Generalization of the Discrete Methods to Arbitrary Networks
Abstract/Contents
- Abstract
- Lattice element methods (LEM) use a network of springs to represent the system of interest (e.g., natural rock). This simple discrete framework has been used to model the mechanical behavior of porous media, including concrete and natural rocks. LEM methods are of special interest in modeling fracturing, which is achieved by removing bonds between nodes that are subject to a failure criterion. Existing LEM models suffer from a limit on the Poisson ratio that can be modeled. Following the recent works of Chen [#chen2014novel, #chen2015non, #chen2016] where nonlocal forces have been introduced for structured networks, we supplement the spring connecting two `particles` with a volumetric energy that depends on how the two particles and their neighbors deform collectively. Our approach deals with periodic networks, in which the unit cells are randomly generated. We prove that enriching the description of the three-dimensional network with these volumetric nonlocal contributions overcomes the limit on the Poisson ratio. Our analysis shows that accounting for neighbor-of -neighbor connections is sufficient to obtain values of Poisson ratio up to 0.5. We derive the expressions of the nonlocal (multibody) interaction force that results from the volumetric contribution, and we prove analytically that the overall Poisson ratio can cover the desired range of values by calibrating the magnitude of this force. We derived the stability criterion for the numerical implementation of the new nonlocal force. Numerical simulation was used to verify our derived criterion for the specific case of the network of springs in one dimension. For the network with local contacts only, we investigate the numerical stability when normal, shear and rotational springs are considered. We consider the specific case where translational and rotational degrees of freedom are decoupled and, for a given dimension, derive separately two critical time steps associated to each degree of freedom. We prove that a sharp time step that applies for any network geometry depends on the network configuration and the dimension. We applied our expression for the critical time step for different configurations and compared the results with the previous works. Numerical validation is used for a specific geometry in two dimensions and three dimensions and a good agreement between theory and numerical results is observed.
Description
| Type of resource | text |
|---|---|
| Date created | March 2017 |
Creators/Contributors
| Author | Mimouna, Ahmed |
|---|---|
| Primary advisor | Tchelepi, Hamdi |
| Degree granting institution | Stanford University, Department of Energy Resources Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
Bibliographic information
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Preferred citation
- Preferred Citation
- Mimouna, Ahmed. (2017). Generalization of the Discrete Methods to Arbitrary Networks. Stanford Digital Repository. Available at: https://purl.stanford.edu/hj368qv6949
Collection
Master's Theses, Doerr School of Sustainability
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