Scaling of Fracture Strength in Disordered Quasi-Brittle Materials

This paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not follow the commonly used Weibull and (modified) Gumbel distributions. Instead, a {\it lognormal} distribution describes more adequately the fracture strengths corresponding to the peak load of the response. Lognormal distribution arises naturally as a consequence of multiplicative nature of large number of random distributions representing the stress scale factors necessary to break the subsequent "primary" bond (by definition, an increase in applied stress is required to break a "primary" bond) leading up to the peak load. Numerical simulations based on two-dimensional triangular and diamond lattice topologies with increasing system sizes substantiate that a {\it lognormal} distribution represents an excellent fit for the fracture strength distribution at the peak load. The second significant result of the present study is that, in materials with broadly distributed microscopic heterogeneities, the mean fracture strength of the lattice system behaves as $\mu_f = \frac{\mu_f^\star}{(Log L)^\psi} + \frac{c}{L}$, and scales as $\mu_f \approx \frac{1}{(Log L)^\psi}$ as the lattice system size, $L$, approaches infinity.Comment: 24 pages including 11 figure

Mechanical modeling of porous oxide fuel pellet A Test Problem

A poro-elasto-plastic material model has been developed to capture the response of oxide fuels inside the nuclear reactors under operating conditions. Behavior of the oxide fuel and variation in void volume fraction under mechanical loading as predicted by the developed model has been reported in this article. The significant effect of void volume fraction on the overall stress distribution of the fuel pellet has also been described. An important oxide fuel issue that can have significant impact on the fuel performance is the mechanical response of oxide fuel pellet and clad system. Specifically, modeling the thermo-mechanical response of the fuel pellet in terms of its thermal expansion, mechanical deformation, swelling due to void formation and evolution, and the eventual contact of the fuel with the clad is of significant interest in understanding the fuel-clad mechanical interaction (FCMI). These phenomena are nonlinear and coupled since reduction in the fuel-clad gap affects thermal conductivity of the gap, which in turn affects temperature distribution within the fuel and the material properties of the fuel. Consequently, in order to accurately capture fuel-clad gap closure, we need to account for fuel swelling due to generation, retention, and evolution of fission gas in addition to the usual thermal expansion and mechanical deformation. Both fuel chemistry and microstructure also have a significant effect on the nucleation and growth of fission gas bubbles. Fuel-clad gap closure leading to eventual contact of the fuel with the clad introduces significant stresses in the clad, which makes thermo-mechanical response of the clad even more relevant. The overall aim of this test problem is to incorporate the above features in order to accurately capture fuel-clad mechanical interaction. Because of the complex nature of the problem, a series of test problems with increasing multi-physics coupling features, modeling accuracy, and complexity are defined with the objective of accurate simulation of fuel-clad mechanical interaction subjected to a wide-range of thermomechanical stimuli

Spatiotemporal Compound Wavelet Matrix Framework for Multiscale/Multiphysics Reactor Simulation: Case Study of a Heterogeneous Reaction/Diffusion System

We present a mathematical method for efficiently compounding information from different models of species diffusion from a chemically reactive boundary. The proposed method is intended to serve as a key component of a multiscale/ multiphysics framework for heterogeneous chemically reacting processes. An essential feature of the method is the merging of wavelet representations of the different models and their corresponding time and length scales. Up-and-downscaling of the information between the scales is accomplished by application of a compounding wavelet operator, which is assembled by establishing limited overlap in scales between the models. We show that the computational efficiency gain and potential error associated with the method depend on the extent of scale overlap and wavelet filtering used. We demonstrate the method for an example problem involving a two-dimensional chemically reactive boundary and first order reactions involving two species

Improving The Convergence Rate Of Parareal-In-Time Power System Simulation Using The Krylov Subspace

The performance of parareal-in-time algorithms is determined on the number of sequential, coarse step iterations. A common tradeoff in designing an efficient parareal-in-time algorithm is between accuracy of the coarse solver and the number of iterations. Traditional parareal implementation for the power system simulation can also have difficulties handling complex power systems. In this paper, we propose a Krylov subspace enhanced parareal algorithm to reduce the number of coarse iterations. The proposed approach is demonstrated on a single-machine-infinite-bus system and the IEEE 10-machine 39-bus system. Noticeable decrease of number of iterations is observed in both cases

Numeric Modified Adomian Decomposition Method for Power System Simulations

This paper investigates the applicability of numeric Wazwaz El Sayed modified Adomian Decomposition Method (WES-ADM) for time domain simulation of power systems. WES-ADM is a numerical method based on a modified Adomian decomposition (ADM) technique. WES-ADM is a numerical approximation method for the solution of nonlinear ordinary differential equations. The non-linear terms in the differential equations are approximated using Adomian polynomials. In this paper WES-ADM is applied to time domain simulations of multi-machine power systems. WECC 3-generator, 9-bus system and IEEE 10-generator, 39-bus system have been used to test the applicability of the approach. Several fault scenarios have been tested. It has been found that the proposed approach is faster than the trapezoidal method with comparable accuracy

Adaptive Model Reduction For Parareal In Time Method For Transient Stability Simulations

Real time or faster than real time simulation can enable system operators to foresee the effect of crucial contingencies on the power system dynamics and take timely actions to prevent system instability. Parareal in time method uses concurrent computations on different segments of the time domain of interest to speed up the dynamic simulations. This paper describes the application of an adaptive nonlinear model reduction method in improving computational speed of the Parareal solver. The proposed method adaptively switches between a hybrid system with selective linearization and a completely linear system based on the size of a disturbance. The functions in the hybrid system are linearized based on the electrical distance between specific generators and the area where disturbances originated. The proposed method is tested on the 327-machine 2383-bus Polish system