Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions

Chyanbin Hwu, Wei Ren Chen, Ting Hsiang Lo

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Green’s function for a two-dimensional anisotropic elastic solid containing a rigid or elastic inclusion has been previously explored. According to the special feature of Stroh formalism for two-dimensional anisotropic elasticity, the same mathematical form of Green’s function can be extended to cases with piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. In this paper, we show that some important constant terms are missing in the existing Green’s functions and the solutions should be corrected to ensure the displacement and traction continuity across the inclusion interface. Besides the necessary analytical check, a further verification is provided by applying the corrected Green’s functions to the problems of crack-inclusion interaction. We consider that the cracks exist in smart materials made by composites embedded with piezoelectric and/or magneto-electro-elastic sensors and actuators. Since the anisotropic elastic, piezoelectric and magneto-electro-elastic materials exist simultaneously, an adaptable adjustment technique is proposed. With this technique, the dislocation superposition method and boundary-based finite element methods developed previously for the problems with a single material type can now be extended to study the coupled-field interaction problems.

Original languageEnglish
Pages (from-to)91-103
Number of pages13
JournalInternational Journal of Fracture
Volume215
Issue number1-2
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Green's function
Inclusion
Elastic Material
Crack
Stroh Formalism
Anisotropic Elasticity
Cracks
Smart Materials
Constant term
Intelligent materials
Dislocation
Interaction
Superposition
Actuator
Elasticity
Adjustment
Actuators
Finite Element Method
Composite
Finite element method

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modelling and Simulation
  • Mechanics of Materials

Cite this

@article{9c1223fd08f8496fab634e98ea51c25c,
title = "Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions",
abstract = "Green’s function for a two-dimensional anisotropic elastic solid containing a rigid or elastic inclusion has been previously explored. According to the special feature of Stroh formalism for two-dimensional anisotropic elasticity, the same mathematical form of Green’s function can be extended to cases with piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. In this paper, we show that some important constant terms are missing in the existing Green’s functions and the solutions should be corrected to ensure the displacement and traction continuity across the inclusion interface. Besides the necessary analytical check, a further verification is provided by applying the corrected Green’s functions to the problems of crack-inclusion interaction. We consider that the cracks exist in smart materials made by composites embedded with piezoelectric and/or magneto-electro-elastic sensors and actuators. Since the anisotropic elastic, piezoelectric and magneto-electro-elastic materials exist simultaneously, an adaptable adjustment technique is proposed. With this technique, the dislocation superposition method and boundary-based finite element methods developed previously for the problems with a single material type can now be extended to study the coupled-field interaction problems.",
author = "Chyanbin Hwu and Chen, {Wei Ren} and Lo, {Ting Hsiang}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10704-018-00338-6",
language = "English",
volume = "215",
pages = "91--103",
journal = "International Journal of Fracture",
issn = "0376-9429",
publisher = "Springer Netherlands",
number = "1-2",

}

Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions. / Hwu, Chyanbin; Chen, Wei Ren; Lo, Ting Hsiang.

In: International Journal of Fracture, Vol. 215, No. 1-2, 01.01.2019, p. 91-103.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Green’s function of anisotropic elastic solids with piezoelectric or magneto-electro-elastic inclusions

AU - Hwu, Chyanbin

AU - Chen, Wei Ren

AU - Lo, Ting Hsiang

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Green’s function for a two-dimensional anisotropic elastic solid containing a rigid or elastic inclusion has been previously explored. According to the special feature of Stroh formalism for two-dimensional anisotropic elasticity, the same mathematical form of Green’s function can be extended to cases with piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. In this paper, we show that some important constant terms are missing in the existing Green’s functions and the solutions should be corrected to ensure the displacement and traction continuity across the inclusion interface. Besides the necessary analytical check, a further verification is provided by applying the corrected Green’s functions to the problems of crack-inclusion interaction. We consider that the cracks exist in smart materials made by composites embedded with piezoelectric and/or magneto-electro-elastic sensors and actuators. Since the anisotropic elastic, piezoelectric and magneto-electro-elastic materials exist simultaneously, an adaptable adjustment technique is proposed. With this technique, the dislocation superposition method and boundary-based finite element methods developed previously for the problems with a single material type can now be extended to study the coupled-field interaction problems.

AB - Green’s function for a two-dimensional anisotropic elastic solid containing a rigid or elastic inclusion has been previously explored. According to the special feature of Stroh formalism for two-dimensional anisotropic elasticity, the same mathematical form of Green’s function can be extended to cases with piezoelectric and magneto-electro-elastic materials by expanding the related matrix dimension. In this paper, we show that some important constant terms are missing in the existing Green’s functions and the solutions should be corrected to ensure the displacement and traction continuity across the inclusion interface. Besides the necessary analytical check, a further verification is provided by applying the corrected Green’s functions to the problems of crack-inclusion interaction. We consider that the cracks exist in smart materials made by composites embedded with piezoelectric and/or magneto-electro-elastic sensors and actuators. Since the anisotropic elastic, piezoelectric and magneto-electro-elastic materials exist simultaneously, an adaptable adjustment technique is proposed. With this technique, the dislocation superposition method and boundary-based finite element methods developed previously for the problems with a single material type can now be extended to study the coupled-field interaction problems.

UR - http://www.scopus.com/inward/record.url?scp=85058784056&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85058784056&partnerID=8YFLogxK

U2 - 10.1007/s10704-018-00338-6

DO - 10.1007/s10704-018-00338-6

M3 - Article

AN - SCOPUS:85058784056

VL - 215

SP - 91

EP - 103

JO - International Journal of Fracture

JF - International Journal of Fracture

SN - 0376-9429

IS - 1-2

ER -