Gradient plasticity modelling of strain localization in granular materials

Abstract

SUMMARYThe flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus.

Shear banding analysis of geomaterials by strain gradient enhanced damage model

“…For example, it was shown by Roscoe (1970), Mü hlhaus and Vardoulakis (1987), that the thickness of the shear band is of several times of the mean grain diameter d 50 for granular materials. In Al Hattamleh et al (2004), it was further demonstrated that other factors, such as the external confining pressures and elastic properties, may also act as influential components to the length scale. However, the internal length scale functions differently in different gradient models, so that there is no unified physical interpretation of l. In this paper, the internal length scale is regarded as a material constant that depends on the mean size of inhomogeneous microstructure in the material and may be experimentally determined, as has been stated in Zhou et al (2002).…”

A finite element implementation of the nonlocal granular rheology

“…The local rheology then relates the shear stress,τ , and the pressure, p, to the shear plastic strain rateγ p (defined in general later in Eqs. (11) and (19), respectively). Basic dimensional analysis applied to this case leads to two dimensionless groups: the inertial number, I =γ p d 2 ρ s /p, and the stress ratio, µ =τ /p, which are then related through a one-to-one functional dependence.…”

Numerical simulation of fabric anisotropy and strain localization of sand under simple shear

“…∇ 2 p represents the Laplacian of effective plastic strain. Note that in the previous contributions by the authors, the term l 2 G was lumped into a single coefficient term as in Al Hattamleh et al [4,5].…”

“…The double-slip gradient model is used to study the characteristics of strain localization and shear band initiation in a simple shear test. Note that a similar constitutive model but using void fabric tensor in the formulation has been used by the authors to solve boundary value problems involving localization in a biaxial shear test [4] and the stress dip in granular heaps [34].…”

“…By splitting the effective plastic strain into a component that is solely dependent on the local point and a component that is contributed by the length scale, Al Hattamleh et al [4,5] utilized the concept of a representative elemental volume to derive l as a function of particle size…”