Advanced structural design by the Finite ElementMethod
SUMMER QUARTER
This course will discuss the use of Advanced Finite Element Analysis of composite, nanocomposite
and multi-functional composite structures for aerospace applications. First, the main opportunities andchallenges introduced by the advent of advanced composite materials in aerospace engineering will be
critically discussed. Particular focus will be devoted to the computational issues arising with the typicalstrain localization phenomena in composites. Fracture size effects in composites and nanocomposites,
as well as their importance for structural design, will be critically analyzed. Methods for the size effectcharacterization and its modeling will be presented. Then, the Spectral Stiffness Microplane Model(S2M2), an advanced formulation capable of capturing the main damage mechanisms in composites
and other quasibrittle materials, will be introduced and described in detail. The use of S2M2 for thecrashworthiness analysis of composites structures will be presented along with its application for theanalysis of another type of composite material: Discontinuous Fiber Composites (DFCs). DFCs, inwhich the reinforcing phase takes the form of carbon fiber platelets randomly distributed throughout
the system, are gaining more and more interest from the aerospace engineering community thanks tothe excellent manufacturability and interesting mechanical properties. The course will describe theirapplication and computational modeling. Finally, the course will focus on the modeling andcharacterization of the thermo-chemo-mechanical process of crosslinking in epoxy-based composites
leveraging advanced FEA. Simulations showing the emergence of curing stresses and their dependence
on the curing cycle will be presented. Then, ongoing investigations on the use of graphene
nanoplatelets to mitigate the curing stresses and damage will be presented critically.
INSTRUCTOR: Marco Salviato, Assistant Professor, William E. Boeing Department of Aeronautics
and Astronautics, University of Washington, Seattle, WA, USA.
Email: salviato@aa.washington.edu
Office Hours: On request. Contact instructor by email.
COURSE LOCATION / DAYS / TIMES: TBD
SUGGESTED READINGS:Salviato, M., Ashari E. S., Cusatis G. "Spectral stiffness microplane model for damage and fracture oftextile composites." Composite Structures 137 (2016): 170-184.
Salviato, M., Kirane K., Ashari S.E., Bažant Z.P., Cusatis G. "Experimental and numericalinvestigation of intra-laminar energy dissipation and size effect in two-dimensional textilecomposites." Composites Science and Technology 135 (2016): 67-75.
Mefford, C. H., Qiao Y., Salviato M. "Failure behavior and scaling of graphene nanocomposites."
Composite Structures 176 (2017): 961-972.

Qiao Y., Salviato M., “A Cohesive Zone Modeling Study on the Fracturing Behavior of Thermoset
Polymer Nanocomposites” 33th ASC conference proceedings, (2018).
Ko S., Chan K., Hawkins R., Jayaram R., Lynch C., El Mamoune R., Nguyen M., Pekhotin N., StokesN., Wu D., Tuttle M.E., Yang J., Salviato M., “Experimental and Numerical Characterization of theIntra-laminar Fracturing Behavior in Discontinuous Fiber Composite Structures” 33th ASC conference
proceedings, (2018).
Heinrich, C., Aldridge M., Wineman A.S., Kieffer J., Waas A.M., Shahwan K.W. "Generation of heatand stress during the cure of polymers used in fiber composites." International Journal of Engineering
Science 53 (2012): 85-111.
REFERENCE BOOKS:
Daryl L. Logan, “A First Course in the Finite Element Method”, sixth Edition.
Zinkiewicz O.C., Taylor R.L., Zhu J.Z. “The Finite Element Method. Its Basis and Fundamentals”
Elsevier, 2013.
Belytschko T., Liu W-K, Moran B., Elkhodary K.I. “Nonlinear Finite Elements for Continua andStructures” 2nd edition, Wiley, 2013.
Bažant Z.P., Planas J., “Fracture and Size Effect in Concrete and Other Quasibrittle Materials”, CRC
press, 1998.

COURSE OUTLINE:
DAY 1
Multi-Functional Composites and Nanocomposites for Aerospace Applications: Opportunities
and Challenges (90 min)
Structural Computational Modeling of Composites and Other Quasibrittle Materials: How toDeal with Strain Localization in a FE Framework (90 min)
In Day 1, the use of Advanced Finite Element Analysis of composite, nanocomposite and multifunctional composite structures for aerospace applications will be presented. In the first part of the day,the main opportunities and challenges introduced by the advent of advanced composite materials inaerospace engineering will be critically discussed. Then, in the second class, particular focus will bedevoted to the computational issues arising with the typical strain localization phenomena incomposites.

