Dr. Robert K. Goldberg


Dr. Robert K. Goldberg

Title: Associate Lecturer
Department: Civil Engineering
Phone: 330-972-7286
Fax: 330-972-6020
Email: rkg@uakron.edu


Biography

PROFESSIONAL EXPERIENCE

1991-present NASA Glenn Research Center, Cleveland, OH - Aerospace Engineer

2003-present University of Akron, Akron, OH – Ad Hoc Temporary Graduate Faculty

1990-1991 Cleveland State University, Cleveland, OH – Research Associate

EDUCATIONAL BACKGROUND

Ph.D. in Aerospace Engineering, University of Cincinnati, December 1999

M.S. in Applied Mechanics, Rensselaer Polytechnic Institute, August 1990

B.S. in Aeronautical and Astronautical Engineering, The Ohio State University, June 1988

COURSES TAUGHT

University of Akron, Akron, OH, Civil Engineering: 4300-683, Plasticity, Fall 2005, Fall 2008, Fall 2010

University of Akron, Akron, OH, Civil Engineering: 4300-694, Time Dependent Inelastic Analysis Methods, Spring 2006

University of Akron, Akron, OH, Civil Engineering: 4300-694, Micromechanics of Composite Materials, Fall 2006, Fall 2009

University of Akron, Akron, OH, Civil Engineering: 4300-694, Numerical Methods in Plasticity Analysis, Spring 2007

University of Akron, Akron, OH, Civil Engineering: 4300-201, Statics, Summer 2007, Spring 2008, Spring 2009

University of Akron, Akron, OH, Civil Engineering: 4300-710, Advanced Composite Mechanics, Fall 2007

University of Akron, Akron, OH, Civil Engineering: 4300-694, Advanced Methods in Plasticity Analysis, Spring 2011

ACTIVITY IN RESEARCH

1. Developed analysis method and constitutive equations to allow for simulation of high strain rate deformation of polymer matrix composites subject to impact loads. Methods involved combination of viscoplasticity based constitutive equations, modified to incorporate key features of polymer nonlinear deformation response, with unique micromechanics techniques. Developed methods represent dramatic leap forward in state of the art, and provide capabilities previously nonexistent in composite material models available within transient dynamic finite element codes such as industry standard LS-DYNA, including combination of material nonlinearity and strain rate effects. Rate effects are significant in the analysis of composite structures, and are required for a proper impact analysis. Boeing currently implementing method for use in the design of composite fuselage structures. Engine manufacturers such as GE have expressed interest in analytical techniques for use in designing aircraft engine fan containment systems made of composite materials.

2. Led, provided key technical guidance to and participated in a collaborative NASA/U Akron team in the extension and further application of the micromechanics methods described above to develop a unique meso-mechanical model for the impact analysis of triaxial braided polymer composites. These efforts were in a direct response to engine companies such as General Electric expressing a need for improved design tools for composite fan containment systems that are predictive and not merely correlated based on component level data. This modeling approach, which is implemented within the environment of LS-DYNA, involves modeling the braided composite as a series of parallel laminated composites, which allows for incorporation of the braid architecture directly within the finite element model. The material property parameters required for the model are determined based on braided composite coupon level tests only, as opposed to traditional methods in which constituent and unidirectional composite data is required, thereby greatly simplifying the required experimental program to characterize the model. This effort is leading to a computationally efficient approach which still captures the details of the material architecture, which is required for the proper simulation of impact damage.

3. Led, provided key technical guidance to and participated in a team effort to investigate the effects of irregularities and variability in the microstructure (such as porosity, irregular fiber tow spacing and ply nesting) of the complex microstructure of woven ceramic matrix composites on the effective properties and life of the material. An additional goal of the project was to relate the microstructural variability to the variability that is observed in effective properties such as elastic modulus and first matrix cracking stress. Specific areas of interest included assessing the variability of as fabricated CMC microstructures. Given the variability, the correlation between the characterized variability in the microstructure and the known variability in the material properties was determined. Finite element analyses were conducted on realistic representations (including the complex microstructure) of cross-sections of representative woven ceramic matrix composites. From the analytical results, key features of the microstructure which contributed to the local and effective response were identified and linked to the irregularity and variability of the microstructure of the material.

4. Leveraged extensive experience and unique expertise in the area of high strain rate analysis of composites to aid in development of material models for use in the impact analysis of Reinforced Carbon Carbon (RCC), which is used in the Space Shuttle Wing Leading Edge, for use in the Shuttle program Return to Flight efforts. As part of an agency-wide Ballistic Impact Analysis Team, developed next generation material model for RCC which incorporated strain rate effects, which are significant for RCC, but are not accounted for in current material models. Analysis techniques were also developed to separate out effects of outer thermal coating and inner substrate, and homogenize results into the effective composite response. Analysis techniques played key role in defining damage and failure criteria which are currently being used in impact analyses for Shuttle program. NASA Silver Snoopy honor was awarded for this effort.

