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

Selected Publications by Topic

Failure of Pressurized Vessels

Failure in Plates on Elastic Foundations and Highway Pavements based on 2D

Viscoplastic and Penetration

3D Fracture in Plates with Through the Thickness Holes or Cracks

Failure in Composite Material Systems Based on 3D Micro & Macro Considerations

Stress Waves in Composite Material Systems

Interlaminar Stresses at the Edge of an Adjacent Hole

Uniqueness and Completeness of the Folias 3D Theory of Fracture

Failure in Plates on Elastic Foundations and Highway Pavements based on 2D

Viscoplastic and Penetration

3D Fracture in Plates with Through the Thickness Holes or Cracks

Failure in Composite Material Systems Based on 3D Micro & Macro Considerations

Stress Waves in Composite Material Systems

Interlaminar Stresses at the Edge of an Adjacent Hole

Uniqueness and Completeness of the Folias 3D Theory of Fracture

# Failure of Pressurized Vessels:

- D.D. Ang, E.S. Folias, & M.L. Williams,

**“The Effect of Initial Spherical Curvature on the Stresses Near a Crack Point,” [semi-infinite crack]***Aeronautical Research Laboratory, U.S. Air Force***ARL 62**(1962) pp. 1-38. .pdf - E.S. Folias,
**“The Stresses in a Spherical Shell Containing a Crack,”**[finite crack]

*Ph.D. Thesis, California Institute of Technology*(1963) pp. 1-76. .pdf - E.S. Folias,
**“The Stresses in a Spherical Shell Containing a Crack,”**[finite crack]*Aeronautical Research Laboratory, U.S. Air Force***ARL 64-23**(1964) pp. 1-76 .pdf - E.S. Folias,
**“The Stresses in a Cylindrical Shell Containing an Axial Crack,”**[finite crack]*Aeronautical Research Laboratory, U.S. Air Force***ARL 64-174**(1964) pp. 1-42 .pdf - E.S. Folias,
**“The Stresses in a Cracked Spherical Shell,”**[part I]*Journal of Mathematics and Physics***XLIV**(1965) pp. 164-176. .pdf - E.S. Folias,
**“A Finite Line Crack in a Pressurized Spherical Shell,”**[part II]

*International Journal of Fracture Mechanics***1**(1965) pp. 20-46. .pdf - E.S. Folias,
**“An Axial Crack in a Pressurized Cylindrical Shell,”***International Journal of Fracture Mechanics***1**(1965) pp. 104-113. .pdf - E.S. Folias,
**“A Circumferential Crack in a Pressurized Cylindrical Shell,”**[small λ]*International Journal of Fracture Mechanics***3**(1967) pp. 1-22. .pdf - E.S. Folias,
**“A Cylindrical Shell Containing a Peripheral Crack,”**[large λ]*UTEC***67-043**(1967) pp. 1-12. .pdf - E.S. Folias,
**“On the Prediction of Failure in Pressurized Vessels,”**

*ASME: Proceedings of the International Conference on Pressure Vessels Technology Vol II,*(1969) pp. 781-791. .pdf

edited by I. Berman - E.S. Folias,
**“On the Effect of Initial Curvature on Cracked Flat Sheets,”**

*International Journal of Fracture Mechanics***5**(1969) pp. 327-346. .pdf - E.S. Folias,
**“On the Theory of Fracture of Curved Sheets,”**

*Engineering Fracture Mechanics***2**(1970) pp. 151-164. .pdf - S.H. Do & E.S. Folias,
**“On the Steady-State Transverse Vibrations of a Cracked Spherical Shell,”**

*International Journal of Fracture Mechanics***7**(1971) pp. 23-37. .pdf - E.S. Folias,
**“Fracture in Pressure Vessels,”**

*Chapter 21, Thin Shell Structures, edited by Y.C. Fung & E.E. Sechler,*Prentice-Hall (1973) pp. 483-518. .pdf - E.S. Folias,
**“Estimating Plastic Zone Sizes,”**

