Hyperelastic homogenized law for reinforced elastomer at finite strain with edge effects
type: Item
instance of: scholarly article
title: Hyperelastic homogenized law for reinforced elastomer at finite strain with edge effects
zbMATH Open document ID: 0916.73028
DOI: 10.1007/BF01176742
author: Erick Pruchnicki
published in: Acta Mechanica
publication date: 1999-07-07T00:00:00Z
review text: The author deals with the static microstructural effects of periodic hyperelastic composites at finite strain. Using the asymptotic process, he develops a homogenization procedure at finite strain and examines hyperelastic behavior of each constituent. The elastomer is assumed as nearly incompressible. An application of this approach is given using periodically stratified composites. A numerical simulation is then investigated on steel/elastomer composite, and the validity of the models is studied. When each constituent is neo-Hookean, the continuum homogenized model can be determined analytically. Since the classical asymptotic solution is not valid in the neighbourhood of the boundaries, boundary layers are added to the classical asymptotic terms. In this way, the effect of only one boundary and the simultaneous effects of two boundaries (angular boundary) are taken into account.
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 1221114
zbMATH Keywords: asymptotic solution
zbMATH Keywords: neo-Hookean material
zbMATH Keywords: static microstructural effects
zbMATH Keywords: periodic composites
zbMATH Keywords: periodically stratified composites
zbMATH Keywords: steel/elastomer composite
zbMATH Keywords: boundary layers
reviewed by: Marco Codegone
MaRDI profile type: Publication
cites work: Q4189539
cites work: Non-homogeneous media and vibration theory
cites work: A General Convergence Result for a Functional Related to the Theory of Homogenization
cites work: Homogenization and Two-Scale Convergence
cites work: Q3789147
cites work: Q4841595
cites work: Homogenization and damage for composite structures
cites work: Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods
cites work: Homogenized nonlinear constitutive properties and local stress concentrations for composites with periodic internal structure
cites work: Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method
cites work: On effective moduli of an elastic body containing periodically distributed voids
cites work: Q3673210
cites work: Q4297445
cites work: Homogenized nonlinear constitutive law using Fourier series expansion
cites work: On constitutive macro-variables for heterogeneous solids at finite strain
cites work: On macroscopic effects of heterogeneity in elastoplastic media at finite strain
cites work: Elastic Potentials and the Structure of Inelastic Constitutive Laws
cites work: Local and overall extremal properties of time-independent materials and non-linear elastic comparison materials
cites work: Extremum principles in non-linear elasticity and their application to composites - I
cites work: The overall constitutive behaviour of nonlinearly elastic composites
cites work: Elastic-plastic composites at finite strains
cites work: Q4123901
cites work: Homogenization of nonconvex integral functionals and cellular elastic materials
cites work: Q3210217
cites work: Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity
cites work: On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites
cites work: Q4692971
cites work: Yield conditions for layered composites
cites work: Q4016440
cites work: A macroscopic elastoplastic constitutive law for multilayered media: Application to reinforced earth material
cites work: Microstructural effects in elastic composites
cites work: Q3967130
cites work: A finite element method for the analysis of rubber parts, experimental and analytical assessment
cites work: Q4039741
cites work: Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
cites work: Finite elements with penalties in nonlinear elasticity
cites work: New variational-asymptotic formulations for interlaminar stress analysis in laminated plates
cites work: Study of a boundary layer problem in elastic composite materials
full work available at URL: https://doi.org/10.1007/bf01176742
OpenAlex ID: W2331491419
Recommended article: Exact results for the homogenization of elastic fiber-reinforced solids at finite strain
Recommended article: Estimations homogénéisées pour les composites hyperélastiques et applications aux élastomères renforcés
Recommended article: Homogenization estimates for fiber-reinforced elastomers with periodic microstructures
Recommended article: Q4024166
Recommended article: Hyperelastic constitutive modeling under finite strain
Recommended article: Functional nonlinear theory of elasticity for given edge conditions in different configurations
Recommended article: Bounded elastic potentials for rubberlike materials with strain-stiffening effects
Recommended article: Un résultat d'homogénéisation pour un matériau élastique renforcé périodiquement par des fibres élastiques de très grande rigidité
Recommended article: Elastodynamics in domains with edges
Recommended article: A finite strain framework for steady-state problems: hyperelasto-viscoplasticity
description: scientific article; zbMATH DE number 1221114