5. Assisted in development of ICAN/PART software, a modification of the NASA Glenn developed ICAN composite micromechanics analysis code, which analyzed particulate composite reinforced materials. Specific tasks included implementing new theory into ICAN code and conducting verification studies to ensure code accuracy. Revised software was transferred to local building company for use in analyzing concrete materials.

6. Conducted analyses of effects of residual stresses, fiber/matrix interface and fiber architecture on the inelastic deformation of metal matrix composites using NASA developed MAC/GMC micromechanics analysis software. Analyses helped to demonstrate ability of MAC/GMC to simulate detailed features of metal matrix composite response.

7. Developed post-processor to facilitate graphical post-processing of results data from NASA Glenn developed MAC/GMC composite micromechanics code. The software executes within the MSC/PATRAN computer aided engineering commercial software platform. MACPOST, which was developed using an MSC/PATRAN internal programming language in a menu driven format, permits easy graphical examination of global and local analysis results. This capability enhanced the usefulness of the MAC/GMC software.

8. Analyzed mechanical, thermal and thermomechanical deformation response of laminated and woven polymer and ceramic matrix composites on the micromechanical scale by using the NASA developed BEST-CMS boundary element code. Developed unique methods to model woven composite architectures, functionally graded materials and fiber/matrix interface effects on the micromechanical scale using BEST-CMS.

9. Developed pre-processor to facilitate development of boundary element models of composite unit cells using MSC/PATRAN computer aided engineering commercial software. COMGEN-BEM, which was developed using MSC/PATRAN internal programming language in a menu driven format, allows user to develop boundary element models with a minimum of user input which increased usefulness of BEST-CMS software.

PROFESSIONAL ORGANIZATIONAL MEMBERSHIPS

AIAA (American Institute of Aeronautics and Astronautics)-Associate Fellow

ASME (The American Society of Mechanical Engineers)-Member

ASCE (American Society of Civil Engineers)-Associate Member

ACADEMIC SERVICE

1. Served as member of PhD dissertation committee for following students:

a. Xiahua Zheng, University of Akron, Graduation: Spring, 2006

b. Jingyun Cheng, University of Akron, Graduation: Spring, 2006

c. Linfa Zhu, Arizona State University, Graduation: Spring, 2006

d. Justin Littell, University of Akron, Graduation: Fall, 2008

e. Xuetao Li, University of Akron, Graduation: Fall, 2010

f. Brina Blinzler, University of Akron, Expected Graduation: Spring, 2012

g. Lee Kohlman, University of Akron, Expected Graduation: Spring, 2012

2. Served as member of Master’s thesis committee for following students:

a. Charles Ruggeri, University of Akron: Graduation: Fall, 2009

PROFESSIONAL SERVICE

1. Session Chair, “Ballistic Impact of Composites”, Earth and Space 2006, 10th ASCE Aerospace Division Conference on Engineering, Construction and Operations in Challenging Environments, Houston, TX, Mar. 5-8, 2006.

2. Symposium Organizer (five sessions), “Ballistic Impact and Crashworthiness Analysis of Advanced Aerospace Structures”, Earth and Space 2008, 11th ASCE Aerospace Division Conference on Engineering, Construction and Operations in Challenging Environments, Long Beach, CA, Mar. 3-5, 2008.

3. Guest Editor, Journal of Aerospace Engineering Special Issue, “Ballistic Impact and Crashworthiness Analysis of Aerospace Structures”, Vol. 22, July, 2009.

4. Associate Editor, ASCE Journal of Aerospace Engineering, 2011-2014.

AWARDS

1. NASA Certificate of Recognition for NASA Tech Brief “Program Helps Generate Boundary Element Mathematical Models” (October 1995).

2. NASA Group Achievement Award for transfer and commercialization of NASA ICAN composite mechanics software (August 1996).

3. NASA Team Achievement Award for paper entitled “Application of the Boundary Element Method to the Micromechanical Analysis of Composite Materials”, which was selected as Structural Mechanics Branch Best Paper (September 1996).

4. NASA Certificate of Recognition for NASA Tech Brief “Computing Fiber/Matrix Interfacial Effects in SiC/RBSN” (November 1996).

5. NASA Certificate of Recognition for NASA Tech Brief “Micromechanics for Particulate Reinforced Composites” (May 1997).

6. NASA Team Achievement Award for contributing towards the establishment of the NASA/GLITeC/Battelle Consortium for the Design and Analysis of Composite Materials (August 1997).

7. NASA Invention Award for development of ICAN/PART software (May 1998).

8. Branch Best Paper Award for NASA Life Prediction Branch for paper entitled “Rate Dependent Deformation and Strength Analysis of Polymer Matrix Composites” (September 1999).

9. NASA Certificate of Recognition for NASA Tech Brief “Postprocessing Software for Micromechanics Analysis Code” (July 2001).

10. NASA Certificate of Recognition for NASA Tech Brief “Analyzing Loads and Strains in Composite Materials” (November 2002).

11. NASA Software Release Award for “Micromechanics Analysis Code Post-Processing (MACPOST) Version 1.0” software (June 2003).

12. NASA Software Release Award for “Strain Rate Dependent Analysis of Polymer Matrix Composites (STRANAL-PMC) Version 1.0” software (June 2003).

13. AIAA Northern Ohio Section Best Paper Award for paper “Incorporation of Mean Stress Effects into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites” (June 2003).

14. NASA Aeronautics Turning Goals Into Reality Award as member of “Jet Engine Containment Concepts and Blade-Out Simulation Team” (July 2004).

15. NASA One NASA Peer Award Team Award as member of “Shuttle RCC Damage Threshold Team” (September 2005).

16. NASA Software Release Award for “Strain Rate Dependent Analysis of Polymer Matrix Composites (STRANAL-PMC) Version 2.0” software (November 2005).

17. NASA One NASA Peer Award GRC Center Best Team Award as member of “NASA Ballistic Impact Test Team” (April 2006).

18. NASA Space Flight Awareness “Silver Snoopy” Astronauts’ Personal Achievement Award (October 2006).

19. AIAA (American Institute of Aeronautics and Astronautics) Associate Fellow (September 2007).

20. NASA Certificate of Recognition for NASA Tech Brief “A Modeling Technique and Representation of Failure in the Analysis of Triaxial Braided Carbon Fiber Composites” (June 2009).

COMMUNITY SERVICE

1. Served as advisor to NASA sponsored Boy Scouts Explorers posts: 1992-1996, 1997-1998, 2000-2001, 2002-2003. Duties involved assisting in development of technical program, supervision of weekly meetings, mentoring of post officers.

2. Served as mentor to summer intern for three summers (1994, 1995, 1996) through NASA L.E.R.C.I.P. summer program for college students.

3. Spoke at area schools describing NASA, personal research work and engineering careers as part of NASA sponsored activities for Engineer’s Week: 1995, 1996, 1999, 2000, 2001, 2003, 2005, 2010.

4. Served as mentor to NASA Graduate Student Researchers program PhD student (2008-present).

PUBLICATIONS

A. Publications in Refereed Journals

Published or Accepted

1. Goldberg, R.K.; and Hopkins, D.A.: “Application of the Boundary Element Method to the Micromechanical Analysis of Composite Materials.” Computers and Structures, Vol. 56, pp. 721-731, 1995.

2. Goldberg, R.K.; and Hopkins, D.A.: “Thermal Analysis of a Functionally Graded Material Subject to a Thermal Gradient Using the Boundary Element Method.” Composites Engineering, Vol. 5, pp. 793-806, 1995.

3. Mital, S.K.; Murthy, P.L.N.; and Goldberg, R.K.: “Micromechanics for Particulate Reinforced Composites.” Mechanics of Composite Materials and Structures, Vol. 4, pp. 251-266, 1997.

4. Goldberg, R.K.; and Stouffer, D.C.: “Strain Rate Dependent Analysis of a Polymer Matrix Composite Utilizing a Micromechanics Approach.” Journal of Composite Materials, Vol. 36, pp. 773-793, 2002.

5. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Experimental Study of Strain Rate Behavior of Carbon/Epoxy Composite.” Composites Science and Technology, Vol. 62, pp. 1469-1476, 2002.

6. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Incorporation of mean stress effects into the micromechanical analysis of the high strain rate response of polymer matrix composites.” Composites Part B: Engineering, Vol. 34, pp. 151-165, 2003.

7. Goldberg, R.K.; and Gilat, A.: “Experimental and Computational Characterization of the High Strain Rate Tensile Response of Polymer Matrix Composites.” Composite Materials, Testing and Design Fourteenth Volume, ASTM STP 1436, C.E. Bakis, Editor, American Society for Testing and Materials, West Conshocken, PA, pp. 207-223, 2003.

8. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Analytical Studies of the High Strain Rate Tensile Response of a Polymer Matrix Composite” Journal of Advanced Materials, Vol. 36, pp. 14-24, 2004.

9. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites.”, Journal of Aerospace Engineering, Vol. 18, pp. 18-27, 2005.

10. Zhu, L.; Kim, H.S.; Chattopadhyay, A.; and Goldberg, R.K.: “Improved Transverse Shear Calculations for Rate-Dependent Analyses of Polymer Matrix Composites”, AIAA Journal, Vol. 43, No. 4, 2005.

11. Tabiei, A.; Yi, W.; and Goldberg, R.: “Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation”, International Journal of Non-Linear Mechanics, Vol. 40, pp. 957-970, 2005.

12. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “Nonlinear transient response of strain rate dependent composite laminated plates using multiscale simulation”, International Journal of Solids and Structures, Vol. 43, pp. 2602-2630, 2006.

13. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “Multiscale Analysis Including Strain Rate Dependency for Transient Response of Composite Laminated Shells”, Journal of Reinforced Plastics and Composites, Vol. 25, pp. 1795-1831, 2006.

14. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading”, Journal of Aerospace Engineering, Vol. 20, pp. 75-89, 2007.

15. Goldberg, R.K.; Roberts, G.D.; Littell, J.D.; and Binienda, W.K.: “Approximation of Nonlinear Unloading Effects In the Strain Rate Dependent Analysis of Polymer Matrix Composites Utilizing a State Variable Approach”, Journal of Aerospace Engineering, Vol.21, pp. 119-131, 2008.

16. Littell, J.D.; Ruggeri, C.R.; Goldberg, R.K.; Roberts, G.D.; Arnold, W.A.; and Binienda, W.K.: “Measurement of Epoxy Resin Tension, Compression and Shear Stress-Strain Curves over a Wide Range of Strain Rates Using Small Test Specimens”, Journal of Aerospace Engineering, Vol. 21, pp. 162-173, 2008.

17. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “A Failure Model for Rate Dependent Polymer Matrix Composite Laminates under High Velocity Impact”, Journal of Aerospace Engineering, Vol. 21, pp. 132-139, 2008.

18. Littell, J.D.; Binienda, W.K.; Roberts, G.D.; and Goldberg, R.K.: “Characterization of Damage in Triaxial Braid Composites Under Tensile Loading”, Journal of Aerospace Engineering, Vol. 22, pp. 270-279, 2009.

19. Goldberg, R.K.; and Binienda, W.K.: “Ballistic Impact and Crashworthiness Response of Aerospace Structures”, Journal of Aerospace Engineering, Vol. 11, pp. 199-200, 2009.

20. Littell, J.D.; Binienda, W.K.; Arnold, W.A.; Roberts, G.D.; and Goldberg, R.K.: “Effect of Microscopic Damage Events on Static and Ballistic Impact Strength of Triaxial Braid Composites”. Composites Part A: Applied Science and Manufacturing, Vol. 40, pp. 1846-1862, 2009.

21. Li, X.; Binienda, W.K.; and Goldberg, R.K.: “Finite Element Model for Failure Study of Two Dimensional Triaxially Braided Composite”. Journal of Aerospace Engineering, Accepted, In Press.

22. Goldberg, R.K.; Blinzler, B.J.; and Binienda, W.K.: “Investigation of a Macromechanical Approach to Analyzing Triaxially-Braided Polymer Composites”. AIAA Journal, Vol. 49, pp. 205-215, 2011.

B. Refereed NASA Technical Publications

1. Goldberg, R.K.: “COMGEN-BEM: Boundary element model generation for composite materials micromechanical analysis.” NASA TM-105548, 1992.

2. Goldberg, R.K.; and Hopkins, D.A.: “Composite micromechanical modeling using the boundary element method.” NASA TM-106127, 1993.

3. Goldberg, R.K.; and Hopkins, D.A.: “Micromechanical modeling of laminated composites with interfaces and woven composites using the boundary element method.” NASA TM-106280, 1993.

4. Goldberg, R.K.; and Hopkins, D.A.: “Thermal analysis of a functionally graded material subject to a thermal gradient using the boundary element method.” NASA TM-106801, 1994.

5. Mital, S.K.; Murthy, P.L.N.; and Goldberg, R.K.: “Micromechanics for Particulate Reinforced Composites.” NASA TM-107276, 1996.

6. Goldberg, R.K.; Murthy, P.L.N.; and Mital, S.K.: “ICAN/PART: Particulate Composite Analyzer, User's Manual and Verification Studies.” NASA TM-107297, 1996.

7. Goldberg, R.K.; and Stouffer, D.C.: “High Strain Rate Deformation Modeling of a Polymer Matrix Composite Part I-Matrix Constitutive Equations.” NASA TM-1998-206969, 1998.

8. Goldberg, R.K.; and Stouffer, D.C.: “High Strain Rate Deformation Modeling of a Polymer Matrix Composite Part II-Composite Micromechanical Model.” NASA TM-1998-208664, 1998.

9. Goldberg, R.K.; and Stouffer, D.C.: “Rate Dependent Deformation and Strength Analysis of Polymer Matrix Composites.” NASA TM-1999-209060, 1999.

10. Goldberg, R.K.; Comiskey, M.D.; and Bednarcyk, B.A.: “Micromechanics Analysis Code Post-Processing (MACPOST) User Guide Version 1.0.” NASA TM-1999-209062, 1999.

11. Goldberg, R.K.; and Stouffer, D.C.: “Strain Rate Dependent Modeling of Polymer Matrix Composites.” NASA TM-1999-209433, 1999.

12. Goldberg, R.K.: “Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach.” NASA TM-1999-209768, 1999.

13. Goldberg, R.K.; and Arnold, S.M.: “A Study of Influencing Factors on the Tensile Response of a Titanium Matrix Composite With Weak Interfacial Bonding.” NASA TM-2000-209758, 2000.

