Finite cover method for linear and non-linear analyses of heterogeneous solids

Kenjiro Terada, Mitsuteru Asai, Michihiro Yamagishi

Research output: Contribution to journalArticle

107 Citations (Scopus)

Abstract

We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non-linear mechanical behaviour of heterogeneous solids and structures. The name 'FCM' is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non-linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM.

Original languageEnglish
Pages (from-to)1321-1346
Number of pages26
JournalInternational Journal for Numerical Methods in Engineering
Volume58
Issue number9
DOIs
Publication statusPublished - Nov 7 2003
Externally publishedYes

Fingerprint

Cover
Finite element method
Debonding
Mechanical Behavior
Discontinuity
Finite Element Method
Rupture
Equilibrium State
Equivalence
Numerical Examples
Formulation
Arbitrary
Approximation
Demonstrate

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

Cite this

Finite cover method for linear and non-linear analyses of heterogeneous solids. / Terada, Kenjiro; Asai, Mitsuteru; Yamagishi, Michihiro.

In: International Journal for Numerical Methods in Engineering, Vol. 58, No. 9, 07.11.2003, p. 1321-1346.

Research output: Contribution to journalArticle

@article{9383900dc4c34b2898a9e1d12afd384d,
title = "Finite cover method for linear and non-linear analyses of heterogeneous solids",
abstract = "We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non-linear mechanical behaviour of heterogeneous solids and structures. The name 'FCM' is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non-linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM.",
author = "Kenjiro Terada and Mitsuteru Asai and Michihiro Yamagishi",
year = "2003",
month = "11",
day = "7",
doi = "10.1002/nme.820",
language = "English",
volume = "58",
pages = "1321--1346",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "9",

}

TY - JOUR

T1 - Finite cover method for linear and non-linear analyses of heterogeneous solids

AU - Terada, Kenjiro

AU - Asai, Mitsuteru

AU - Yamagishi, Michihiro

PY - 2003/11/7

Y1 - 2003/11/7

N2 - We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non-linear mechanical behaviour of heterogeneous solids and structures. The name 'FCM' is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non-linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM.

AB - We introduce the finite cover method (FCM) as a generalization of the finite element method (FEM) and extend it to analyse the linear and non-linear mechanical behaviour of heterogeneous solids and structures. The name 'FCM' is actually an alias for the manifold method (MM) and the basic idea of the method has already been established for linear analyses of structures with homogeneous materials. After reviewing the concept of physical and mathematical covers for approximating functions in the FCM, we present the formulation for the static equilibrium state of a structure with arbitrary physical boundaries including material interfaces. The problem essentially involves the discontinuities in strains, and possibly has the discontinuities in displacement caused by interfacial debonding or rupture of material interfaces. We simulate such non-linear mechanical behaviour after presenting simple numerical examples that demonstrate the equivalence between the approximation capabilities of the FCM and those of the FEM.

UR - http://www.scopus.com/inward/record.url?scp=0242414720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242414720&partnerID=8YFLogxK

U2 - 10.1002/nme.820

DO - 10.1002/nme.820

M3 - Article

AN - SCOPUS:0242414720

VL - 58

SP - 1321

EP - 1346

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 9

ER -