A. Books

1.  J. Fish and T. Belytschko, “A First Course in Finite Elements,” John Wiley, 2007.

2. J. Fish (ed), "Bridging the Scales in Science and Engineering," Oxford University Press, 2009

3. J. Fish, “Practical Multiscaling,” John Wiley, 2013

4. J. Fish, T. Zohdi and J.S. Chen, “Nonlinear Finite Element Method,” Springer, to appear in 2014.

     B. Book Chapters

5. T. Belytschko and J. Fish, “Numerical studies of two-dimensional shear banding with the spectral overlay on finite elements,” eds. M. Kleiber and J. A.Konig, Antony Sawczuk Memorial Volume, (1990).

6. J. Fish, S.Markolefas, R.Guttal and P.Nayak, “On adaptive multilevel superposition of finite element meshes," Adaptive Methods for Partial Differential Equations, eds. J.E.Flaherty and M.S.Shephard, SIAM, (1994).

7. J.Fish and V.Belsky "Adaptive multi-grid method for a periodic heterogeneous medium in 1-D," IMA Volumes in Mathematics and its Applications: "Modeling, Mesh Generation, and Adaptive Numerical Methods for PDEs,” eds. J.Flaherty, I.Babuska, W.D.Henshay, J.E. Uglier, P.A. Tezduyar, Springer Verlag, NY, Vol. 75, pp. 243-267, (1995).

8. J. Fish and V.Belsky “Adaptive multi-grid method for a periodic heterogeneous medium” The IMA Volumes in Mathematics and its Applications, Volume 75 Springer - Verlag, NY, pp. 243-266, 1995.

9. “Computational Advances in Modeling Composites and Heterogeneous Materials,” edited by J. Fish. Special Issue of Comp. Meth. Appl. Mech. Engng, ELSEVIER, Vol. 127, 1999.

10. J. Fish and Q. Yu, “Computational Multiscale Fatigue Analysis and Life Prediction for Composite Structures,” in Modeling and Simulation Based Life Cycle Engineering, ed. K. Chong and S. Saigal. Taylor & Francis/Spon Press, 11 New Fetter Lane, London, EC4P 4EE, 2001.

11. J. Fish, “Discrete to Continuum Multiscale Bridging,” in Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size from Macro to Nano, Ed. G.C. Sih,  Springer 2006.

12. M.S. Shephard, M.A. Nuggehally, B. Franz Dale, C.R. Picu and J. Fish, "Component Software for Multiscale Simulation" in Bridging the Scales in Science and Engineering, J. Fish (ed), Oxford University Press, 2009

13. J. Fish, "Multiscale Modeling and Simulation of Composite Materials and Structures," Multiscale Methods in Computational Mechanics, E. Ramm (ed.) Springer series, Lecture Notes in Applied and Computational Mechanics, Vol. pp. 215-231, 2011.

14.  J. Fish and Z. Yuan, "N-scale Model Reduction Theory," in Bridging the Scales in Science and Engineering, J. Fish (ed), Oxford University Press, 2009

15. J. Fish, V. Filonova and Z. Yuan, Chapter 7: Multiscale Design: From Theory to Practice, in Innovations in Biomolecular Modeling and Simulation, series entitled Biomolecular Sciences published by The UK Royal Society of Chemistry, 2011

16. J. Fish, Towards General Purpose Design System for Composites, in Multiscale Simulations and Mechanics of Biological Materials, eds. S. Li and D. Qiang, John Wiley, 2013

     C. Refereed journal articles

17. T. Belytschko, J. Fish and B.E. Engelman, “A finite element with embedded localization zones,” Comp. Meth. Appl. Mech. Engng., Vol. 70, (1988), pp. 59 - 89.

18. T. Belytschko and J. Fish, “Embedded hinge lines for plate elements,” Comp. Meth. Appl. Mech. Engng., Vol. 76, No. 1, (1989), pp. 67-86.

19. T. Belytschko, J. Fish and A. Bayliss, “The spectral overlay on the finite element solutions with high gradients,” Comp. Meth. Appl. Mech. Engng., Vol 81, (1990), pp.71-89.

20. J. Fish and T. Belytschko, "Elements with embedded localization zones for large deformation problems," Computers and Structures, Vol. 30, No. 1/2, (1988), pp. 247-256.

21. J. Fish and T. Belytschko, “A finite element with a unidirectionally enriched strain field for localization analysis,” Comp. Meth. Appl. Mech. Engng., Vol. 78, No. 2, (1990), pp. 181-200.

22. J. Fish and T. Belytschko, “A general finite element procedure for problems with high gradients,” Computers and Structures, Vol. 35, No. 4, pp.309-319, (1990).

23. J. Fish and T. Belytschko, “Stabilized rapidly convergent shell element with drilling degrees-of-freedom,” International Journal for Numerical Methods in Engineering, Vol. 33, pp. 149-162 (1992).

24. J. Fish, “The s-version of the finite element method,” Computers and Structures, Vol. 43, No. 3, pp. 539-547, (1992).

25. J. Fish and S. Markolefas, “The s-version of the finite element method for multilayer laminates,” International Journal for Numerical Methods in Engineering, Vol. 33, no. 5, pp. 1081-1105 (1992).

26. J. Fish, “Hierarchical modeling of discontinuous fields,” Communications in Applied Numerical Methods, Vol. 8, pp. 443-453, (1992).

