Accuracy of quasicontinuum approximations near instabilities
From MaRDI portal
Publication:602817
DOI10.1016/j.jmps.2010.06.011zbMath1200.74005arXiv0905.2914OpenAlexW2017929480MaRDI QIDQ602817
Christoph Ortner, Matthew Dobson, Mitchell Luskin
Publication date: 5 November 2010
Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.2914
Bifurcation and buckling (74G60) Molecular, statistical, and kinetic theories in solid mechanics (74A25)
Related Items
A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN ⋮ Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation ⋮ A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods ⋮ Multiscale modeling of complex dynamic problems: an overview and recent developments ⋮ A field theoretical approach to the quasi-continuum method ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ Finite element analysis of Cauchy-Born approximations to atomistic models ⋮ A priori error analysis of two force-based atomistic/continuum models of a periodic chain ⋮ Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem ⋮ A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D ⋮ Analysis of a Predictor-Corrector Method for Computationally Efficient Modeling of Surface Effects in 1D ⋮ Stability, instability, and error of the force-based quasicontinuum approximation ⋮ Theory-based benchmarking of the blended force-based quasicontinuum method ⋮ (In-)stability and Stabilization of QNL-Type Atomistic-to-Continuum Coupling Methods ⋮ A Study on the Quasi-continuum Approximations of a One-Dimensional Fracture Model ⋮ Loss of ellipticity and structural transformations in planar simple crystal lattices
Cites Work
- Unnamed Item
- Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions
- Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem
- Cauchy-Born rule and the stability of crystalline solids: Static problems
- Stability, instability, and error of the force-based quasicontinuum approximation
- An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
- Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation
- On the stability of Bravais lattices and their Cauchy–Born approximations
- A Quadrature-Rule Type Approximation to the Quasi-Continuum Method
- An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
- A Posteriori Existence in Numerical Computations
- An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method
- On Atomistic-to-Continuum Coupling by Blending
- An analysis of the effect of ghost force oscillation on quasicontinuum error
- Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
- An Introduction to Numerical Analysis
- Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
- Analysis of a quasicontinuum method in one dimension
- Analysis of a force-based quasicontinuum approximation
- Convergence Analysis of a Quasi‐Continuum Approximation for a Two‐Dimensional Material Without Defects
- Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics