemented using the explicit stress integration method. The nonlocal model has been used in simulating both drained plane strain compression and the response of a strip footing on dry sand. In plane strain compression, mesh-independent results for the force–displacement relationship and shear band thickness can be obtained when the mesh size is smaller than the internal length. The force–displacement relationship of strip footings predicted by the nonlocal model is much less mesh-sensitive than the local model prediction. The strain localization under the strip footing predicted by the nonlocal model is mesh independent. The regularization method is thus proper for application in practical geotechnical engineering problems.

Variability and loss of uniqueness of numerical solutions in FEM×DEM modeling with second gradient enhancement

“…Several attempts have been made to avoid this problem by introducing an internal length into enhanced models. These enhanced models are generally divided into nonlocal models [10][11][12][13] and models based on gradient theory. 8,[14][15][16] Both approaches have been successful in regularizing mesh-dependency issues.…”

A robust stress update algorithm for elastoplastic models without analytical derivation of the consistent tangent operator and loading/unloading estimation

“…The stress update problem of elastoplastic models is an initial value problem of the ordinary differential equations (ODEs) constrained by inequalities. The ODEs are usually transformed into algebraic equations to solve based on the explicit 1,2 or implicit [3][4][5][6] integral schemes. The implicit algorithm requires the Jacobian matrix in the local stress update iteration, which can be difficult to derive, especially for sophisticated soil models.…”