Continuum Representation of the Micromechanics of Granular Materials via Homogenization and Statistical Approaches
| atmire.migration.oldid | 3975 | |
| dc.contributor.advisor | Wan, Richard | |
| dc.contributor.author | Pouragha, Mehdi | |
| dc.contributor.committeemember | Wong, Ron C.K. | |
| dc.contributor.committeemember | Priest, Jeffrey | |
| dc.contributor.committeemember | Federico, Salvatore | |
| dc.contributor.committeemember | Rothenburg, Leo | |
| dc.date.accessioned | 2015-12-24T17:56:12Z | |
| dc.date.available | 2015-12-24T17:56:12Z | |
| dc.date.issued | 2015-12-24 | |
| dc.date.submitted | 2015 | en |
| dc.description.abstract | Granular media display distinct constitutive features such as phase transition, dilatancy and localization that are difficult to analyze within traditional continuum mechanics. Such shortcoming has led to a paradigm shift from continuum to micromechanical approaches to highlight the discrete nature of granular media. Recent micromechanical studies have proven that most subtleties observed in granular mechanics can be clearly explained as a collective response of a large number of particles interacting through simple physics at the micro-/meso-scale. However, the emergence of an analytical constitutive model transcending the various scales highly relies on the extent to which statistical generalization methods are applicable to the problem at hand. From a statistical viewpoint, a continuum constitutive model can emerge from homogenizing discrete mechanisms if: (1) all the concerned parameters at the macroscopic level are expressed in terms of the same set of statistical descriptors, and (2) there exist enough internal consistencies among the statistical descriptors to ensure bijectivity of the formulation. Therefore, the current study sets out to first develop such a multiscale relation between strain and contact structure evolution through an investigation of the topology of the underlying Dirichlet tessellation network. A detailed study of the various mechanisms operating at the particle scale has resulted into an expression for macroscopic strain in terms of key micro-variables. These, together with the well-established ``Love-Weber'' formula for stress, satisfy the first above-mentioned requirement of having a common basis for statistical description. The second requirement about internal consistencies is addressed by exploring the interrelation between the evolution of the various micro-variables. For instance, changes in force network statistics enter an analytical scheme to describe the loss and gain of contacts during the initial stages of loading. On the other hand, post-yield microstructure characteristics have been studied by considering redundancy in the static equilibrium of the force network. Hence, a reference material state that unifies jamming and critical state concepts with the yielding properties of granular materials is proposed. Finally, a plastic potential naturally emerges from the proposed analytical framework which describes the stress-dilatancy relation of granular media with only a few material parameters, all micromechanical in nature. | en_US |
| dc.identifier.citation | Pouragha, M. (2015). Continuum Representation of the Micromechanics of Granular Materials via Homogenization and Statistical Approaches (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25443 | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/25443 | |
| dc.identifier.uri | http://hdl.handle.net/11023/2719 | |
| dc.language.iso | eng | |
| dc.publisher.faculty | Graduate Studies | |
| dc.publisher.institution | University of Calgary | en |
| dc.publisher.place | Calgary | en |
| dc.rights | University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. | |
| dc.subject | Engineering--Civil | |
| dc.subject.classification | Granular Material | en_US |
| dc.subject.classification | Micromechanics | en_US |
| dc.subject.classification | Constitutive Modelling | en_US |
| dc.subject.classification | Discrete Element Methods | en_US |
| dc.subject.classification | Homogenization | en_US |
| dc.subject.classification | Statistical Approach | en_US |
| dc.title | Continuum Representation of the Micromechanics of Granular Materials via Homogenization and Statistical Approaches | |
| dc.type | doctoral thesis | |
| thesis.degree.discipline | Civil Engineering | |
| thesis.degree.grantor | University of Calgary | |
| thesis.degree.name | Doctor of Philosophy (PhD) | |
| ucalgary.item.requestcopy | true |