*International Journal of Fracture***10**(1974) pp. 109-111. .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. 405-418. .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,
**“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. 117-160. .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. 104-113. .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,
**“The Stress Field at the Base of a Port in a Cylindrical Pressure Vessel,”***International Journal of Pressure Vessels and Piping***36**(1989) pp. 249-255. .pdf - E.S. Folias,
**“Failure of Pressurized Vessels,”**(Chapter 12)*Fracture: A Topical Encyclopedia of Current Knowledge, edited by G.P. Cherepanov*(1998) pp. 275-288. .pdf - E.S. Folias & P. Bogert,
**“Static Failure in A1 2219–T87 Pressurized Vessels,”***ASME PVP-Vol. 373*(1998) pp. 287-300. .pdf - L.J. Perry & E.S. Folias,
**“Failure of a Threaded Pressurized Vessel,”***International Journal of Pressure Vessels and Piping***76**(1999) pp. 685-692. .pdf - E.S. Folias,
**“Failure Correlation Between Pressurized Vessels and Plates,”***International Journal of Pressure Vessels and Piping***76**(1999) pp. 803-811. .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. 893-903. .pdf

# Failure in Plates on Elastic Foundations and Highway Pavements based on 2D:

- D.D. Ang, E.S. Folias, & M.L. Williams,
**“The Bending Stress in a Cracked Plate on an Elastic Foundation,”**[semi-infinite crack]*Journal of Applied Mechanics***30**(1963) pp. 245-254. .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. 365-367. .pdf - E.S. Folias,
**“On the Steady-State Transverse Vibrations of a Cracked Plate,”**

*Engineering Fracture Mechanics***1**(1968) pp. 363-368. .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. 257-263. .pdf - E.S. Folias,
**“Estimating Plastic Zone Sizes,”**

*International Journal of Fracture***10**(1974) pp. 109-111. .pdf - S.-T. Lin & E.S. Folias,
**“On the Fracture of Highway Pavements,”**

*International Journal of Fracture***11**(1975) pp. 93-106. .pdf

# Viscoplastic and Penetration:

- 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. 121-127. .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. 115-129. .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. 409-415.

# 3D Fracture in Plates with Through the Thickness Holes or Cracks:

- E.S. Folias,
**“On the Three-Dimensional Theory of Cracked Plates,”**

*Journal of Applied Mechanics***7**(1975) pp. 245-254. .pdf - E.S. Folias,
**“Closure to the Discussion on ‘Discussion on the Three-Dimensional Theory of Cracked Plates,’”**

*Journal of Applied Mechanics***43**(1976) pp. 374-375. .pdf - E.S. Folias,
**“The Effect of Thickness in Fracture,”**

*Proceedings of the Symposium on Three-Dimensional Fracture,*Battelle (1978). .pdf - E.S. Folias,
**“Three Dimensional Stress Fields in Cracked Plates,”**

*Air Force Office of Scientific Research final report*(1980) pp 1-146. .pdf - E.S. Folias,
**“Method of Solution of a Class of Three-Dimensional Elastostatic Problems under Mode I Loading,”**

*International Journal of Fracture***16**(1980) pp. 335-348. .pdf - E.S. Folias & J.-J. Wang,
**“On the Corner Singularity of a Three-Dimensional Griffith Crack,”**

*Air Force Office of Scientific Research final report*(1984) pp. 245-254. .pdf - E.S. Folias,
**“On the Prediction of Fatigue Cracks at Holes,”**

*Proceedings of the Third International Conference on Computational Methods and Experimental Measurements,*Springer-Verlag

edited by G.A. Keramidas & C.A. Brebbia, Vol. II,**7**(1986) pp. 627-638. .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. 187-194. .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. 56-72. .pdf - E.S. Folias,
**“Recent Advances on 3D Elasticity Problems Related to Fracture,”***ASME AMD-Vol 91: Analytical, Numerical, and Experimental Aspects of Three Dimensional Fracture Processes,*(1988) pp. 267-277. .pdf