DAY 2Size Effect on the Structural Behavior of Composites, Nanocomposites and other Quasibrittle
Materials: Theoretical Background (90 min)

Size Effect on the Structural Behavior of Composites, Nanocomposites and other Quasibrittle
Materials: an Examples in Graphene Nanocomposites (90 min)Day 2 will focus on a very important aspect related to the structural behavior of composite andnanocomposites which is, unfortunately, often overlooked: type I and type II size effect. In the firstpart of the day, the theoretical derivations of size effect will be introduced and demonstrated rigorouslywith clear reference to materials used in aerospace engineering including unidirectional composites,
textile composites, nanocomposites and ceramics. The second part of the talk will exemplify size effectand its importance for the structural design of graphene nanocomposites and other nanocomposites.

DAY 3
Spectral Stiffness Microplane Model (S2M2) for the Computational Modeling of Composites:
Theoretical Framework (90 min)Spectral Stiffness Microplane Model (S2M2) for the Computational Modeling of Composites:
Implementation in FE and Applications (90 min)
In Day 3, the Spectral Stiffness Microplane Model (S2M2), an advanced formulation capable ofcapturing the main damage mechanisms in composites and other quasibrittle materials, will be
introduced and described in detail. The use of S2M2 for the crashworthiness analysis of composites
structures will be presented along with its application for the analysis of another type of composite
material: Discontinuous Fiber Composites (DFCs).

DAY 4
Discontinuous Fiber Composites (DFCs): Advantages and Challenges for their StructuralApplications (90 min)Discontinuous Fiber Composites (DFCs): Experimental Characterization and Modeling of TheirFracturing Behavior (90 min)Day 4, will focus on Discontinuous Fiber Composites (DFCs). In DFCs, the reinforcing phase takes
the form of carbon fiber platelets randomly distributed throughout the system. It will be shown that,the randomness of the platelet orientations leads to a significant spatial distribution of mechanicalproperties whereas the large dimensions of the platelets generally promote damage tolerance. Byexperiments on geometrically-scaled specimens and computational modeling, it will be also shownthat the scaling of the fracturing behavior of DFCs is particularly interesting. In fact, the behavior
transitions from quasi-ductile to brittle for increasing system sizes compared to the platelet dimensions.
Leveraging these results, it is possible to design the platelet as a function of the size and geometry of
the system to achieve quasi-ductility. To conclude the talk, a stochastic computational framework tocapture the large variability in mechanical performance of the system will be presented. The use of themodel for designing and certification of aerospace components will be discussed.

DAY 5
FE Modeling of Curing Stresses in Thermoset Composites: State-of-the-Art and Future
Challenges (90 min)Graphene Nanoplatelets for the Mitigation of Curing Stresses in Ultra-Thick Compositesmin)(90Day 5 will focus on the modeling and characterization of the thermo-chemo-mechanical process ofcrosslinking in epoxy-based composites leveraging advanced FEA. Simulations showing theemergence of curing stresses and their dependence on the curing cycle will be presented. Then, ongoinginvestigations on the use of graphene nanoplatelets to mitigate the curing stresses and damage will bepresented critically.

DAY 6
Mitigation of Stress Intensity in Bodies of Revolution Reinforced by Curvilinear Fibers: ClosedForm Solution (90 min)FEA Modeling of Composites Reinforced by Curvilinear Fibers(90 min)Day 6 will discuss the new opportunities arising with the use of reinforcements following curvilinear
paths. In the first part of the talk, a recent closed-form solution for the stress fields, stiffening effectand optimum fiber path in structures subject to shear and torsional loadings will be derived rigorously.
It will be shown that, if proper paths are choses, not only the stiffening and strengthening effects canbe maximized but also the stress intensity in the presence of notches or crack can be minimized. Thesecond part of the talk discuss the formulation of an Iso-Geometric Analysis framework for the analysisof curvilinear fiber composites.

Bio-SketchDr. Salviato is assistant professor at the Department of Aeronautics andAstronautics of University of Washington where he serves as the PI of thelaboratory for Multiscale Analysis of Materials and Structures (MAMS). Dr.
Salviato obtained a Ph.D. in Theoretical and Applied Mechanics from theUniversity of Padova (Padova, Italy) with a doctoral dissertation focusing on theexperimental characterization and computational modeling of polymer
nanocomposites. He later joined the Department of Civil and Environmental
Engineering at Northwestern University as postdoctoral scholar (2013-14) andresearch assistant professor (2014-15).
Dr. Salviato’s research and teaching interests lie in the area of Computational Mechanics andFracture Mechanics of Quasibrittle Solids. His focus is the understanding the mechanical behavior ofmaterials and structures at multiple length-scales through the formulation of advanced computationaland analytical approaches and new experimental techniques. He believes that the next-generation,

damage-tolerant infrastructure will be enabled by the elimination of the old dichotomy between theconcepts of “structure” and “material”.
In 2017, Dr. Salviato received the prestigious ASME Haythornthwaite Young Investigator Awardfor “excellence in theoretical and applied mechanics”. He also co-authored the book “Quasibrittle
Fracture Mechanics and Size Effect: First Course”.