Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
From MaRDI portal
Publication:5695403
DOI10.1051/m2an:2005035zbMath1330.74066OpenAlexW4296944107MaRDI QIDQ5695403
Frédéric Legoll, Xavier Blanc, Claude Le Bris
Publication date: 12 October 2005
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=M2AN_2005__39_4_797_0
Numerical optimization and variational techniques (65K10) Energy minimization in equilibrium problems in solid mechanics (74G65) Numerical approximation of solutions of equilibrium problems in solid mechanics (74G15) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)
Related Items
Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation, A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods, Analysis of Transition State Theory Rates upon Spatial Coarse-Graining, Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model, Non-local energetics of random heterogeneous lattices, Accuracy of quasicontinuum approximations near instabilities, Asymptotic numerical analysis of the diffusion-discrete absorption equation, Iterative solution of the quasicontinuum equilibrium equations with continuation, Finite element analysis of Cauchy-Born approximations to atomistic models, Partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation, Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem, BOUNDARY LAYER ENERGIES FOR NONCONVEX DISCRETE SYSTEMS, A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D, Partial homogenization of discrete models, Stability, instability, and error of the force-based quasicontinuum approximation, Analysis of a force-based quasicontinuum approximation, Atomistic to Continuum limits for computational materials science, Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches, Theory-based benchmarking of the blended force-based quasicontinuum method, Harnack inequalities and discrete-continuous error estimates for a chain of atoms with two-body interactions, Asymptotic expansions by \(\Gamma \)-convergence, An analysis of the effect of ghost force oscillation on quasicontinuum error, Homogenization of a one-dimensional diffusion - discrete absorption equation with feedback, A Theoretical Examination of Diffusive Molecular Dynamics, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics: the convex case
Cites Work
- Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
- From molecular models to continuum mechanics
- An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
- An \(O(h^ 2)\) method for a non-smooth boundary value problem
- An analysis of the quasicontinuum method
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