27. M. S. Shephard, J. Fish and M .W. Beall, “Idealization control for the analysis of composite materials,” Computing Systems in Engineering, Vol.3, pp. 443-456, (1992).

28. J. Fish and S. Markolefas, “Adaptive s-method for linear elastostatics,” Comp. Meth. Appl. Mech. Engng., Vol. 103, pp. 363-396, (1993).

29. J. Fish, N. Fares and A. Nath, “Micromechanical elastic cracktip stresses in a fibrous composite,” International Journal of Fracture, Vol. 60, pp. 135-146, (1993).

30. J. Fish and A. Wagiman, “Multiscale finite element method for heterogeneous medium,”, Computational Mechanics: The International Journal, Vol. 12, pp. 1-17 (1993).

31.  J. Fish and A. Nath, “Adaptive and hierarchical modeling of fatigue crack propagation,” International Journal for Numerical Methods in Engineering, Vol. 36, pp. 2825- 2836 (1993).

32. J.Fish and S. Markolefas, R. Guttal and P. Nayak, “On adaptive multilevel superposition of finite element meshes,” Applied Numerical Mathematics, Vol. 14, pp. 135-164, (1994).

33. J. Fish and S. Markolefas, “Adaptive global-local refinement strategy based on the interior error estimates of the h-method,” International Journal for Numerical Methods in Engineering, Vol. 37, pp. 827-838, (1994).

34.  J. Fish, P. Nayak, and M. H. Holmes, “Microscale Reduction Error Indicators and Estimators for a Periodic Heterogeneous Medium,” Computational Mechanics: The International Journal, Vol. 14, pp. 1-16, (1994).

35. J. Fish and V. Belsky, “Multigrid method for a periodic heterogeneous medium. Part I: Convergence studies for one-dimensional case,” Comp. Meth. Appl. Mech. Engng., Vol. 126, pp. 1-16, (1995).

36. J. Fish and V. Belsky, “Multigrid method for a periodic heterogeneous medium. Part 2: Multiscale modeling and quality control in mutidimensional case,” Comp. Meth. Appl. Mech. Engng., Vol. 126, 17-38, (1995).

37. J. Fish, M. Pandheeradi and V. Belsky, “An efficient multilevel solution scheme for large scale nonlinear systems,” International Journal for Numerical Methods in Engineering, Vol. 38, pp. 1597-1610, (1995).

38. J. Fish and R. Guttal, “The p-version of the finite element method for shell analysis,” Computational Mechanics: The International Journal, Vol. 16, pp. 1-13, (1995).

39. J. Fish V. Belsky and M. Pandheeradi, “Iterative and Direct Solvers for Interface Problems with Lagrange Multipliers,” International Journal of Computing Systems in Engineering, Vol. 6, No. 3, pp. 261-273, (1995).

40. V. Belsky, M.W. Beall, J. Fish, M.S. Shephard, S. Gomaa, “Computer-Aided Multiscale Modeling Tools for Composite Materials and Structures,” International Journal of Computing Systems in Engineering, Vol. 6, No. 3, pp. 213-223, (1995).

41. J. Fish and R. Guttal, “Recent advances in the p-version of the finite element method for shell analysis,” International Journal of Computing Systems in Engineering, Vol. 6, No. 3, pp. 195-211, (1995).

42. M. S. Shephard, T. L. Sham, L. Y. Song, R. Garimella, H. F. Tersten, B. J. Lwo, Y. L. Le Coz, R.B. Aversion, and J. Fish, "Global/Local heat conduction and Thermomechanical Analyses of Multitude Modules," Japanese Journal of Applied Mechanics, (1996).

43. J.Fish, P. Lei, V. Belsky, S. Gomaa, “Unstructured Multigrid Method for Shells,” International Journal for Numerical Methods in Engineering, Vol. 39, pp. 1181-1197, (1996).

44. J. Fish, V. Belsky and M. Pandheeradi, “Composite grid method for hybrid systems,” Comp. Meth. Appl. Mech. Engng., Vol. 135, pp. 307-325, (1996).

45. J. Fish, M. Panheeradi and V. Belsky, “Efficient Solution Schemes for Interface Problems,” Finite Elements in Analysis and Design, Vol. 22, pp. 267-280, (1996).

46. J. Fish and R. Guttal, “The s-version of Finite Element Method for Laminated Composites,” International Journal for Numerical Methods in Engineering, Vol. 39, pp. 3641-3662, (1996).

47. J. Fish and R. Guttal, “On the assumed strain formulation with selective polynomial order enrichment for p-version shells,” Computers and Structures, Vol. 63, No.5. pp.899-913, (1997).

48. J. Fish, A. Suvorov and V. Belsky, “Hierarchical Composite Grid Method for Global-Local Analysis of Laminated Composite Shells,” Applied Numerical Mathematics, Vol. 23, pp.241-258, (1997).

49. J. Fish and V. Belsky, “Generalized Aggregation Multilevel Solver,” International Journal for Numerical Methods in Engineering, Vol. 40, pp.4341-4361, (1997).

50. J. Fish and R. Guttal, “Adaptive Solver for the p-version of Finite Element Method,” International Journal for Numerical Methods in Engineering, Vol. 40, pp. 1767-1784, (1997).