14. Goldberg, R.K.: “Implementation of Laminate Theory Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites.” NASA TM-2000-210351, 2000.

15. Goldberg, R.K.: “Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites.” NASA TM-2001-210822, 2001.

16. Goldberg, R.K.: “Computational Simulation of the High Strain Rate Tensile Response of Polymer Matrix Composites.” NASA TM-2002-211489, 2002.

17. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Incorporation of Mean Stress Effects Into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites.” NASA TM-2002-211702, 2002.

18. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites.” NASA TM-2003-212382, 2003.

19. Zheng, X.; Goldberg, R.K.; Binienda, W.K.; and Roberts, G.D.: “LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact.” NASA TM-2003-212583, 2003.

20. Goldberg, R.K.; and Carney, K.S.: “Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included.” NASA TM-2004-213125, 2004.

21. Zhu, L.; Kim, H.S.; Chattopadhyay, A.; and Goldberg, R.K.: “Implementation of Improved Transverse Shear Calculations and Higher Order Laminate Theory into Strain Rate Dependent Analyses of Polymer Matrix Composites.” NASA TM-2004-213420, 2004.

22. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Strain Rate Sensitivity of Epoxy Resin in Tensile and Shear Loading.” NASA TM-2005-213595, 2005.

23. Littell, J.D.; Binienda, W.K.; Goldberg, R.K.; and Roberts, G.D.: “A Modeling Technique and Representation of Failure in the Analysis of Triaxial Braided Carbon Fiber Composites”, NASA TM-2008-215245, 2008.

24. Littell, J.D.; Binienda, W.K.; Goldberg, R.K.; and Roberts, G.D.: “Full-Field Strain Methods for Investigating Failure Mechanisms in Triaxial Braided Composites.” NASA TM-2008-215197, 2008.

25. Littell, J.D.; Binienda, W.K.; Roberts, G.D.; and Goldberg, R.K.: “Characterization of Damage in Triaxial Braid Composites Under Tensile Loading”, NASA TM-2009-215645, 2009.

26. Roberts, G.D.; Goldberg, R.K.; Binienda, W.K.; Arnold, W.A.; Littell, J.D.; and Kohlman, L.W.: “Characterization of Triaxial Braided Composite Material Properties for Impact Simulation”, NASA TM-2009-215660, 2009.

27. Arnold, S.M.; Goldberg, R.K.; Lerch, B.A.; and Saleeb, A.F.: “An Overview of Prognosis Health Management at Glenn Research Center for Gas Turbine Engine Structures With Special Emphasis on Deformation and Damage Modeling”, NASA TM-2009-215827, 2009.

28. Littell, J.D.; Binienda, W.K.; Arnold, W.A.; Roberts, G.D.; and Goldberg, R.K.: “Effect of Microscopic Damage Events on Static and Ballistic Impact Strength of Triaxial Braid Composites”. NASA TM-2010-216095, 2010.

29. Goldberg, R.K.; Blinzler, B.J.; and Binienda, W.K.: “Investigation of a Macromechanical Approach to Analyzing Triaxially-Braided Polymer Composites”. NASA TM-2010-216371, 2010.

30. Li, X.; Binienda, W.K.; and Goldberg, R.K.: “Finite Element Model for Failure Study of Two-Dimensionally Triaxially Braided Composite”. NASA TM-2010-216372, 2010.

31. Goldberg, R.K.; Blinzler, B.J.; and Binienda, W.K.: Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially-Braided Composites, NASA TM-2010-216922, 2010.

C. Unrefereed Conference Proceedings and Presentations

1. Goldberg, R.K.; and Hopkins, D.A.: “Composite Micromechanical Modeling Using the Boundary Element Method.” Proceedings of the American Society for Composites Seventh Technical Conference, University Park, PA, Oct. 13-15, 1992, H.T. Hahn, editor, Technomic Publishing Company, pp. 349-358, 1992.

2. Goldberg, R.K.; and Hopkins, D.A.: “Micro Mechanical Modeling of Laminated and Woven Composites Using the Boundary Element Method.” Proceedings of the 5th Annual HITEMP Review, Westlake, OH, Oct. 27-28, 1992, NASA CP-10104, 1992.

3. Lerch, B.A.; Melis, M.E.; Goldberg, R.K.; and Tong, M.: “Experimental and Numerical Studies of Inelastic Deformation in SiC/Ti Laminates.” Proceedings of Meet’n’93-First Joint ASCE/ASME/SES Meeting, Charlottesville, VA, June 6-9, 1993, C.T. Herakovich and J.M. Duva, editors, 1993.

4. Goldberg, R.K.; and Hopkins, D.A.: “Micromechanical Modeling of Laminated Composites with Interfaces and Woven Composites Using the Boundary Element Method.” Proceedings of the American Society for Composites Eighth Technical Conference, Cleveland, OH, Oct. 19-21, 1993, G.M. Newaz, editor, Technomic Publishing Company, pp. 1035-1044, 1993.

