Mesoscale Models and Approximate Solutions for Solids Containing Clouds of Voids

DOI10.1137/151006068zbMath1381.35176arXiv1501.07524OpenAlexW2963832699MaRDI QIDQ2806403

M. J. Nieves, Alexander B. Movchan, Vladimir Gilelevich Maz'ya

Publication date: 18 May 2016

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.07524

zbMATH Keywords

elasticityasymptotic analysissingularly perturbed problemsmesoscale approximationsmultiply perforated domains

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) PDEs in connection with mechanics of deformable solids (35Q74) Boundary value problems for second-order elliptic systems (35J57)

Related Items (9)

The Dirichlet problem in a planar domain with two moderately close holes ⋮ A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary ⋮ Asymptotic Analysis of Solutions to Transmission Problems in Solids with Many Inclusions ⋮ Mesoscale asymptotic approximations in the dynamics of solids with defects ⋮ The effective permittivity and permeability generated by a cluster of moderately contrasting nanoparticles ⋮ A Local Version of Einstein's Formula for the Effective Viscosity of Suspensions ⋮ Unnamed Item ⋮ Estimation of the Heat Conducted by a Cluster of Small Cavities and Characterization of the Equivalent Heat Conduction ⋮ Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homogenization of partial differential equations. Translated from the original Russian by M. Goncharenko and D. Shepelsky
• On inequalities of Korn, Friedrichs and Babuska-Aziz
• The Laplacian in regions with many small obstacles: Fluctuations around the limit operator
• The effect of spatial distribution on the effective behavior of composite materials and cracked media
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• Green's kernels and meso-scale approximations in perforated domains
• Mesoscale approximations for solutions of the Dirichlet problem in a perforated elastic body
• Uniform asymptotic formulae for Green's functions in singularly perturbed domains
• Homogenization estimates for fiber-reinforced elastomers with periodic microstructures
• On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. I: Theory
• Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
• Green's kernels for transmission problems in bodies with small inclusions
• Mesoscale Asymptotic Approximations to Solutions of Mixed Boundary Value Problems in Perforated Domains
• Homogenization method for the study of composite media
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Uniform asymptotic approximations of Green's functions in a long rod
• Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
• Asymptotic treatment of perforated domains without homogenization

This page was built for publication: Mesoscale Models and Approximate Solutions for Solids Containing Clouds of Voids