edited by A. Rosakis, K. Ravi-Chandar, & Y. Rajapakse - J.D. Walker & E.S. Folias,
**“Effect of Stress Waves in Laminated Composite Plates,”***ASME AMD-Vol. 13: Fracture and Failure of Composite Materials*(1988) pp. 193-198. - 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. 1-107. .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. 133-142. .pdf - F.E. Penado & E.S. Folias,
**“The Three-Dimensional Stress Field around a Cylindrical Inclusion in a Plate of an Arbitrary Thickness,”***International Journal of Fracture***39**(1989) pp. 129-146. .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. 25-34. .pdf - E.S. Folias,
**“On the Three-Dimensional Bending Theory of Cracked Plates,”***International Journal of Solids and Structures***25**(1989) pp. 497-513. .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. 1193-1200. .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. 249-255. .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. 63-67. .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 Three-Dimensional Stress Field around a Circular Hole in a Plate of Arbitrary Thickness,”***Computational Mechanics***6**(1990) pp. 379-391. .pdf - E.S. Folias,
**“Failure in Laminated Composite Plates Containing a Hole,”***Air Force Office of Scientific Research final report*(1990) pp. 104-113. .pdf - E.S. Folias & W.G. Reuter,
**“On the Equilibrium of a Linear Elastic Plate,”***Computational Mechanics***5**(1990) pp. 459-468. .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. 869-886. .pdf - C.C. Li & E.S. Folias,
**“Edge Effect of a Carbon Fiber Meeting a Free Surface,”***Mechanics of Materials***12**(1991) pp. 267-278. .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. 171-186. .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. 1-326. .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. 233-247. .pdf - Y.-K. Choi & E.S. Folias,
**“The 3D Stress Field in a Laminated Composite Plate with a Hole Based on a h-r Finite Element Method,”***AMSE AMD-Vol 196*(1994) pp. 31-42. .pdf - E.S. Folias,
**“Load Transfer Characteristics and Residual Stresses in Composite Material Systems,”***Air Force Office of Scientific Research final report*(1997) pp. 1-67. .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. 335-349. .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. 203-224. .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. 1-24. .pdf

# Failure in Composite Material Systems Based on 3D Micro & Macro Considerations:

- J.D. Walker & E.S. Folias,
**“Effect of Stress Waves in Laminated Composite Plates,”***ASME AMD-Vol. 13: Fracture and Failure of Composite Materials*(1988) pp. 193-198. - 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. 1-107. .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. 133-142. .pdf - F.E. Penado & E.S. Folias,
**“The Three-Dimensional Stress Field around a Cylindrical Inclusion in a Plate of an Arbitrary Thickness,”***International Journal of Fracture***39**(1989) pp. 129-146. .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. 25-34. .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. 1193-1200. .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,
**“Failure in Laminated Composite Plates Containing a Hole,”***Air Force Office of Scientific Research final report*(1990) pp. 104-113. .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. 869-886. .pdf - C.C. Li & E.S. Folias,
**“Edge Effect of a Carbon Fiber Meeting a Free Surface,”***Mechanics of Materials***12**(1991) pp. 267-278. .pdf - J. Walker & E.S. Folias,
**“Effect of Stress Waves on Laminated Composite Plates,”***International Journal of Solids and Structures***29**(1992) pp. 145-170. .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. 171-186. .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. 1-326. .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. 233-247. .pdf - Y.-K. Choi & E.S. Folias,
**“The 3D Stress Field in a Laminated Composite Plate with a Hole Based on a h-r Finite Element Method,”***AMSE AMD-Vol 196*(1994) pp. 31-42. .pdf - E.S. Folias,
**“Load Transfer Characteristics and Residual Stresses in Composite Material Systems,”***Air Force Office of Scientific Research final report*(1997) pp. 1-67. .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. 335-349. .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. 203-224. .pdf

# Stress Waves in Composite Material Systems:

- J.D. Walker & E.S. Folias,
**“Effect of Stress Waves in Laminated Composite Plates,”***ASME AMD-Vol. 13: Fracture and Failure of Composite Materials*(1988) pp. 193-198. - 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. 1-107. .pdf - J. Walker & E.S. Folias,
**“Effect of Stress Waves on Laminated Composite Plates,”***International Journal of Solids and Structures***29**(1992) pp. 145-170. .pdf

# Interlaminar Stresses at the Edge of an Adjacent Hole:

- 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. 1193-1200. .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,
**“Failure in Laminated Composite Plates Containing a Hole,”***Air Force Office of Scientific Research final report*(1990) pp. 104-113. .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. 869-886. .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. 171-186. .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. 1-326. .pdf1 .pdf2 - E.S. Folias,
**“Load Transfer Characteristics and Residual Stresses in Composite Material Systems,”***Air Force Office of Scientific Research final report*(1997) pp. 1-67. .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. 335-349. .pdf

# Uniqueness and Completeness of the Folias 3D Theory of Fracture:

- C.H. Wilcox,
**“Uniqueness Theorems for Displacement Fields with Local Finite Energy in Linear Elastostatics,”**

*Journal of Elasticity,***9**(1979) pp. 221-243. .pdf - C.H. Wilcox,
**“Completeness of the Eigenfunctions for Griffith Cracks in Plates of Finite Thickness,”**

*Air Force Office of Scientific Research final report,*(1978) pp. 1-45. .pdf