5. Goldberg, R.K.; and Hopkins, D.A.: “Utilization of Boundary Element Method in Modeling Interface Effects in SiC/RBSN Composites.” Proceedings of the 6th Annual HITEMP Review, Westlake, OH, Oct. 25-27, 1993, NASA CP-19117, 1993.

6. Goldberg, R.K.; and Hopkins, D.A.: “Micromechanical Analysis of Functionally Graded Materials Using the Boundary Element Method.” Proceedings of ICCE/1, First International Conference on Composites Engineering, New Orleans, LA, Aug. 28-31, 1994, D. Hui, editor, pp. 167-168, 1994.

7. Goldberg, R.K.; and Hopkins, D.A.: “Utilization of the Boundary Element Method in Modeling the Thermoelastic Behavior of SiC/RBSN and Functionally Graded SiC/Ti-15-3 Composites.” Proceedings of the 7th Annual HITEMP Review, Westlake, OH, Oct. 24-26, 1994, NASA CP-10146, 1994.

8. Goldberg, R.K.; and Comiskey, M.D.: “COMGEN-BEM: Boundary Element Model Generation for Composite Materials Micromechanical Analysis.” MSC 1995 World Users’ Conference Proceedings, Universal City, CA, May 8-12, 1995, The MacNeal-Schwendler Corporation, 1995.

9. Goldberg, R.K.; and Hopkins, D.A.: “Further Applications of the Boundary Element Method in the Micromechanical Modeling of Woven Composites.” Proceedings of the Annual HITEMP Review, Westlake, OH, Oct. 23-23, 1995, NASA CP-10178, 1995.

10. Wilt, T.E.; Arnold, S.M.; and Goldberg, R.: “Micromechanics Analysis Code, MAC: Features and Applications.” Proceedings of the Annual HITEMP Review, Westlake, OH, Apr. 29-30, 1997, NASA CP-10192, 1997.

11. Goldberg, R.K.; and Stouffer, D.C.: “High Strain Rate Characterization of a Polymer Matrix Composite Utilizing a Micromechanics Approach.” Modeling and Simulation Based Engineering, Proceedings of the International Conference on Computational Engineering, Atlanta, GA, Oct. 6-9, 1998, S.N. Atluri and P.E. O’Donoghue, editors, pp. 1090-1095, 1998.

12. Goldberg, R.K.; and Stouffer, D.C.: “Strain Rate Dependent Deformation and Strength Analysis of Polymer Matrix Composites.” Proceedings of the American Society for Composites Fourteenth Technical Conference, Dayton, OH, Sept. 27-29, 1999, J.M. Whitney, editor, Technomic Publishing Company, pp. 551-560, 1999.

13. Goldberg, R.K.; and Murthy, P.L.N.: “Strain Rate Dependent Analysis of Polymer Matrix Composite Laminates Utilizing a Micromechanics Approach.” Proceedings of the American Society for Composites Fifteenth Technical Conference, College Station, TX, Sept. 25-27, 2000, O.O. Ochoa, T.K. O’Brien, D. Lagoudas, H.J. Sue, editors, Technomic Publishing Company, pp. 631-638, 2001.

14. Goldberg, R.K.; Roberts, G.D.; Gilat, A.; and Stouffer, D.C.: “Experimental and Analytical Studies of the High Strain Rate Tensile Response of a Polymer Matrix Composite Utilizing a Micromechanics Approach.” ASME International Mechanical Engineering Congress and Exposition, Orlando, FL, Nov. 11-16, 2000.

15. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Experimental Study of Strain Rate Sensitivity of Carbon Fiber/Epoxy Composite.” ICCM 13 Conference, Beijing, China, June, 2001.

16. Goldberg, R.K.: “Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites.” Proceedings of the American Society for Composites Sixteenth Technical Conference, Blacksburg, VA, Sept. 10-12, 2001, M.W. Hyer and A.C. Loos, editors, CRC Press, 2001.

17. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Constitutive Modeling of the Strain Rate Tensile Response of Polymer Matrix Composites.” TMS Fall Meeting 2001, Indianapolis, IN, Nov. 4-8, 2001.

18. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Incorporation of Mean Stress Effects into the Micromechanical Analysis of the High Strain Rate Response of Polymer Matrix Composites.” Proceedings of ICCE/9, Ninth International Conference on Composites Engineering, San Diego, CA, July 1-6, 2002, D. Hui, editor, pp. 245-246, 2002.

19. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Analytical Modeling of the High Strain Rate Deformation of Polymer Matrix Composites.” Paper AIAA-2003-1754, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, VA, April 7-10, 2003.

20. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Strain Rate Sensitivity of Epoxy in Tensile and Shear Loading.” 2003 ASME Mechanics and Materials Conference, Scottsdale, AZ, June 17-20, 2003.

21. Zheng, X.; Goldberg, R.K.; Binienda, W.K.; and Roberts, G.D.: “LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact.” 35th SAMPE International Conference, Dayton, OH, Sept. 28-Oct. 3, 2003.

22. Zheng, X.; Goldberg, R.K.; Binienda, W.K.; and Roberts, G.D.: “Development and Implementation of Rate Dependent Composite Material Model for Shell Element Application in LS-DYNA.” Earth & Space 2004, 9th ASCE Aerospace Division International Conference on Engineering, Construction and Operations in Challenging Environments, Houston, Texas, March 7-10, 2004.

23. Zhu, L.; Kim, H.S.; Chattopadhyay, A.; and Goldberg, R.K.: “Implementation of Higher Order Laminate Theory into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites.” Paper AIAA 2004-1638, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Palm Springs, CA, April 19-22, 2004.

24. Goldberg, R.K.; and Carney, K.S.: “Modeling the Nonlinear, Strain Rate Dependent Deformation of Shuttle Leading Edge Materials with Hydrostatic Stress Effects Included.” Proceedings of 8th International LS-DYNA Users Conference, Dearborn, MI, May 2-4, 2004.

25. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “The Effects of Strain Rate and Temperature on the Response of Epoxy in Shear Loading.” International Symposium on Plasticity 2005, Kauai, HI, Jan. 3-8, 2005.

26. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “Transient Response of Strain Rate Dependent Polymer Matrix Composite Laminates.” Paper AIAA 2005-1828, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, TX, April 18-21, 2005.

27. Zheng, X.; Binienda, W.K.; Goldberg, R.K.; and Roberts, G.D.: “Rate Dependent Shell Element Composite Material Model Implementation in LS-DYNA.” Paper AIAA 2005-2242, 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, TX, April 18-21, 2005.

28. Gilat, A.; Goldberg, R.K.; and Roberts, G.D.: “Testing Epoxy Resin with the Tensile and Torsional Split Hopkison Bar Techniques.” 2nd JSME/ASME International Conference on Materials and Processing 2005, Seattle, WA, June 19-22, 2005.

29. Ramachandran, S.; Chattopadhyay, A.; Goldberg, R.K.; Seaver, M; and Zhu, L.: “Development of Localized Constitutive Relations for Fiber Optic Sensors Using a Unit Cell Based Slicing Approach.” SPIE Smart Structures and Materials and NDE for Health Monitoring and Diagnostics Conference, San Diego, CA, Feb. 26-Mar. 2, 2006.

30. Goldberg, R.K.; Roberts, G.D.; and Gilat, A.: “Incorporation of the Effects of Temperature and Unloading Into the Strain Rate Dependent Analysis of Polymer Matrix Materials Utilizing a State Variable Approach.” Earth and Space 2006, 10th ASCE Aerospace Division Conference on Engineering, Construction and Operations in Challenging Environments, Houston, TX, Mar. 5-8, 2006.

31. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “Multiscale Numerical Simulation of High-Velocity Impact on Polymer Matrix Composite Laminates.” Earth and Space 2006, 10th ASCE Aerospace Division Conference on Engineering, Construction and Operations in Challenging Environments, Houston, TX, Mar. 5-8, 2006.

32. Zhu, L.; Chattopadhyay, A.; and Goldberg, R.K.: “A 3D Micromechanics Model for Strain Rate Dependent Inelastic Polymer Matrix Composites.” Paper AIAA-2006-1689, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Newport, RI, May 1-4, 2006.

33. Zhu, L; Chattopadhyay, A.; and Goldberg, R.K.: “A failure model for rate dependent polymer matrix composite laminates under high velocity impact.” ACUN-5: International Composites Conference, Developments in Composites: Advanced, Infrastructural, Natural and Nano-composites, Sydney, Australia, July 11-14, 2006.

34. Littell, J.D.; Ruggeri, C.R.; Goldberg, R.K.; Roberts, G.D.; Arnold, W.A.; and Binienda, W.K.: “An Optical Measurement Technique for Measuring Mechanical Properties of Polymer Resins.” 2007 Society of Experimental Mechanics Annual Conference and Exposition, Springfield, MA, June 3-6 2007.

35. Carney, K.S.; Goldberg, R.K.; Lee, R.S.; and Santhanam, S.: “A Heterogeneous Constitutive Model for Reinforced Carbon Carbon.” SAMPE Fall Technical Conference 2007, Cincinnati, OH, October 29-November 1, 2007.

36. Littell, J.D.; Braley, M.; Goldberg, R.K.; Roberts, G.D.; and Binienda, W.K.: “Characterization of Triaxial Braided Composites using Optical Measurement Techniques.” Earth and Space 2008, 11th ASCE Aerospace Division Conference on Engineering, Construction and Operations in Challenging Environments, Long Beach, CA, Mar. 3-5, 2008.

