Local dynamics of a randomly pinned crack front: A numerical study

We investigate numerically the dynamics of crack propagation along a weak plane using a model consisting of fibers connecting a soft and a hard clamp. This bottom-up model has previously been shown to contain the competition of two crack propagation mechanisms: coalescence of damage with the front on small scales and pinned elastic line motion on large scales. We investigate the dynamical scaling properties of the model, both on small and large scale. The model results compare favorable with experimental results

Onset of Localization in Heterogeneous Interfacial Failure

We study numerically the failure of an interface joining two elastic materials under load using a fiber bundle model connected to an elastic half space. We find that the breakdown process follows the equal load sharing fiber bundle model without any detectable spatial correlations between the positions of the failing fibers until localization sets in. The onset of localization is an instability, not a phase transition. Depending on the elastic constant describing the elastic half space, localization sets in before or after the critical load causing the interface to fail completely, is reached. There is a crossover between failure due to localization or failure without spatial correlations when tuning the elastic constant, not a phase transition. Contrary to earlier claims based on models different from ours, we find that a finite fraction of fibers must fail before the critical load is attained, even in the extreme localization regime, i.e.\ for very small elastic constant. We furthermore find that the critical load remains finite for all values of the elastic constant in the limit of an infinitely large system.Comment: 4 pages, 5 figure

Role of the quenched disorder in fracture front propagation

The process of materials fracture is not yet understood across all levels. This thesis contains detailed description on a model of in-plane fracture along with results obtained using this model. The results from the model are in very good agreement with experimental observations, both with respect to the static scaling of the front (morphology) and a dynamic study of the underlying processes. This is quite remarkable, considering our model is quasistatic, meaning that the dynamics are time independent. Using this model, I have found two scaling regimes which corresponds to the two different regimes found experimentally for in-plane fracture. This is the first model to successfully reproduce these two scaling regimes, allowing us to clearly state the important processes in this constrained form of fracture. Only the geometry is constrained, any material obeying the quite general assumptions in the model should contain the same processes and fracture in the same way. The results indicate that a percolation process is controlling the fracture on small scales. At larger scales, the elastic material properties leads to a stress concentration which eventually constrains damage formation to the immediate area near the fracture front. In the large scale regime I have measured a roughness exponent of large = 0.39 ± 0.04 . In the small scale regime, I show data consistent with and present evidence based on several different analyses for a roughness exponent of small = 2/3

Increased Information Flow between Hydropower Scheduling Models through Extended Cut Sharing

-We present initial results and description of a method for coupling long term hydro scheduling models to short term hydro schedul- ing models. The method is based on an established approach but extends on the principle to increase the available information of the future estimates provided by the long term model

Stochastic optimization model with individual water values and power flow constaints

publishedVersio

Stochastic optimization model with individual water values and power flow constaints

publishedVersio