51. J. Fish, K. Shek, M. Pandheeradi, and M.S. Shephard, “Computational Plasticity for Composite Structures Based on Mathematical Homogenization: Theory and Practice,” Comp. Meth. Appl. Mech. Engng., Vol. 148, pp. 53-73, (1997)

52. J. Fish, Y. Qu and A. Suvorov, “Automated Adaptive Multilevel Solver,” Comp. Meth. Appl. Mech. Engng., Vol. 149, pp. 267-287, (1997).

53. J. Fish, “Holistic approach for problems in heterogeneous media,” USACM Bulletin, Vol. 10, No. 1, pp. 4-13, (1997).

54. J. Fish and K.L. Shek, “Computational Aspects of Incrementally Objective Algorithms for Large Deformation Plasticity,” International Journal for Numerical Methods in Engineering, Vol. 44, pp. 839-851, (1999).

55. J. Fish and K. L. Shek, “Computational Plasticity and Viscoplasticity for Composite Materials and Structures," Journal of Composites Part B, (29B), pp. 613-619, (1998).

56. J.Fish, J. LeMonds, and K. Shek, "Modeling and Simulation of Wrinkling in Compression Molding process of Fiber Reinforced Composites,” Journal of Engineering Mechanics, Vol. 125, No. 8, pp. 951-955, (1999).

57. R. Collar, R. Wentorf, M.S. Shephard, J.Fish, Y.Qu, K. L. Shek, “Automated Analyses of Three-Dimensional Composite Unit Cells”, International Journal for Numerical Methods in Engineering, (1999), in print.

58. J. Fish and K. L. Shek, “Finite Deformation Plasticity of Composite Structures: Computational Models and Adaptive Strategies,” Comp. Meth. Appl. Mech. Engng., Vol. 172, pp. 145-174, (1999).

59. R. Wentorf, R. Collar, M.S. Shephard, J. Fish, “Automated Modeling for Complex Woven Mesostructures,” Comp. Meth. Appl. Mech. Engng., Vol. 172, pp. 273-291, (1999).

60. J. Fish, Y. Qu and A. Suvorov, “Towards robust two-level methods for indefinite systems,” International Journal for Numerical Methods in Engineering, Vol. 45, pp. 1433-1456, (1999).

61. J. Fish, Q. Yu and K. L. Shek, “Computational Damage Mechanics for Composite Materials Based on Mathematical Homogenization,” International Journal for Numerical Methods in Engineering, Vol. 45, pp. 1657-1679, (1999).

62. J. Fish and W. Chen, “On Accuracy, Stability and Efficiency of Implicit Methods with Incomplete Solution by Multilevel Methods,” International Journal for Numerical Methods in Engineering, Vol. 46, pp. 253-273, (1999).

63. R. Guttal and J. Fish, “Hierarchical Assumed Strain-Vorticity Shell Element With Drilling Degrees-of-Freedom,” Finite Elements in Analysis and Design, Vol. 33, pp. 61-70, (1999).

64. V. Korneev, J.E Flaherty, T. Oden, J. Fish,  Hp-Version Additive Schwarz Algorithms on Triangular Meshes, I.  Mathematical Modelling. No. 11, pp. 38-50, (2000).

65. V. Korneev, J.E Flaherty, T. Oden, J. Fish. Hp-Version Additive Schwarz Algorithms on Triangular Meshes, II.  Mathematical Modelling No.12,  pp. 28-37, (2000).

66. J. Fish and V. Korneev, “On Two-Level Methods Based on Aggregation for 3D Problems,” Matematika, (in Russian) Vol. 11, pp. 42-60, (2000).

67. J. Fish and K. L. Shek, “Finite Deformation Plasticity Based on the Additive Split of the Rate of Deformation and Hyperelasticity,” Comp. Meth. Appl. Mech. Engng., Vol. 190, pp. 75-93, (2000).

68. J. Fish and K.L. Shek, “Multiscale Analysis Of Large Scale Nonlinear Structures and Materials,” International Journal for Computational Civil and Structural Engineering, Vol. 1. No. 1, pp. 79-90, (2000).  

69. J. Fish and K.L. Shek, “Multiscale Analysis for Composite Materials and Structures,” Composites Science and Technology: An International Journal, Vol. 60, pp.2547-2556, (2000).

70. T. E. Giddings and J. Fish,  “An Algebraic two-level preconditioner for asymmetric, positive-definite systems,” International Journal for Numerical Methods in Engi­neering”, Vol. 52, pp. 1443-1463,  (2001).

71. J. Fish and Y. Qu, "Global Basis Two-Level Method for Indefinite Systems. Part 1: Conver­gence Studies," International Journal for Numerical Methods in Engineering, Vol. 49, pp. 439-460, (2000).

72. Y. Qu and J. Fish, ""Global Basis Two-Level Method for Indefinite Systems. Part 2: Com­putational Issues," International Journal for Numerical Methods in Engineering, Vol. 49, pp. 461-478, (2000).

73. J. Fish and W. Chen, "Higher-Order Homogenization of Initial/Boundary-Value Problem" Vol. 127, No. 12, pp. 1223-1230,  Journal of Engineering Mechanics, (2001).

74.  T. E. Giddings, J. Fish, and Z.Rusak, "A stabilized Finite Element Formulation for the Tran­sonic Small-Disturbance System," International Journal for Numerical Methods in Engi­neering, Vol. 50, pp. 2069-2091, (2001).

