Summer Shahzad STRESS SINGULARITIES, ANNIHILATIONS AND INVISIBILITIES INDUCED BY ...

146 Pages·2016·17.54 MB·English

UNIVERSITY
OF TRENTO – Italy
Summer Shahzad
S S A
TRESS INGULARITIES, NNIHILATIONS
I I
AND NVISIBILITIES NDUCED BY
P I
OLYGONAL NCLUSIONS IN
L E
INEAR LASTICITY
April, 2016
University of Trento
University of Bergamo
University of Brescia
University of Padova
University of Trieste
University of Udine
University IUAV of Venezia
Summer Shahzad
S S A
TRESS INGULARITIES, NNIHILATIONS AND
I I P
NVISIBILITIES NDUCED BY OLYGONAL
I L E
NCLUSIONS IN INEAR LASTICITY
Advisor: Prof. Davide Bigoni
Co-Advisor: Dr. Francesco Dal Corso
2016
UNIVERSITY OF TRENTO
Engineering of Civil and Mechanical Structural Systems
XXVIII cycle
Ph.D. Program Head: Prof. Davide Bigoni
Final Examination: April 21, 2016
Board of Examiners:
Prof. Alexander Movchan, University of Liverpool
Prof. Bozidar Stojadinovic, ETH Zu¨rich
Prof. Daniele Zonta, University of Trento
Dedicated to my beloved wife Anna and family
Ph.D.Thesis–SummerShahzad iii

Synopsis
Notches,wedges,cracks,stiffeners,inclusionsanddefectsinplaneelas-
tostatics are known to generate singular stresses and limit the overall
strength of a composite material.
In the present thesis, after showing experimentally that the singular
stress field predicted by the linear elastic solution for the rigid inclusion
model can be generated in reality and with great accuracy within a ma-
terial, attention is devoted then in achieving the out-of-plane response of
aninfiniteplanecontainingpolygonalandhypocycloidal-shapedvoidsand
rigid inclusions subject to generalized remote loading conditions.
The analytical solution obtained for the case of polygonal inclusions
shows some unexpected and interesting features such as an infinite set of
geometries and loading conditions exist for which not only the singular-
ity is absent, but the stress vanishes (annihilates) at the corners. Thus
the material, which even without the inclusion corners would have a finite
stress, remains unstressed at these points in spite of the applied remote
load. Moreover, similar conditions are determined in which a star-shaped
crack or stiffener leaves the ambient stress completely unperturbed, thus
reaching a condition of ‘quasi-static invisibility’.
Thesolutioninclosed-formisalsoobtainedforthecaseofhypocycloidal-
shaped voids and rigid inclusions, showing that cusps may in certain con-
ditions act as stress reducers, situations for which the stress at the cusp
tip in the presence of the inclusion is smaller than in the case when the
inclusion is absent.
Ph.D.Thesis–SummerShahzad v
The obtained solutions provide closed-form expressions for Stress In-
tensityFactorsandNotchStressIntensityFactorsatvaryingtheinclusion
geometryandofloadingconditions,fundamentalquantitiesindefiningcri-
teria of fracture initiation/propagation or inclusion detachment.
Thefindingsofstressannihilation,stressreductionandinclusioninvis-
ibilitydefineoptimalloadingmodesfortheoverallstrengthofacomposite
and are useful in the design of ultra-resistant materials.
vi Ph.D.Thesis–SummerShahzad
Acknowledgements
First and foremost, I would like to express my gratitude to Profes-
sor Davide Bigoni and Dr. Francesco Dal Corso for their constant pa-
tience, encouragements, motivation, suggestions and support given to me
throughout the doctoral period.
I am also deeply grateful to Dr. Luca Argani, Dr. Gourgiotis, P.A.,
Dr. Andrea Bacigalupo, Dr. Daniele Veber, Dr. Bosi Federico, Dr. Diego
Misseroni and Dr. Diego Pedrazzoli for their help and to all members of
the Solid and Structural Mechanics Group at the University of Trento.
Moreover, IwouldliketothankmybelovedwifeAnnaforherconstant
support and love.
A special thanks goes to my family: mom Treeza, Dad Sardar, mom
Sabrina, Augusto, Uzma, Lubna, Elena, Aurora.
Last but not the least, thanks go to Bruno Fronza, Rita Ruffoli, Don
RinoBreoni,SirAbbasandMadamShafqat,Ritor,PieroandRoseMussi,
RupertoBattiston, AndrewCamelleri, AlessandroMaggi, FondazioneSan
Zeno,FocolareMovement,MarioFranzoiaandfamily,AndreaDelamaand
family, Mario Farina and family, Luca Perolo, Andrea Perolo and family,
Bruna, Franco Mucchiut and family, to all the gen and friends that i did
not mention because of the limited space.
Finally, the financial support from the ERC Advanced Grant ‘Insta-
bilities and nonlocal multiscale modelling of materials’ ERC-2013-ADG-
340561- INSTABILITIES (2014-2019) is gratefully acknowledged.
Trento, March 21, 2016
Summer Shahzad
Ph.D.Thesis–SummerShahzad vii

Scientific articles
The main results presented in this thesis have been summarized in the
following papers:
1. Shahzad, S., Dal Corso, F., and Bigoni, D. (2016)
Hypocycloid inclusions in nonuniform out-of-plane elasticity: stress
singularity vs stress reduction.
Submitted.
2. Dal Corso, F., Shahzad, S., Bigoni, D. (2016)
Isotoxalstar-shapedpolygonalvoidsandrigidinclusionsinanonuni-
form antiplane shear fields. I. Formulation and full-field solution.
International Journal of Solids and Structures,
doi:10.1016/j.ijsolstr.2016.01.027.
3. Dal Corso, F., Shahzad, S., Bigoni, D. (2016)
Isotoxal star-shaped polygonal voids and rigid inclusions in nonuni-
form antiplane shear fields. II. Stress singularities, stress annihila-
tion and inclusion invisibility.
International Journal of Solids and Structures,
doi:10.1016/j.ijsolstr.2016.01.026.
4. Misseroni, D., Dal Corso, F., Shahzad, S., Bigoni, D. (2014)
stressconcentrationnearstiffinclusions: validationofrigidinclusion
model and boundary layers by means of photoelasticity.
Engineering Fracture Mechanics, 121-122, 87-97.
Ph.D.Thesis–SummerShahzad ix