Efthymios S. Folias
Professor of Mechanics & Mathematics (emeritus)
Department of Mathematics
University of Utah
Ph.D. Aeronautics (Solid Mechanics), California Institute of Technology, 1963
M.S. Mathematics, University of New Hampshire, 1960
B.S. Electrical Engineering, University of New Hampshire, 1959
Professor of Mechanics & Mathematics (emeritus)
Department of Mathematics
University of Utah
Ph.D. Aeronautics (Solid Mechanics), California Institute of Technology, 1963
M.S. Mathematics, University of New Hampshire, 1960
B.S. Electrical Engineering, University of New Hampshire, 1959
Research Interests:
Applied Mechanics with special emphasis on:
 Fracture of structural materials
 Failure of pressurized vessels
 Elasticity and shell theory
 Failure of composites
 Macromechanical and micromechanical behavior of composite material systems
 Fiber/matrix interfaces, interlaminar stresses, delamination, residual stresses
 Stress wave behavior
New article (updated appendix)
E.S. Folias, “On the Structure of the 3D Stress Field and Its 3D Stress Singularity in a 3D Griffith Crack,”
submitted to International Journal of Fracture (2012) pp. 124. .pdf
Selected Publications
Selected Publications by Topic
Research Interests and Activities
Folias Factor
Partial List of Publications and Reports:
 D.D. Ang, E.S. Folias, & M.L. Williams,
“The Effect of Initial Spherical Curvature on the Stresses Near a Crack Point,” [semiinfinite crack]
Aeronautical Research Laboratory, U.S. Air Force ARL 62 (1962) pp. 138. .pdf  E.S. Folias, “The Stresses in a Spherical Shell Containing a Crack,” [finite crack]
Ph.D. Thesis, California Institute of Technology (1963) pp. 176. .pdf  D.D. Ang, E.S. Folias, & M.L. Williams,
“The Bending Stress in a Cracked Plate on an Elastic Foundation,” [semiinfinite crack]
Journal of Applied Mechanics 30 (1963) pp. 245254. .pdf  D.D. Ang, E.S. Folias, & M.L. Williams, “Discussion of Bending Stress in an Cracked Plate on an Elastic Foundation,” Journal of Applied Mechanics 31 (1964) pp. 365367. .pdf
 E.S. Folias, “The Stresses in a Spherical Shell Containing a Crack,” [finite crack]
Aeronautical Research Laboratory, U.S. Air Force ARL 6423 (1964) pp. 176 .pdf  E.S. Folias, “The Stresses in a Cylindrical Shell Containing an Axial Crack,” [finite crack]
Aeronautical Research Laboratory, U.S. Air Force ARL 64174 (1964) pp. 142 .pdf  E.S. Folias, “The Stresses in a Cracked Spherical Shell,” [part I]
Journal of Mathematics and Physics XLIV (1965) pp. 164176. .pdf  E.S. Folias, “A Finite Line Crack in a Pressurized Spherical Shell,” [part II]
International Journal of Fracture Mechanics 1 (1965) pp. 2046. .pdf  E.S. Folias, “An Axial Crack in a Pressurized Cylindrical Shell,”
International Journal of Fracture Mechanics 1 (1965) pp. 104113. .pdf  E.S. Folias, “A Circumferential Crack in a Pressurized Cylindrical Shell,” [small λ]
International Journal of Fracture Mechanics 3 (1967) pp. 122. .pdf  E.S. Folias, “A Cylindrical Shell Containing a Peripheral Crack,” [large λ]
UTEC 67043 (1967) pp. 112. .pdf  E.S. Folias, “On the SteadyState Transverse Vibrations of a Cracked Plate,”
Engineering Fracture Mechanics 1 (1968) pp. 363368. .pdf  E.S. Folias, “On the Prediction of Failure in Pressurized Vessels,”
ASME: Proceedings of the International Conference on Pressure Vessels Technology Vol II,
edited by I. Berman (1969) pp. 781791. .pdf  E.S. Folias, “On the Effect of Initial Curvature on Cracked Flat Sheets,”
International Journal of Fracture Mechanics 5 (1969) pp. 327346. .pdf  E.S. Folias, “On a Plate Supported by an Elastic Foundation and Containing a Finite Crack,”
International Journal of Fracture Mechanics 6 (1970) pp. 257263. .pdf  E.S. Folias, “On the Theory of Fracture of Curved Sheets,”
Engineering Fracture Mechanics 2 (1970) pp. 151164. .pdf  S.H. Do & E.S. Folias, “On the SteadyState Transverse Vibrations of a Cracked Spherical Shell,”
International Journal of Fracture Mechanics 7 (1971) pp. 2337. .pdf  E.S. Folias, “Fracture in Pressure Vessels,”
Chapter 21, Thin Shell Structures, edited by Y.C. Fung & E.E. Sechler, PrenticeHall (1973) pp. 483518. .pdf  E.S. Folias, “Estimating Plastic Zone Sizes,”
