Browsing by Author "Scholz, Bernd"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    Application of a micropolar model to the localization phenomena in granular materials : general model, sensitivity analysis and parameter optimization
    (2007) Scholz, Bernd; Ehlers, Wolfgang (Prof. Dr.-Ing.)
    In the present work, the localization phenomena of granular material has been analyzed in order to provide a method for the computation of realistic boundary-value problems. The reason for this localization effects are material instabilities caused by the softening behavior of the material, which can be observed at homogeneous material tests. For this purpose, in the first step, the non-polar behavior of granular material is considered. Based on observations from material tests, a non-linear elastic law as well as hardening and softening laws in the context of the elasto-plasticity have been developed. In the next step, based on the described non-polar behavior, inhomogeneous biaxial tests are taken into account for the investigation of the micropolar behavior. As a consequence of the material softening, localization zones, so-called shear bands, appear. For the numerical computation of such localization phenomena, regularization techniques are required, since the standard continuum theory results in an ill-posed problem. Due to the fact that in the biaxial tests a finite thickness of the shear band can be observed, a regularization of the problem is naturally given by the effects due to the microstructure of the material. In case of granular material, the microstructure can be taken into account by application of the Cosserat or micropolar theory, which is applied in this thesis for the computation of localization problems. One of the main problems by use of the micropolar theory is, beside the numerically implementation, the identification of the associated material parameters. Considering inhomogeneous biaxial tests with shear banding, the effect of regularization can be observed by two facts. Firstly, by the gradual decrease of the stress after the appearance of the shear band and, secondly, by the finite thickness of the incoming shear band. Hence, both effects are used for the determination of the additional parameters of the Cosserat theory. Whereas the usage of stress-strain relations,in the context of the literature concerning the parameter identification procedure is a usual method, the consideration of the shear band thickness is a new challenge. Hence, a new method has therefore been developed. In addition to the Cosserat parameters, all the other material parameters, namely, the parameters of the elastic behavior as well as the parameters of the plastic hardening and softening must be identified. In consequence of the high number of material parameters given therewith, the overall identification process was performed by two major steps. Thus, in the first step, homogeneous material tests are applied for the determination of the parameters governing the non-polar behavior. In the second step, the material parameters of the micropolar behavior are determined basing on inhomogeneous biaxial tests, which enable the observation of the incoming shear band by use of the stereophotogrammetry. Generally, the identification procedure yields an inverse problem. For the solution of such problems, a lot of methods in theframework of the non-linear optimization exist. With a view to the high numerical costs for the computation of the boundary-value problem of the biaxial test, the gradient-based SQP method has been applied in this work. The computational cost can be further reduced by the application of the semi-analytical sensitivity analysis, which is also discussed in this work.The stepwise realization of the overall identification process as well as the semi-analytical computation of the sensitivities is demonstrated exemplarily by use of experimental data basing on Hostun sand. Finally, in the present work, with the particle model a completely different approach for the modeling of granular material is discussed which traces back to the Molecular Dynamics. Using this particle model, one is able to simulate the granular microstructure of the material, i.e., the single material grains, directly.Basing on a two-dimensional particle model, the biaxial test has been modeled, with a set of $30,000$ monodisperse, circular particles.With these simulations, the appearance of shear bands were shown and, furthermore, the occurrence of couple stress along the shear band was demonstrated in the same manner as done before with the continuum model. With these results, it has been illustrated that the Cosserat theory is a correct approach for the simulation of localization effects of granular media.