Discrete-to-continuum linearization in atomistic dynamics

Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Equations linearized about a deformed state (small deformations superposed on large) (74B15) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

Cites Work

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On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime
Local minimization, variational evolution and \(\Gamma\)-convergence
An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem
Variational evolution of one-dimensional Lennard-Jones systems
\{Euclidean, metric, and Wasserstein\} gradient flows: an overview
Connecting atomistic and continuous models of elastodynamics
Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity
On the passage from atomic to continuum theory for thin films
Variational formulation of softening phenomena in fracture mechanics: The one-dimensional case
Linearized elasticity as \(\Gamma\)-limit of finite elasticity
On Lennard-Jones systems with finite range interactions and their asymptotic analysis
From molecular models to continuum mechanics
Justification of the Cauchy-Born approximation of elastodynamics
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings
On the derivation of linear elasticity from atomistic models
An analysis of crystal cleavage in the passage from atomistic models to continuum theory
Discrete stochastic approximations of the Mumford-Shah functional
Topics on concentration phenomena and problems with multiple scales
On the passage from atomistic systems to nonlinear elasticity theory for general multi-body potentials with p-growth
A derivation of linear elastic energies from pair-interaction atomistic systems
Cauchy-Born rule and the stability of crystalline solids: dynamic problems
Effective cohesive behavior of layers of interatomic planes
Discrete-to-continuum convergence of charged particles in 1D with annihilation
Surface energies in a two-dimensional mass-spring model for crystals
A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models
Gamma-convergence of gradient flows with applications to Ginzburg-Landau
A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
Continuum Limits of Discrete Systems without Convexity Hypotheses
Discrete-to-Continuum Limits of Multibody Systems with Bulk and Surface Long-Range Interactions
Mathematical Methods in Continuum Mechanics of Solids
Gradient Flows as a Selection Procedure for Equilibria of Nonconvex Energies
Atomistic to Continuum limits for computational materials science
Geometric Flows on Planar Lattices
Homogenization of discrete thin structures
Asymptotic behavior of the Dirichlet energy on Poisson point clouds

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