75. W.Chen and J.Fish, "A Dispersive Model For Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales," Journal of Applied Mechanics, Vol. 68, No. 2, pp. 153-161, (2001).

76.  J. Fish and A. Ghouli, "Multiscale Analytical Sensitivity Analysis for Composite Materials," International Journal for Numerical Methods in Engineering, Vol. 50, pp. 1501-1520, (2001).

77. V. Korneev and J.Fish, “Two-level methods for spatial problems based on aggregation,” Izv. VUZ. Matematika, Vol. 11, pp. 42-61, Allerton Press Inc., 18 West 27 st. NY, (2001).

78. T. E. Giddings, Z. Rusak  and J. Fish,"A Transonic small-disturbance model for the propa­gation of weak shock waves in heterogeneous gases,” International Journal of Fluids, Vol. 429, pp. 255-281, (2001).

79. J. Fish and Q.Yu, "Multiscale Damage Modeling for Composite Materials: Theory and Com­putational Framework," International Journal for Numerical Methods in Engi­neering,  Vol. 52, No 1-2, pp. 161-192 (2001).

80. J. Fish and Q.Yu, "Two-scale damage modeling of brittle composites" Compos­ites Science and Technology: An International Journal, Vol. 61, pp.2215-2222, (2001).

81. J. Fish and W. Chen, “Uniformly Valid Multiple Spatial-Temporal Scale Modeling for Wave Propagation in Heterogeneous Media,” Mechanics of Composite Materials and Structures, Vol. 8, pp. 81-99, (2001).

82. Y. Qu and J. Fish, "Multifrontal Incomplete Factorization for Indefinite and Complex Sym­metric Systems," International Journal for Numerical Methods in Engineering, Vol. 53, Issue 6,  pp. 1433-1459, (2002).  

83. V. Korneev, J. E. Flaherty,  T. Oden and J. Fish, "Additive Schwarz Algorithms for solving hp- Version Finite Element Systems on Triangular Meshes," Applied Numerical Mathematics, Vol. 43, pp. 399-421,  (2002).

84. J. Fish  and Q. Yu, “Asymptotic Homogenization of Coupled Thermo-Viscoelastic Composites with Multiple Spatial and Temporal Scales,” in print, Composites Science and Technology: An International Journal, (2002).

85.  J. Fish and Q.Yu, "Computational Mechanics of Fatigue and Life Predictions for Composite Materials and Structures," Comp. Meth. Appl. Mech. Engng., Vol. 191, pp. 4827-4849,  (2002).

86. Q.Yu and J. Fish, “Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: A coupled thermo-viscoelastic example problem,” International Journal of Solids and Structures, Vol. 39/26, pp. 6429-6452 , (2003).

87. J. Fish, W.Chen and G. Nagai, “Nonlocal dispersive model for wave propagation in heterogeneous media. Part 1: One-Dimensional Case,” International Journal for Numerical Methods in Engineering, Vol. 54, pp. 331-346, (2002).

88. J. Fish, W.Chen and G. Nagai, “Nonlocal dispersive model for wave propagation in heterogeneous media. Part 2: Multi-Dimensional Case,” International Journal for Numerical Methods in Engineering, Vol. 54, pp. 347-363, (2002).

89. V. Korneev, J.E. Flaherty, J.T. Oden and J. Fish, “Hp-Version Additive Schwarz Algorithms on Triangular Meshes,” Matematicheskoe Moshelirovanie, volume 14, no. 2, pp. 61-94, 2002.

90. Q. Yu and J. Fish, “Temporal Homogenization of Viscoelastic and Viscoplastic Solids Subjected to Locally Periodic Loading”,  Computational Mechanics, Vol. 29, pp. 199-211, (2002).

91. M.W.Beall, V.Belsky, J.Fish, M.Shephard,’Automated multiple scale fracture analysis,’ Journal of Multiscale Computational Engineering, Vol. 1, No. 1, pp. 29-48, (2002).

92. J. Fish and W. Chen, "RVE Based Multilevel Method For Periodic Heterogeneous Media With Strong Scale Mixing," Journal of Applied Mathematics, Vol. 46, pp. 87-106, (2003).

93.  J. Fish and C. Schwob, "Towards Constitutive Model Based on Atomistics,"  Journal of Multiscale Computational Engineering, Vol. 1 pp. 43-56, (2003).

94.  M. Zeghal, E.L. Shamy, M.S. Shephard, R.Dobry, J. Fish, T. Abdoun, "Micro-Mechanical Analysis of Saturated Granular Soils," Journal of Multiscale Computational Engineering, Vol. 3, (2003).

95. J. Fish and W. Chen, "Modeling and Simulation of Piezocomposites,"  Comp. Meth. Appl. Mech. Engng., Vol. 192, pp. 3211-3232, (2003).

96. J. Fish and W. Chen, “Discrete-to-Continuum Bridging Based on Multigrid Principles,” Comp. Meth. Appl. Mech. Engng., Vol. 193, pp. 1693-1711, (2004).

97. Z. Xu, R.C. Picu and J. Fish, "Higher Order Continuum Wave Equation Calibrated on Lattice Dynamics," International Journal of Computational Engineering Science, Vol. 5, No. 3, pp.557-574, (2004).

98. C. Oskay and J. Fish, "Fatigue Life Prediction using 2-Scale Temporal Asymptotic Homogenization,"  International Journal for Numerical Methods in Engineering, Volume 61, Issue 3, pp. 329-359 (2004).

99. H. Waisman, J. Fish, .R S. Tuminaro and J. Shadid, "The Generalized Global-Basis (GGB) Method" International Journal for Numerical Methods in Engineering, Vol. 61, No. 8, pp. 1243-1269, (2004)

100. G. Nagai, J. Fish and K.Watanabe, "Stabilized Nonlocal Model for Wave Propagation in Heterogeneous Media,"  Computational Mechanics, Vol. 33. No. 2, (2004).

101. J. Fish and W. Chen, “Space-Time Multiscale Model for Wave Propagation in Heterogeneous Media” Comp. Meth. Appl. Mech. Engng, Vol. 193, pp. 4837-4856, (2004).

102. C. Oskay and J. Fish, “Multiscale Modeling of Fatigue for Ductile Materials,” International Journal of Multiscale Computational Engineering, Vol. 2, Issue 3, pp. 1-25, (2004)

103.  R. Lund and J. Fish, “Space-time multiscale laminated theory,” International Journal of Multiscale Computational Engineering, Vol. 2, Issue 3, pp. 26-47, (2004).

104. J. Fish and Z. Yuan, “Multiscale Enrichment based on the Partition of Unity,” International Journal for Numerical Methods in Engineering, Volume 62, Issue 10, pp. 1341-1359 (2005).

105. H. Waisman, J. Fish, .R S. Tuminaro and J. Shadid, “Accelerated Generalized Global-Basis (GGB) Method for Nonlinear Problems” International Journal of Computational Physics, Vol. 210, Issue 1, pp. 274-291, (2005)

106. W. Gressick, J.T. Wen, and J. Fish, “Order Reduction for Large scale finite Element Models: a System Perspective,” International Journal of Multiscale Computational Engineering, Vol. 3, Issue 3, pp. 337-362, (2005).

107. J. Fish and C. Oskay, “Nonlocal Multiscale Fatigue Model,” Mechanics of Advanced Materials and Structures, Vol. 12, Issue 6, pp. 485-500, (2005).

108. J. Fish , W. Chen, and Y. Tang, “Generalized Mathematical Homogenization of Atomistic Media at Finite Temperatures,” International Journal for Multiscale Computational Engineering, Vol. 3, Issue 4, 2005.

109. W. Chen and J. Fish, “A Generalized Space-Time Mathematical Homogenization Theory for Bridging Atomistic and Continuum Scales,” International Journal for Numerical Methods in Engineering, Vol. 67, pp. 253-271, (2006)

110.  J. G. Michopoulos, C. Farhat and J. Fish, “Survey on Modeling and Simulation of Multiphysics Systems,” Journal of Computing and Information Science in Engineering, Volume 5, Issue 3, pp. 198-213 (2005)

111. W. Chen and J. Fish, “A Mathematical Homogenization Perspective of Virial Stress,” International Journal for Numerical Methods in Engineering, Vo. 67, pp. 189-207, (2006).

112. J. Fish and Z. Yuan, “Multiscale Enrichment based on Partition of Unity for Nonperiodic Fields and Nonlinear Problems, Computational Mechanics, Vol. 40, pp. 249–259, (2007).

113.  H. Waisman and J. Fish, “Space-time multigrid method for molecular dynamics simulations,” Comp. Meth. Appl. Mech. Engng., Volume 195, Issues 44-47, pp. 6542-6559, (2006)

114. W. Evans, J. Fish and P. Keblinski, “Role of Brownian Motion Hydrodynamics on Nanofluid Thermal Conductivity,” Applied Physics Letters, Vol. 88. pp. 093116-1-093116-3 (2006).

115. S. De, J. Fish, M .S. Shephard, P. Keblinski, S. K. Kumar, “Multiscale modeling of polymer rheology,” PHYSICAL REVIEW E 74, 030801-1- 030801-4, (2006).

116. J. Fish, W. Chen, R. Li, “Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions,” Comp. Meth. Appl. Mech. Engng., Vol. 196, pp. 908-922, (2007)

117. J. Fish, “Bridging the scales in nano engineering and science,” Vol. 8, pp. 577-594, Journal of Nanoparticle Research, (2006).

118. J. Heckman and J. Fish, “Obstacle Test for Large Deformation Plasticity Problems,” International Journal of Computational Methods in Engineering Science and Mechanics, Vol. 8, Issue 6, pp. 401 - 410 (2007).

119. C. Oskay and J. Fish, “Eigendeformation-Based Reduced Order Homogenization,” Comp. Meth. Appl. Mech. Engng., Vol. 196, pp. 1216-1243, (2007).

120. Z. Yuan and J. Fish, “Towards Realization of  Computational Homogenization in Practice,” Journal for Numerical Methods in Engineering,” Vol. 73, Issue 3, pp. 361-380 (2008).

121. R. Prasher, W. Evans, J. Fish, P. Meaken, P. Phelan, and P. Keblinski, “Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids,” Applied Physics Letters, Vol. 89, pp. 143119, (2006).

122. W. Evans, J. Fish and P. Keblinski, “Thermal Conductivity of Ordered Molecular Water,” Journal of Chemical Physics, Vol. 126., No. 15, pp. 154504 (2007). Also in Virtual Journal of Biological Physics Research, May 1, 2007.

123. H. Waisman and J. Fish, “A Heterogeneous Space-Time Full Approximation Storage Multilevel Method for Molecular Dynamics Simulations,” International Journal for Numerical Methods in Engineering,” Vol. 73, pp. 407-426, (2008).

124. J. Fish, M. A. Nuggehally, M. S. Shephard, C. R. Picu, S. Badia, M. L. Parks and M. Gunzburger “Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force,”  Comp. Meth. Appl. Mech. Engng., Vol. 196, Issue 45, pp. 4548-4560, (2007)

125. E. Gal, Z. Yuan, W. Wu and J. Fish, "A Multiscale Design System for Fatigue Life Prediction," International Journal of Multiscale Computational Engineering, Vol. 5, Issue 6, pp.  435-446 (2007)

126. A. Li, H. Waisman, and J. Fish, “A space-time multiscale method for molecular dynamics simulation of biomolecules,” International Journal of Multiscale Computational Engineering, Vol. 4, No 5-6, pp. 791-803, (2006).

127. J. Fish, "Multiscale Computations: Boom or Bust," IACM Expressions, Vol. 22, January 2008.

128. C. Oskay and J. Fish, “On Calibration and Validation of Eigendeformation-Based Multiscale Models for Failure Analysis of Heterogeneous Systems”, Computational Mechanics, Volume 42, Number 2, pp. 181-195, (2008).

129. M. A. Nuggehally, M. S. Shephard, C. R. Picu and J. Fish, "Adaptive Model Selection Procedure for Concurrent Multiscale Problems," Vol. 5, Issue 5, pp.369-386 (2007.)

130. R. Fan and J. Fish, "The rs-method for material failure simulations" International Journal for Numerical Methods in Engineering, Vol. 73, Issue 11, pp. 1607-1623 (2008).

131. W. Evans, R. Prasher, J. Fish, P. Meaken, P. Phelan, and P. Keblinski, “Effect of Aggregation with Interfacial Resistance on Thermal Conduction in Colloidal Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 51, Issues 5-6,  2008, pp. 1431-1438, (2008).

132. E. Gal and J. Fish, "Anisotropic Micromechanical Creep Damage Model for Composite Materials: A Reduced-Order Approach," International Journal of Multiscale Computational Engineering, Vol. 6, Issue 2, pp. 113-121 (2008)

133.  S. Badia, P. Bochev, J. Fish, M. Gunzburger, R. Lehoucq, M. Nuggehally, M. L. Parks, "A Force-Based Blending Model for Atomistic-to-Continuum Coupling," Int. J. for Multiscale Computational Engineering, Volume 5,  Issue 5, pp. 369-386, 2007.

134. J. Fish and R. Fan, "Mathematical Homogenization of Nonperiodic Heterogeneous Media Subjected to Large Deformation Transient Loading,” International Journal for Numerical Methods in Engineering, Vol. 76 , Issue 7, pp. 1044-1064 (2008)

135. A. Li, R. Li and J. Fish, "Generalized Mathematical Homogenization: From Theory to Practice," Comp. Meth. Appl. Mech. Engng., Vol. 197, no 41-42, pp. 245-269,  (2008).

136. Z. Yuan and J. Fish, "Multiple Scale Eigendeformation-Based Reduced Order Homogenization," Comp. Meth. Appl. Mech. Engng., Vol. 198, Issues 21-26, pp. 2016-2038 (2009)

137. R. Fan and J. Fish, "Adaptive Two-Scale Nonlinear Homogenization, "International Journal of Computational Methods in Engineering Science and Mechanics, Vol. 11, Number 1 , pp. 27-36 (2010)

138. Z. Yuan and J. Fish, "Hierarchical Model Reduction at Multiple Scales," International Journal for Numerical Methods in Engineering, Vol. 79, Issue 3, pp. 314–339, (2009)

139. J. Fish, A. Li, and F. Yavari, “Adaptive Generalized Mathematical Homogenization Framework for Modeling the Deformation of Ultra-Strong Nano-Structured Materials, International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9, pp. 1133-1154  (2010)

140. J. Fish and S. Kuznetsov, "Computational Continua,” International Journal for Numerical Methods in Engineering, Vol. 84, pp. 774-802, (2010)

141. W. Wu, Z. Yuan and J. Fish, Eigendeformation-Based Homogenization of Concrete, International Journal of Multiscale Computational Engineering, Vol. 8, Issue 1, pp. 1-16, (2010)

142. J. Fish and S. Kuznetsov, "From Homogenization to Generalized Continua,” International Journal for Computational Methods in Engineering Science and Mechanics, Volume 13, Issue 2, pp. 77-87  (2012)

143. W. Wu, Z. Yuan  J. Fish, and V. Aitharaju, “On the Canonical Structure of the Eigendeformation-Based Reduced Order Homogenization,” to appear in International Journal of Multiscale Computational Engineering, (2010)

144. W. Wu and J. Fish, “Towards Nonintrusive Stochastic Multiscale Design System for Composite Materials,”  International Journal of Multiscale Computational Engineering, Vol.8, pp. 549-559, (2010)

145. J. Fish and W. Wu, "Nonintrusive Stochastic Multiscale Solver," International Journal for Numerical Methods in Engineering Vol. 88, pp. 862-879, (2011)

146. J. Fish, V. Filonova and S. Kuznetsov, “Micro Inertia Effects in Nonlinear Heterogeneous Media,”  International Journal for Numerical Methods in Engineering, Vol. 91, Issue 13, pp. 1406-1426,  (2012)

147. J. Fish, M. Bailakanavar, L. Powers and T. Cook, “Multiscale fatigue life prediction model for heterogeneous materials,” International Journal for Numerical Methods in Engineering,  Vol. 91(10), pp. 1087–1104,  (2012)

148. M. Xia, H. Waisman, J. Fish, “XFEM with embedded HRR fields,” International Journal for Numerical Methods in Engineering, Vol. 10, Issue 4, pp. 343-360,  (2012)

149. S. Kuznetsov and J. Fish, “Mathematical homogenization theory for electroactive continuum,” International Journal for Numerical Methods in Engineering, Vol. 91, Issue 11, pp.1199-1226,  (2012)

150. J. Fish, V. Filonova and Z. Yuan, “Reduced Order Computational Continua,” Comp. Meth. Appl. Mech. Engng., Vol. 221-222, pp. 104-116, (2012)

151. J. Fish, T. Jiang and Z. Yuan, “A Staggered Nonlocal Multiscale Model for Heterogeneous Medium”, International Journal for Numerical Methods in Engineering, Vol. 91, Issue 2, pp. 142–157, (2012)

152. Z. Yuan, T. Jiang, J. Fish. G. Morscher, “Reduced Order Multiscale-Multiphysics Model for Heterogeneous Materials,” International Journal for Multiscale Computational Engineering, Vol. 12 (1), pp. 45-64, 2014.

153. Z. Yuan, M. Ruggles-Wrenn, J. Fish, Computational Viscoplasticity Based on Overstress (CVBO) Model,” International Journal for Computational Methods in Engineering Science and Mechanics, DOI:10.1080/15502287.2013.874059, (2013)

154. M. Bailakanavar, Y. Liu, J. Fish, Z. Yuan, “Automated Modeling of Random Inclusion Composites,” Engineering with Computers, DOI 10.1007/s00366-012-0310, (2013)

155. J. Fish, V. Filonova and Z. Yuan, Hybrid impotent-incompatible eigenstrain approximation,  International Journal for Numerical Methods in Engineering,  Volume 95, Issue 1, pages 1–32, (2013)

156. V. Filonova , Y. Liu, M. Bailakanavar, J. Fish and Z. Yuan, Corotational Formulation of Reduced Order Homogenization, Journal of Computers, Materials and Continua, vol.34, no.3, pp.177-198, (2013)

157. M. Bailakanavar, J. Fish, V. Aitharaju and W. Rodgers, Coupling of moisture diffusion and mechanical deformation in polymer matrix composites, accepted in International Journal for Numerical Methods in Engineering, (2013)

 

158. Y. Liu, V. Filonova, N. Hu, Zi. Yuan, J. Fish, Z. Yuan, T. Belytschko, A Regularized Phenomenological Multiscale Damage Model. Submitted to International Journal for Numerical Methods in Engineering. 2013.

 

159. J. Fish, V. Filonova and D. Fafalis, Computational Continua Revisited, submitted to  International Journal for Numerical Methods in Engineering,  2014

 

160. A. Shojaei, G. Li, J. Fish and P.J. Tan, Microscale Continuum Damage Constitutive Modeling of Ceramic Matrix Composites, submitted to Journal of Applied Mechanics, 2014.

 

161. A. Shojaei, G. Li, S.R. Reid, P.J. Tan, and J. Fish, Dynamic Delamination Analysis of Laminated Fiber Reinforced Polymers: A Continuum Damage Mechanics Approach, submitted to International Journal for Solids and Structures, 2014.

 

 

D. Proceeding Papers

162. T. Belytschko and J. Fish, "Spectral superposition on finite elements for shear banding problems," proceedings of the Fifth International Symposium on Numerical Methods in Engineering, Lausanne, eds. R.Grouper, J.Perrux and R.P.Show, Springer Verlag, Berlin (1989).

163. T. Belytschko, J. Fish and Y. Y .Lu, "Numerical studies of two-dimensional shear banding with the spectral overlay on finite elements," proceedings of the Second World Congress on Computational Mechanics, Stuttgart, FRG, pp. 27-31 (1990).

164. J. Fish and S. Markolefas, "Adaptive s-method for linear elastostatics," proceedings of the AIAA 33rd Structures, Structural Dynamics & Materials Conference, Dallas, TX, pp. 313 - 317, (1992).

165. J. Fish and A. Wagiman, "Multiscale finite element method for a periodic and nonperiodic heterogeneous medium," AMD, Vol. 157, pp.95-117, (1992).

166. J. Fish, "Micromechanical studies of composite materials with the s-version of the finite element method," proceedings of the XVIII International Congress of Theoretical and Applied Mechanics, Haifa, Israel, (1992).

167. J. Fish and A.Nath, "Adaptive and hierarchical modeling of fatigue crack propagation," proceedings of the AIAA 34rd Structures, Structural Dynamics & Materials Conference. LaJolla, CA, pp. 1704-1711, (1993).

168. J. Fish and A. Wagiman, "Assessment of Computational Techniques for Analyzing Microscopic Fields in Locally Nonperiodic Heterogeneous Media" proceedings of the Second U.S. National Congress on Computational Mechanics, Washington, D.C., 1993,.

169.  M. Beall, J. Fish, M. Shephard, "Two-field mesh superposition technique for laminated composites," proceedings of the Second U.S. National Congress on Computational Mechanics, Washington, D.C.,1993.

170.  M.W. Beall, J. Fish, M.S. Shephard, G.J. Dvorak, K.L.Sheck, R.Wentorf, "Computer-Aided Modeling Tools for Composite Materials," Ceramic Engineering and Science proceedings of the American Ceramic Society’s 18th Annual Meeting, Cocoa Beach, FL, Jan 9-12, 1994

171. V.Belsky and J. Fish, "Towards an ultimate finite element oriented solver on unstructured meshes," proceedings of 1995 ASME/CIE, Boston, MA.

172. J.  Fish and R. Guttal, "h- versus p- version of the finite element method for shell analysis," proceedings of 1995 ASME/CIE, Boston, MA.

173. S. Adjerid, M.W. Beall, G.J. Dvorak, J. Fish, J.E. Flaherty, J.Hudson, K.L. Shek, M.S. Shephard, R. Wentorf, "Mechanism-Based Design of Composite Structures," proceedings of ASME Symposium on Failure Mechanism-Based Modeling in High Temperature Composites, Nov. 17-22, Atlanta, 1996.

174. J. Fish and K. Shek, "Computational Plasticity for Composite Structures based on Mathematical Homogenization: Theory and Practice, proceedings of 14th US Army Symposium on Solid Mechanics, 16-18 October 1996, Myrtle Beach, SC.

175. J. Fish, K. Shek, S. Gomaa, M.S. Shephard, G.J. Dvorak, W.E. Bachrach and A.M. Wafa, "Modeling and Simulation of Processes in Composites," Proceedings of American Ceramic Society publishing, Cocoa Beach meeting, Jan 12-16, 1997.

176. R. Wentorf, M.S. Shephard, G.J. Dvorak, J. Fish, M.W. Beall, R. Collar, K. Shek, "Software framework for mechanism-based design of composite structures," Proceedings of American Ceramic Society publishing, Cocoa Beach meeting, Jan 12-16, 1997.

177. J. Fish, Q. Yu and D. Wildman, "Simulation of Progressive Damage for High Temperature Woven Composites," Proceedings of American Ceramic Society publishing, Cocoa Beach meeting, Jan 12-16, 1999.

178. J. Fish and Q. Yu, "Computational Damage Mechanics for Composite Materials Subjected to Fatigue Loading," Proceedings of Fourth International Conference on Constitutive Laws for Engineering Materials, Rensselaer Polytechnic Institute, Troy, NY, July 27-30, pp. 285-288, 1999.

179. J. Fish, M.S. Shephard and M.W. Beall, "Automated Multiscale Analysis of Micromechanical Cracking Propagation," Proceedings of IUTAM/IACM Symposium on Discretization Methods in Structural Mechanics II, Vienna, 2-6 June, 1997, pp. 249-256, Kluwer Academic Publishers, 1999.

180. E. Kaplan and J. Fish, "Performance Improvement of a Generalized Aggregation Method Employing Cache and Parallel Processing," Proceedings of Pan American Workshops in Applied and Computational Mathematics, Universidad Nacional de Trujillo, April 24-28, 2000.

181. G. Nagai and J. Fish, "Nonlocal three-field variational principal for wave propagation in heterogeneous media," proceedings of the Japanese Society for Mechanical Engineers, Tokyo, Japan November 11, 2001.

182.   E.L.Shamy, M.Zeghal, M.Shaphard, R.Dobry, J.Fish and T.Abdoun, "Discrete Element Simulation of Water Flow through Granular Soils," Proceeding of 15th Engineering Mechanics Conference, June 2-5, Columbia University, NY., 2002.

183. C. Oskay and J. Fish, “A Multiscale Model Of Composite Failure Under Impact,” Proceedings of IMECE2006,  ASME International Mechanical Engineering Congress and Exposition November 5-10, 2006, Chicago, Illinois, USA

184. J. Fish, M. Shephard, C. Picu, A. Li, M. Nuggehally, A. Rakshit, "Progress in Discrete to Continuum Coupling," Proceedings of Third Asian-pacific Congress on Computational  Mechanics, December 3-6, 2007 Kyoto, Japan

185. E. Gal, Z. Yuan, W. Wu and J. Fish "Fatigue Life Prediction Reduced Order (Mesoscale) Model For Composite Material" The Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, St. Julians, Malta, 18-21 September 2007

186. J. Fish and Z. Yuan, "Hierarchical Model Reduction at Multiple Scales," 2nd South-east Conference on Computational Mechanics, Papadrakakis and Kojic (eds), Rhodes, Greece, June 2009.

187. J. Fish, V. Filonova, Z. Yuan, “Reduced Order Computational Continua,” Proceedings 25th European Conference on Modelling and Simulation ©ECMS Tadeusz Burczynski, Joanna Kolodziej Aleksander Byrski, Marco Carvalho (Editors), 2009.