International Journal of Fracture 10 (1974) pp. 109111. .pdf  E.S. Folias, “On the Prediction of Catastrophic Failures in Pressurized Vessels,”
Prospects of Fracture Mechanics, edited by G. Sih, Noordhoff International (1974) pp. 405418. .pdf  S.T. Lin & E.S. Folias, “On the Fracture of Highway Pavements,”
International Journal of Fracture 11 (1975) pp. 93106. .pdf  E.S. Folias, “On the Fracture of Nuclear Reactor Tubes,”
Transactions of the Third International Conference on Structural Mechanics in Reactor Technology (1975). .pdf  E.S. Folias, “On the ThreeDimensional Theory of Cracked Plates,”
Journal of Applied Mechanics 7 (1975) pp. 245254. .pdf  E.S. Folias, “Closure to the Discussion on ‘Discussion on the ThreeDimensional Theory of Cracked Plates,’”
Journal of Applied Mechanics 43 (1976) pp. 374375. .pdf  E.S. Folias, “Asymptotic Approximation to Crack Problems in Shells,”
Chapter 4 in Plates and Shells with Cracks: A Collection of Stress Intensity Factor Solutions for Cracks in Plates and Shells (Mechanics of Fracture), edited by G. Sih, Noordhoff International (1977) pp. 117160. .pdf  E.S. Folias, “The Effect of Thickness in Fracture,”
Proceedings of the Symposium on ThreeDimensional Fracture, Battelle (1978). .pdf  E.S. Folias, “Three Dimensional Stress Fields in Cracked Plates,”
Air Force Office of Scientific Research final report (1980) pp 1146. .pdf  E.S. Folias, “Method of Solution of a Class of ThreeDimensional Elastostatic Problems under Mode I Loading,”
International Journal of Fracture 16 (1980) pp. 335348. .pdf  E.S. Folias, “An Axial Crack in a Pressurized Cylindrical Shell,”
(20th year reprint issue, Editors’ selection of 16 papers)
International Journal of Fracture 26 (1984) pp. 104113. .pdf  E.S. Folias & J.J. Wang, “On the Corner Singularity of a ThreeDimensional Griffith Crack,”
Air Force Office of Scientific Research final report (1984) pp. 245254. .pdf  E.S. Folias, “On the Prediction of Fatigue Cracks at Holes,”
Proceedings of the Third International Conference on Computational Methods and Experimental Measurements,
edited by G.A. Keramidas & C.A. Brebbia, Vol. II, SpringerVerlag 7 (1986) pp. 627638. .pdf  E.S. Folias, “The 3D Stress Field at the Intersection of a Hole and a Free Surface,”
International Journal of Fracture 35 (1987) pp. 187194. .pdf  E.S. Folias, “Some Remarks on Three Dimensional Fracture,”
ASTM STP 969 Publication, Fracture Mechanics 19th Symposium, editied by T.A. Cruse (1988) pp. 5672. .pdf  E.S. Folias, “Fracture of Pressurized Metal and Graphite/Epoxy Cylinders for Applications to Pressure Vessel Design,” Transactions of the Sixth International Conference on Pressure Vessel Technology (1988). .pdf
 E.S. Folias, “Recent Advances on 3D Elasticity Problems Related to Fracture,”
ASME AMDVol 91: Analytical, Numerical, and Experimental Aspects of Three Dimensional Fracture Processes,
edited by A. Rosakis, K. RaviChandar, & Y. Rajapakse (1988) pp. 267277. .pdf  J.D. Walker & E.S. Folias, “Effect of Stress Waves in Laminated Composite Plates,”
ASME AMDVol. 13: Fracture and Failure of Composite Materials (1988) pp. 193198.  J.D. Walker & E.S. Folias, “On the Interaction between Stress Waves and Cracks in Laminated Composite Plates,”
Idaho National Engineering Labs final report (1989) pp. 1107. .pdf  E.S. Folias, “The 3D Stress Field at the Edge of a Circular Hole and the Interface of a Laminated Composite Plate,”
Journal of Thermoplastic Composite Materials 2 (1989) pp. 133142. .pdf  F.E. Penado & E.S. Folias, “The ThreeDimensional Stress Field around a Cylindrical Inclusion in a Plate of an Arbitrary Thickness,” International Journal of Fracture 39 (1989) pp. 129146. .pdf
 E.S. Folias, “On the Stress Singularities at the Intersection of a Cylindrical Inclusion with the Free Surface of a Plate,” International Journal of Fracture 39 (1989) pp. 2534. .pdf
 D.D. Ang, E.S. Folias, F. Keinert, & F. Stenger, “Viscoplastic Flow Due to Penetration: A Free Boundary Value Problem,” International Journal of Fracture 39 (1989) pp. 121127. .pdf
 E.S. Folias, “On the ThreeDimensional Bending Theory of Cracked Plates,”
International Journal of Solids and Structures 25 (1989) pp. 497513. .pdf  E.S. Folias, “On the Interlaminar Stresses of a Composite Plate around the Neighborhood of a Hole,”
International Journal of Solids and Structures 25 (1989) pp. 11931200. .pdf  E.S. Folias, “The Stress Field at the Base of a Port in a Cylindrical Pressure Vessel,”
International Journal of Pressure Vessels and Piping 36 (1989) pp. 249255. .pdf  E.S. Folias, “The 3D Stress Field at the Intersection of a Partial Through Crack and a Free Surface,”
Proceedings of the Seventh International Conference on Fracture Vol. 1 (1989) pp. 6367. .pdf  E.S. Folias, “The 3D Stress Field at the Intersection of a Hole and a Free Surface in a Transversely Isotropic Plate,”
UTEC (1989). .pdf  E.S. Folias & J.J. Wang, “On the ThreeDimensional Stress Field around a Circular Hole in a Plate of Arbitrary Thickness,” Computational Mechanics 6 (1990) pp. 379391. .pdf
 E.S. Folias, “Failure in Laminated Composite Plates Containing a Hole,”
Air Force Office of Scientific Research final report (1990) pp. 104113. .pdf  E.S. Folias & W.G. Reuter, “On the Equilibrium of a Linear Elastic Plate,”
Computational Mechanics 5 (1990) pp. 459468. .pdf  E.S. Folias, “On the Prediction of Failure at a Fiber/Matrix Interface in a Composite Subjected to a Transverse Tensile Load,” Journal of Composite Materials 25 (1991) pp. 869886. .pdf
 D.D. Ang, E.S. Folias, & F. Keinert, “Penetration Mechanics: Predicting the Location of a Viscoplastic Boundary and its Effect on the Stresses,” International Journal of Solids and Structures 28 (1991) pp. 115129. .pdf
 C.C. Li & E.S. Folias, “Edge Effect of a Carbon Fiber Meeting a Free Surface,”
Mechanics of Materials 12 (1991) pp. 267278. .pdf  J. Walker & E.S. Folias, “Effect of Stress Waves on Laminated Composite Plates,”
International Journal of Solids and Structures 29 (1992) pp. 145170. .pdf  E.S. Folias, “Boundary Layer Effects of Interlaminar Stresses Adjacent to a Hole in a Laminated Composite Plate,” International Journal of Solids and Structures 29 (1992) pp. 171186. .pdf
 E.S. Folias, “Failure Considerations in Composite Material Systems Based on 3D Micromechanical Stress Fields : Part A,” Air Force Office of Scientific Research (1992) pp. 1326. .pdf1 .pdf2
 F. Zhong & E.S. Folias, “The 3D Stress Field of a Fiber Embedded into a Matrix and Subjected to an Axial Load,”
Computational Mechanics 9 (1992) pp. 233247. .pdf  Y.K. Choi & E.S. Folias, “The 3D Stress Field in a Laminated Composite Plate with a Hole Based on a hr Finite Element Method,” AMSE AMDVol 196 (1994) pp. 3142. .pdf
 D.D. Ang, T.A. Ngoc, D.D. Trong, & E.S. Folias, “Global Solutions of a Free Boundary Value Problem in Penetration Mechanics,” Engineering Mechanics Today, Vol. II (1996) pp. 409415.
 E.S. Folias, “Load Transfer Characteristics and Residual Stresses in Composite Material Systems,”
Air Force Office of Scientific Research final report (1997) pp. 167. .pdf  E.S. Folias, “Failure of Pressurized Vessels,” (Chapter 12)
Fracture: A Topical Encyclopedia of Current Knowledge, edited by G.P. Cherepanov (1998) pp. 275288. .pdf  E.S. Folias & P. Bogert, “Static Failure in A1 2219–T87 Pressurized Vessels,”
ASME PVPVol. 373 (1998) pp. 287300. .pdf  E.S. Folias, M. Hohn, & T. Nicholas “Predicting Crack Initiation in Composite Material Systems Due to a Thermal Expansion Mismatch,” International Journal of Fracture 93 (1999) pp. 335349. .pdf
 L.J. Perry & E.S. Folias, “Failure of a Threaded Pressurized Vessel,”
International Journal of Pressure Vessels and Piping 76 (1999) pp. 685692. .pdf  E.S. Folias, “Failure Correlation Between Pressurized Vessels and Plates,”
International Journal of Pressure Vessels and Piping 76 (1999) pp. 803811. .pdf  E.S. Folias, “Predicting Failures in Cylindrical Pressurized Vessels from Tests Carried Out on Flat Plates,”
Proceedings of the 9th International Conference on Pressure Vessel Technology Vol. 1 (2000) pp. 893903. .pdf  E.S. Folias, “The 3D Stress Field in a [0°/90°] Laminated Composite Plate Containing a Finite Crack,”
International Journal of Fracture 114 (2002) pp. 203224. .pdf  E.S. Folias, “On the Structure of the 3D Stress Field and Its 3D Stress Singularity in a 3D Griffith Crack,”
submitted to International Journal of Fracture (2012) pp. 124. .pdf
Books:

E.S. Folias (editor), “Structural Integrity: Theory and Experiment,”
Kluwer Academic Publishers, March 1989.