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Publication 14-CNA-005
Stable Disarrangement Phases of Granular Media I: Luca Deseri David R. Owen Abstract: We model granular media as continuous bodies that are aggregates of many small elastic bodies (elastic aggregates). Our model rests on the multiscale geometry of structured deformations through the field theory "elasticity with disarrangements". This setting provides a tensorial consistency relation $D\Psi (G)(F^{T}-G^{T})=0$ and an accommodation inequality $0< \det G\leq \det F $ that relate, through the free energy response $\Psi $ of the individual pieces of the aggregate, the deformation gradient $F$ of the aggregate and the average deformation $G$ of the pieces of the aggregate. The solutions $G$ of these two relations are called disarrangement phases corresponding to $F$. In Part I we classify all of the disarrangement phases for a model elastic aggregate. The compact phase $G=F$, in which the pieces of the aggregate all deform in the same way as the aggregate, itself, forms one category in the classification, while the non-compact phases $G\neq F$ are categorized as to whether the stress $(\det F)^{-1}D\Psi (G)F^{T}$ is planar, uniaxial, or zero. Our classification will form the basis for the solution of boundary value problems for the model aggregate as well as for a broader class of aggregates. In Part II we use the classification to obtain an unexpected connection between elastic aggregates and materials with no-tension response. Get the paper in its entirety as |
