A Study on the Quasi-continuum Approximations of a One-Dimensional Fracture Model
نویسندگان
چکیده
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond bifurcation points, which enables us to evaluate the approximation over a finite range of loading and multiple mechanical equilibria.
منابع مشابه
A Continuum Model For Stone-wales Defected Carbon Nanotubes
In this paper, a continuum model is proposed so that a Stone-Wales (SW) defected carbon nanotube (CNT) is replaced by an initial circumferential crack in a continuum cylindrical shell. For this purpose, the critical energy release rate and then the fracture toughness of a defected CNT are calculated using the results of an existing atomistic-based continuum finite element simulation. Finally, t...
متن کاملAn Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the quasi-nonlocal quasicontinuum approximation. For simplicity, the analysis is restricted to the case of second-neighbor interactions and is linearized about a uniforml...
متن کاملA new conforming mesh generator for three-dimensional discrete fracture networks
Nowadays, numerical modelings play a key role in analyzing hydraulic problems in fractured rock media. The discrete fracture network model is one of the most used numerical models to simulate the geometrical structure of a rock-mass. In such media, discontinuities are considered as discrete paths for fluid flow through the rock-mass while its matrix is assumed impermeable. There are two main pa...
متن کاملDeveloping a 3D stochastic discrete fracture network model for hydraulic analyses
Fluid flow in jointed rock mass with impermeable matrix is often controlled by joint properties, including aperture, orientation, spacing, persistence and etc. On the other hand, since the rock mass is made of heterogeneous and anisotropic natural materials, geometric properties of joints may have dispersed values. One of the most powerful methods for simulation of stochastic nature of geometri...
متن کاملAbout an analytical verification of quasi-continuum methods with !-convergence techniques
Quasi-continuum (QC) methods are computational techniques, which reduce the complexity of atomistic simulations in a static setting while keeping information on smallscale structures and effects. The main idea is to couple atomistic and continuum models and thus to obtain quite detailed but still not too expensive numerical simulations. We aim at a mathematically rigorous verification of QC met...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Multiscale Modeling & Simulation
دوره 12 شماره
صفحات -
تاریخ انتشار 2014