Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media

DOI10.1051/m2an/2015080zbMath1348.74287OpenAlexW2497187940MaRDI QIDQ2830704

Qiang Du, Tadele Mengesha, Robert P. Lipton

Publication date: 28 October 2016

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2015080

zbMATH Keywords

homogenizationheterogeneous materialsnonlocal equationsmultiscale analysisNavier equationtwo-scale convergenceperidynamics

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Inhomogeneity in solid mechanics (74E05) Homogenization in equilibrium problems of solid mechanics (74Q05) Integral operators (45P05) Systems of linear integral equations (45F99)

Related Items (13)

Numerical methods for nonlocal and fractional models ⋮ Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics ⋮ An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems ⋮ Machine learning of nonlocal micro-structural defect evolutions in crystalline materials ⋮ Quasistatic Evolution with Unstable Forces ⋮ An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems ⋮ Peridynamics review ⋮ Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients ⋮ Nonlocal \(H\)-convergence ⋮ An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems ⋮ Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling ⋮ Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues ⋮ Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition

Cites Work

• Unnamed Item
• Unnamed Item
• Analysis of the volume-constrained peridynamic Navier equation of linear elasticity
• Nonlocal constrained value problems for a linear peridynamic Navier equation
• Multiscale analysis of linearized peridynamics
• Force flux and the peridynamic stress tensor
• Peridynamic modeling of membranes and fibers
• Linearized theory of peridynamic states
• Functional analysis, Sobolev spaces and partial differential equations
• Semigroups of linear operators and applications to partial differential equations
• Integrated semigroups and their applications to the abstract Cauchy problem
• Traveling waves in a convolution model for phase transitions
• Multiscale dynamics of heterogeneous media in the peridynamic formulation
• Reformulation of elasticity theory for discontinuities and long-range forces
• Memory effects and homogenization
• Peridynamic states and constitutive modeling
• Nonlocal convection-diffusion volume-constrained problems and jump processes
• A nonlocal convection-diffusion equation
• Peridynamics: A Nonlocal Continuum Theory
• A constitutive model for a linearly elastic peridynamic body
• Towards a two-scale calculus
• Homogenization and Two-Scale Convergence
• Homogenization of linear and nonlinear transport equations
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• One-Parameter Semigroups for Linear Evolution Equations
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Homogenization of plasticity equations with two-scale convergence methods

This page was built for publication: Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media