37. Littell, J.D.; Binienda, W.K.; Goldberg, R.K.; and Roberts, G.D.: “A modeling technique and representation of failure in the analysis of triaxial braided carbon fiber composites.” Aging Aircraft 2008, 11th Joint NASA/FAA/DoD Conference on Aging Aircraft, Phoenix, AZ, April 21-24, 2008.

38. Carney, K.S.; Goldberg, R.K.; Pereira, J.M.; Lee, R.S.; and Albert, J.J.: “A Heterogeneous Constitutive Model for Carbon-Carbon Using LS-DYNA.” Proceedings of 10th International LS-DYNA Users Conference, Dearborn, MI, June 8-10, 2008.

39. Littell, J.D.; Binienda, W.K.; Arnold, W.A.; Roberts, G.D.; and Goldberg, R.K.: “Effect of microscopic damage events on static and ballistic impact strength of triaxial braid composites”, CompTest 2008 4th International Conference on Composites Testing and Model Identification, Dayton, OH, October 20-22, 2008.

40. Roberts, G.D.; Goldberg, R.K.; Littell, J.D.; Kohlman, L.W.; and Binienda, W.K.: “Characterization of Triaxial Braided Composite Material Properties for Impact Simulation”, American Helicopter Society 65th Annual Forum, Grapevine, Texas, May 27-29, 2009.

41. Poulain, X.; Goldberg, R.K.; Talreja, R.; and Benzerga, A.A.: “A multiscale modeling methodology for damage progression in polymer-based composites”, 12th International Conference on Fracture, Ottawa, Canada, July 12-17, 2009.

42. Arnold, S.M.; Goldberg, R.K.; Lerch, B.A.; and Saleeb, A.F.: “An Overview of Prognosis Health Management at Glenn Research Center for Gas Turbine Engine Structures With Special Emphasis on Deformation and Damage Modeling”, Annual Conference of the Prognostics and Health Management Society 2009, San Diego, California, Sept. 27-Oct. 1, 2009.

43. Goldberg, R.K.; Roberts, G.D.; Blinzler, B.J.; Binienda, W.K.; and Littell, J.D.: “Development of a Macroscopic, Non-homogeneous, Finite Element Based Approach to Analyze the Impact Response of Triaxially Braided Polymer Composites”, American Helicopter Society National Technical Specialists’ Meeting on Rotorcraft Structures and Survivability, Williamsburg, Virginia, Oct. 27-29, 2009.

44. Goldberg, R.K.; Bednarcyk, B.A.; Blinzler, B.J.; Li, X.; Binienda, W.K.; Liu, K.C.; and Chattopadhyay, A.: “Multiscale Modeling of Triaxial Braided Composites”, NASA Aviation Safety Conference, Mclean, Virginia, Nov. 17-19, 2009.

45. Goldberg, R.K.; Blinzler, B.J.; Binienda, W.K.: “Investigation of a Macromechanical Approach to Analyzing Triaxially Braided Polymer Composites”, AIAA/ASME/ASCE/AHS/ASC 51st Structures, Structural Dynamics and Materials (SDM) Conference, Orlando, Florida, April 12-15, 2010.

46. Goldberg, R.K.; Blinzler, B.J.; Binienda, W.K.: “Characterization of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially Braided Composites”, 2010 Aircraft Airworthiness and Sustainment Conference, Austin, Texas, May 10-12, 2010.

47. Poulain, X.; De Castro, A; Roberts, G.; Goldberg, R.; and Benzerga, A.: “Towards Physics-based Multiscale Modeling of The Ballistic Impact of Carbon/Epoxy Composites”, 2010 Aircraft Airworthiness and Sustainment Conference, Austin, Texas, May 10-12, 2010.

48. Blinzler, B.J.; Goldberg, R.K.; and Binienda, W.K.: “Investigation of *MAT_58 for Modeling Braided Composites”, 11th International LS-DYNA User’s Conference, Dearborn, MI, June 7-8, 2010.

49. Janapala, N.R.; Chang, F.-K.; Goldberg, R.K.; Roberts, G.D.; and Jackson, K.E.: “Crashworthiness of Composite Structures with Various Fiber Architectures”, 11th International LS-DYNA User’s Conference, Dearborn, MI, June 7-8, 2010.

50. Goldberg, R.K.; Blinzler, B.J.; and Binienda, W.K.: “Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially Braided Composites”, Proceedings of the American Society for Composites Twenty-Fifth Technical Conference, Dayton, OH, Sept. 20-22, 2010, J.B. Lantz, N. Takeda, B.M. Doudican, G.A. Shoeppner, and S.L. Donaldson, editors, DEStech Publications, Inc., 2010.

51. Goldberg, R.K.; Mital, S.K.; Bonacuse, P.J.; and Lang, J: “Effects of Material Microstructure on Elastic Response of Woven Ceramic Matrix Composites”, USACA 35th Annual Conference on Composites, Materials and Structures, Cocoa Beach, FL, January 24-27, 2011.