# COMPUTATION of generalized stress intensity factors for bonded elastic structures

Marius Bochniak; Anna–Margarete Sändig

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 4, page 853-878
- ISSN: 0764-583X

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topBochniak, Marius, and Sändig, Anna–Margarete. "COMPUTATION of generalized stress intensity factors for bonded elastic structures." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 853-878. <http://eudml.org/doc/197551>.

@article{Bochniak2010,

abstract = {
We consider coupled structures consisting of two different linear elastic
materials bonded along an interface. The material discontinuities combined with
geometrical peculiarities of the outer boundary lead to unbounded stresses. The
mathematical analysis of the singular behaviour of the elastic fields,
especially near points where the interface meets the outer boundary, can be
performed by means of asymptotic expansions with respect to the distance from
the geometrical and structural singularities. The coefficients in the
asymptotics, which are called generalized stress intensity factors, play an
important role in classical fracture criteria. In this paper we present several
formulas for the generalized stress intensity factors for 2D and 3D coupled
elastic structures. The formulas have the form of scalar products or convolution
integrals of the given data or the unknown displacement field and the so–called
weight functions, similar to Maz'ya/Plamenevsky functionals introduced in
[19] for elliptic boundary value problems. The weight functions are non–
energetic elastic fields, which admit a decomposition into a known singular part
and a more regular one, which is computed by boundary element domain
decomposition methods. Numerical experiments for two–dimensional problems
illustrate the theoretical results.
},

author = {Bochniak, Marius, Sändig, Anna–Margarete},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Stress singularities; stress intensity factors; boundary
element methods; error estimates; Aubin–Nitsche trick.; bonded elastic structures; asymptotic expansions; structural singularities; unbounded stresses; generalized stress intensity factors},

language = {eng},

month = {3},

number = {4},

pages = {853-878},

publisher = {EDP Sciences},

title = {COMPUTATION of generalized stress intensity factors for bonded elastic structures},

url = {http://eudml.org/doc/197551},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Bochniak, Marius

AU - Sändig, Anna–Margarete

TI - COMPUTATION of generalized stress intensity factors for bonded elastic structures

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 4

SP - 853

EP - 878

AB -
We consider coupled structures consisting of two different linear elastic
materials bonded along an interface. The material discontinuities combined with
geometrical peculiarities of the outer boundary lead to unbounded stresses. The
mathematical analysis of the singular behaviour of the elastic fields,
especially near points where the interface meets the outer boundary, can be
performed by means of asymptotic expansions with respect to the distance from
the geometrical and structural singularities. The coefficients in the
asymptotics, which are called generalized stress intensity factors, play an
important role in classical fracture criteria. In this paper we present several
formulas for the generalized stress intensity factors for 2D and 3D coupled
elastic structures. The formulas have the form of scalar products or convolution
integrals of the given data or the unknown displacement field and the so–called
weight functions, similar to Maz'ya/Plamenevsky functionals introduced in
[19] for elliptic boundary value problems. The weight functions are non–
energetic elastic fields, which admit a decomposition into a known singular part
and a more regular one, which is computed by boundary element domain
decomposition methods. Numerical experiments for two–dimensional problems
illustrate the theoretical results.

LA - eng

KW - Stress singularities; stress intensity factors; boundary
element methods; error estimates; Aubin–Nitsche trick.; bonded elastic structures; asymptotic expansions; structural singularities; unbounded stresses; generalized stress intensity factors

UR - http://eudml.org/doc/197551

ER -

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