A severe, spurious dependence of numerical simulations on the mesh size and orientation can be observed in elasto-plastic models with a non-associated flow rule. Such mesh dependency effects are quite well-known and vastly investigated in problems with the presence of strain softening in the constitutive relation. However, other material instabilities, like non-associated plastic flow, can also cause mesh sensitivity. Indeed, loss of well-posedness of the problem in quasi-static analyses is the fundamental cause of the observed mesh dependence. It has been known since long that non-associated plastic flow can cause loss of stability, but the consequence for mesh sensitivity, and subsequently, for the difficulty of the equilibrium-finding iterative procedure to converge, have remained largely unnoticed. The present thesis deals with exploring the possibility of using non-standard continua, namely the Cosserat continuum models, in non-associated plasticity problems to tackle the pathological mesh dependencies not only on the size of the elements but also on the orientation of them. The motivation in this thesis for using the Cosserat continuum models for this purpose, lies in the additional parameters that are specified in such a model, i.e. the micro-rotations and characteristic length scale. These features make the Cosserat continuum model a suitable choice to simulate and capture the behavior of the granular and geomaterials. The characteristic length scale helps regularise the strain localisation problems and prevent loss of uniqueness of solution.
The mesh size dependency of the results for classical non-associated plasticity models is analysed in depth using an infinitely long shear layer. It is shown that the mesh effect disappears when the standard continuum model is replaced by a Cosserat continuum. Next, the dependence of the shear-band inclination in a biaxial test
on the mesh size as well as on the mesh orientation is investigated. The orientation of the developed shear band is found to be dependent on the orientation of the mesh for classical models. Using a Cosserat continuum model, numerical solutions result for shear-band formation
which are independent of the size and the orientation of the discretisation
