Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity

DOI10.1007/s00205-010-0378-7zbMath1294.74056OpenAlexW2017025711MaRDI QIDQ717486

Antoine Gloria, Marco Cicalese, Roberto Alicandro

Publication date: 4 October 2011

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/134983/1/ACG_09_5.pdf

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Nonlinear elasticity (74B20) Signal detection and filtering (aspects of stochastic processes) (60G35) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

Related Items (37)

Homogenization theory: periodic and beyond. Abstracts from the workshop held March 14--20, 2021 (online meeting) ⋮ On the Variational Limits of Lattice Energies on Prestrained Elastic Bodies ⋮ Foundation, analysis, and numerical investigation of a variational network-based model for rubber ⋮ Stochastic homogenization of nonconvex unbounded integral functionals with convex growth ⋮ Numerical homogenization: survey, new results, and perspectives ⋮ Random parking, Euclidean functionals, and rubber elasticity ⋮ Non-local energetics of random heterogeneous lattices ⋮ Hexagonal lattices with three-point interactions ⋮ Continuum limit and stochastic homogenization of discrete ferromagnetic thin films ⋮ Homogenisation of dynamical optimal transport on periodic graphs ⋮ On continuum limits of heterogeneous discrete systems modelling cracks in composite materials ⋮ Onset of fracture in random heterogeneous particle chains ⋮ Discrete stochastic approximations of the Mumford-Shah functional ⋮ A compactness theorem for functions on Poisson point clouds ⋮ Stochastic homogenization of degenerate integral functionals and their Euler-Lagrange equations ⋮ Asymptotic behavior of the Dirichlet energy on Poisson point clouds ⋮ Approximation of the Willmore energy by a discrete geometry model ⋮ Discrete-to-Continuum Limits of Multibody Systems with Bulk and Surface Long-Range Interactions ⋮ An Integral-Representation Result for Continuum Limits of Discrete Energies with MultiBody Interactions ⋮ Discrete-to-continuum limits of long-range electrical interactions in nanostructures ⋮ Atomic to continuum passage for nanotubes: a discrete Saint-Venant principle and error estimates ⋮ Convergences of the squareroot approximation scheme to the Fokker–Planck operator ⋮ Interplay of analysis and probability in applied mathematics. Abstracts from the workshop held February 11--17, 2018 ⋮ Domain formation in magnetic polymer composites: an approach via stochastic homogenization ⋮ Mathematical derivation of a rubber-like stored energy functional ⋮ Discrete spin systems on random lattices at the bulk scaling ⋮ Stochastic Unfolding and Homogenization of Spring Network Models ⋮ Motion of discrete interfaces in low-contrast random environments ⋮ ELASTIC LIMIT OF SQUARE LATTICES WITH THREE-POINT INTERACTIONS ⋮ Variational convergence of discrete geometrically-incompatible elastic models ⋮ Stochastic Homogenization of Nonconvex Discrete Energies with Degenerate Growth ⋮ New counterexamples to the cell formula in nonconvex homogenization ⋮ Local and Nonlocal Continuum Limits of Ising-Type Energies for Spin Systems ⋮ Homogenization of random convolution energies ⋮ From statistical polymer physics to nonlinear elasticity ⋮ Random Finite-Difference Discretizations of the Ambrosio--Tortorelli Functional with Optimal Mesh-Size ⋮ Homogenization of ferromagnetic energies on Poisson random sets in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A proof of crystallization in two dimensions
• A variant of stochastic homogenization theory for elliptic operators.
• Cauchy-Born rule and the stability of crystalline solids: Static problems
• Sufficient conditions for the validity of the Cauchy-Born rule close to \(\mathrm{SO}(n)\)
• A direct approach to numerical homogenization in finite elasticity
• The energy of some microscopic stochastic lattices
• The diffusion limit for reversible jump processes on \(Z^ m\) with ergodic random bond conductivities
• Homogenization of reticulated structures
• On the ubiquity of fracture in nonlinear elasticity
• Lectures on random Voronoi tessellations
• Integral functionals determined by their minima
• Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice
• Stochastic homogenization and random lattices
• Finite element modelling of rubber-like polymers based on chain statistics
• Mathematical derivation of a rubber-like stored energy functional
• A derivation of linear elastic energies from pair-interaction atomistic systems
• Effective cohesive behavior of layers of interatomic planes
• Discrete to continuum limit for some models of stochastic lattices of atoms
• Mechanics of materials with periodic truss or frame micro-structures
• Variational limit of a one-dimensional discrete and statistically homogeneous system of material points
• Stochastic Diffeomorphisms and Homogenization of Multiple Integrals
• AVERAGING OF DIFFERENCE SCHEMES
• Ergodic theorems for superadditive processes.
• The mechanics of rubber elasticity
• A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
• Continuum Limits of Discrete Systems without Convexity Hypotheses
• HOMOGENIZATION OF MATERIALS WITH PERIODIC TRUSS OR FRAME MICRO-STRUCTURES
• Cell-to-Muscle homogenization. Application to a constitutive law for the myocardium
• Random parking, sequential adsorption, and the jamming limit

This page was built for publication: Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity