References
References for Nonlinear Structural Materials
1. G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, John Wiley & Sons, 2000.
2. R.S. Rivlin and D.W. Saunders, “Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber,” Phil. Trans. R. Soc. Lond. A, vol. 243, no. 865, pp. 251–288, 1951.
3. E.M. Arruda and M.C. Boyce, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, vol. 41, pp. 389–412, 1993.
4. J.C. Simo and T.J.R. Hughes, Computational Inelasticity, Springer, 1998.
5. J. Lubliner, Plasticity Theory, Dover, 2008.
6. K. Grote and E. Antonsson, Springer Handbook of Mechanical Engineering, Springer, 2009.
7. R. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, John Wiley & Sons, 1996.
8. F. Garofalo, “An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals,” Trans AIME, vol. 227, no. 351, 1963.
9. S. Brown, K. Kim, and L. Anand, “An Internal Variable Constitutive Model for Hot Working of Metals,” Int. J. Plasticity, vol. 5, pp. 95–130, 1989.
10. S. Hartmann and P. Neff, “Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility,” International Journal of Solids and Structures, vol 40, pp. 2767-2791, 2003.
11. M. Attard, “Finite Strain - Isotropic Hyperelasticity,” Int. J. Solids Struct., vol. 40, pp. 4353–4378, 2003.
12. I. Babuska and M. Suri, “On Locking and Robustness in the Finite Element Method,” SIAM Journal on Numerical Analysis, vol. 29, pp. 1261–1293, 1992.
13. A.F. Bower, Applied Mechanics of Solids, CRC Press, 2009.
14. A. Gent, “A new Constitutive Relation for Rubbers,” Rubber Chem. Technol., vol. 69, pp. 59–61, 1996.
15. C. Horgan and G. Saccomandi, “Constitutive Models for Compressible Nonlinearly Elastic Materials with Limiting Chain Extensibility,” J. Elasticity, vol. 7, pp. 123–138, 2004.
16. H. Ambacher, H. Enderle, H. Kilian, A. Sauter, “Relaxation in permanent networks”. In: Pietralla M., Pechhold W. (eds) Relaxation in Polymers. Progress in Colloid & Polymer Science, vol. 80, pp. 209–220, Steinkopff, 1989.
17. M. Kaliske and H. Rothert, “On the finite element implementation of rubber-like materials at finite strains”, Eng. Comput., vol. 14, pp. 216–232, 1997.
18. G. Marckmann and E. Verron, “Comparison of hyperelastic models for rubber-like materials” Rubber Chem. Technol., vol. 79, pp. 835–858, 2006.
19. B. Storakers, “On Material Representation and Constitutive Branching in Finite Compressible Elasticity,” J. Mech. Phys. Solids, vol. 34, pp. 125–145, 1986.
20. Y. Gao, “Large Deformation Field Near a Crack Tip in a Rubber-like Material,” Theor. Appl. Fract. Mec., vol. 26, pp. 155–162, 1997.
21. R.L. Taylor, “Thermomechanical analysis of viscoelastic solids,” Int. J. Numer. Meth., vol. 2, pp. 45-59, 1970.
22. G. Holzapfel, T. Gasser, and R. Ogden, “A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models,” J. Elasticity, vol. 61, pp. 1–48, 2000.
23. T. Gasser, R. Ogden, and G. Holzapfel, “Hyperelastic modelling of arterial layers with distributed collagen fibre orientations,” J. R. Soc. Interface, vol. 3, pp. 15-35, 2006
24. M. Kaliske and G. Heinrich. “An Extended Tube Model for Rubber Elasticity: Statistical-Mechanical Theory and Finite Element Implementation,” Rubber Chem. Technol. vol. 72, pp. 602–632, 1999.
25. R. Behnke and M. Kaliske. “The Extended Non-affine Tube Model for Crosslinked Polymer Networks: Physical Basics, Implementation, and Application to Thermomechanical Finite Element Analyses,” in Designing of Elastomer Nanocomposites: From Theory to Applications, Springer, 2017.
26. J. Bergstrom. Mechanics of Solid Polymers: Theory and Computational Modeling. Elsevier 2015.
27. A. Souza et al., “Three-dimensional model for solids undergoing stress-induced phase transformations,” European J. Mech. A Solids, vol. 17, pp. 789–806, 1988.
28. F. Auricchio and L. Petrini, “A three-dimensional model describing stress-temperature induced solid phase transformations. Part I: solution algorithm and boundary value problems,” Int. J. Numer. Meth. Eng., vol. 61, pp. 807–836. 2004.
29. D. Lagoudas (Ed.) Shape Memory Alloys: Modeling and Engineering Applications, Springer, 2008.
30. D. Lagoudas et al, “Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys,” Int. J. Plast., vol. 32–33, pp. 155-183. 2012.
31. L. Mullins, “Effect of stretching on the properties of rubber,” Journal of Rubber Research, vol. 16, pp. 275–289, 1947.
32. L. Mullins and N. R. Tobin, “Theoretical model for the elastic behavior of filled-reinforced vulcanized rubbers,” Rubber Chem. Technol., vol. 30, pp. 555–571, 1957.
33. L. Mullins. “Softening of rubber by deformation,” Rubber Chem. Technol., vol. 42, pp. 339–362, 1969.
34. R. Ogden and D. Roxburgh, “A pseudo-elastic model for the Mullins effect in filled rubber,” Proc. R. Soc. Lond., vol. A 455, pp. 2861–2878, 1999.
35. A. Dorfmann and R. Ogden, “A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber,” Int. J. Solids Struct., vol. 41, pp. 1855–1878, 2004.
36. Z. Guo and L. Sluys, “Computational modelling of the stress-softening phenomenon of rubber-like materials under cyclic loading,” European Journal of Mechanics A/Solids, vol. 25, pp. 877–896, 2006.
37. C. Miehe, “Discontinuous and continuous damage evolution in Ogden-type large strain elastic materials,” European Journal of Mechanics, A/Solids, vol. 14, pp. 697–720, 1995.
38. R. Koeller, “Application of fractional calculus to the theory of viscoelasticity,” J. Appl. Mech., vol. 51. pp. 299–307, 1984.
References for Geomechanics Materials
1. W.F. Chen and E. Mizuno, Nonlinear Analysis in Soil Mechanics: Theory and Implementation (Developments in Geotechnical Engineering), 3rd ed., Elsevier Science, 1990.
2. D. Drucker and W. Prager, “Soil Mechanics and Plastic Analysis or Limit Design,” Quarterly of Applied Mathematics, vol. 10, no. 2, pp. 157–165. 1952.
3. S. Dolarevic and A. Ibrahimbegovic, “A modified three-surface elasto-plastic cap model and its numerical implementation,” Computers and Structures, vol. 85, pp. 419-430, 2007.
4. B. Bresler and K. Pister, “Strength of Concrete Under Combined Stresses,” ACI Journal, vol. 551, no. 9, pp. 321–345, 1958.
5. H. Matsuoka and T. Nakai, “Stress-deformation and Strength Characteristics of Soil Under Three Different Principal Stresses,” Proc. JSCE, vol. 232, 1974.
6. H. Matsuoka and T. Nakai, “Relationship Among Tresca, Mises, Mohr-Coulomb, and Matsuoka-Nakai Failure Criteria,” Soils and Foundations, vol. 25, no. 4, pp. 123–128, 1985.
7. H.S. Yu, Plasticity and Geotechnics, Springer, 2006.
8. V. Marinos, P. Marinos, and E. Hoek, “The Geological Strength Index: Applications and Limitations,” Bull. Eng. Geol. Environ., vol. 64, pp. 55–65, 2005.
9. J. Jaeger, N. G. Cook, and R. Zimmerman, Fundamentals of Rock Mechanics, 4th ed., Wiley-Blackwell, 2007.
10. G. C. Nayak and O. C. Zienkiewicz, “Convenient Form of Stress Invariants for Plasticity,” J. Struct. Div. ASCE, vol. 98, pp. 949–954, 1972.
11. A.J. Abbo and S.W. Sloan, “A Smooth Hyperbolic Approximation to the Mohr-Coulomb Yield Criterion,” Computers and Structures, vol. 54, no. 3, pp. 427–441, 1995.
12. K.J. Willam and E.P. Warnke, “Constitutive Model for the Triaxial Behavior of Concrete,” IABSE Reports of the Working Commissions, Colloquium (Bergamo): Concrete Structures Subjected to Triaxial Stresses, vol. 19, 1974.
13. B.H.G. Brady and E.T. Brown, Rock Mechanics for Underground Mining, 3rd ed., Springer, 2004.
14. H.A. Taiebat and J.P. Carter, “Flow Rule Effects in the Tresca Model,” Computer and Geotechnics, vol. 35, pp. 500–503, 2008.
15. A. Stankiewicz and others, “Gradient-enhanced Cam-Clay Model in Simulation of Strain Localization in Soil,” Foundations of Civil and Environmental Engineering, no.7, 2006.
16. D.M. Wood, Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, 2007.
17. D.M. Potts and L. Zadravkovic, Finite Element Analysis in Geothechnical Engineering, Thomas Telford, 1999.
18. W. Tiecheng and others, Stress-strain Relation for Concrete Under Triaxial Loading, 16th ASCE Engineering Mechanics Conference, 2003.
19. W.F. Chen, Plasticity in Reinforced Concrete, McGraw-Hill, 1982.
20. N. Ottosen, “A Failure Criterion for Concrete,” J. Eng. Mech. Division, ASCE, vol. 103, no. 4, pp. 527–535, 1977.
21. N. Ottosen and M. Ristinmaa, The Mechanics of Constitutive Modelling, Elsevier, 2005.
22. J. Suebsuk, S. Horpibulsuk, and M. Liu, “Modified Structured Cam Clay: A generalised critical state model for destructured, naturally structured and artificially structured clays,” Computers and Geotechnics, vol. 37, pp. 956–968, 2010.
23. M. Lui and J.P. Carter, “A structured Cam Clay model,” Can. Geotech. J., vol. 39, pp. 1313–1332, 2002.
24. E. Alonso, A. Gens, and A. Josa, “A constitutive model for partially saturated soils,” Géotechnique, vol. 40, 1990.
25. D. Pedroso and M. Farias, “Extended Barcelona Basic Model for unsaturated soil under cyclic loadings,” Computers and Geotechnics, vol. 38, no. 5, pp. 731–740, 2011.
26. T. Bower, Constitutive modelling of soils and fibre-reinforced soils, PhD Thesis, Cardiff University 2017.
References for the Nonlinear Elastic Material Theory
1. W. Ramberg and W.R. Osgood, “Description of stress-strain curves by three parameters,” NACA Technical Note, no. 902, 1943.
2. A.F. Bower, Applied Mechanics of Solids, CRC Press, 2009.
3. B.O. Hardin and V.P. Drnevich, “Shear modulus and damping in soils: Design equations and curves,” J. Soil Mechanics and Foundations Division, ASCE 98, pp. 667–692, 1972.
4. J.M. Duncan and C.Y. Chang, “Nonlinear analysis of stress and strain in soils,” J. Soil Mechanics and Foundations Division, vol. 96, no. 5, pp. 1629–1653, 1970.
5. J.M. Duncan, P. Byrne, K.S. Wong, and P. Mabry, “Strength, stress strain and bulk modulus parameters for finite element analysis of stresses and movements in soil,” Geotechnical Engineering Report: UCB/GT/80-01, University of California, Berkeley, 1980.
6. E.T. Selig, Soil Parameters for Design of Buried Pipelines, Pipeline Infrastructure, B.A. Bennett, ed., ASCE, New York, pp. 99–116, 1988.
References for Elastoplastic Materials
1. P. Armstrong and C. Frederick, “A Mathematical Representation of the Multiaxial Bauschinger Effect”, Technical Report RD/B/N731 CEGB, 1966. Reprinted in Mater. High Temp. 24 (1) pp. 1–26, 2007.
2. M. Jirasek and Z. Bazant, Inelastic Analysis of Structures, Ch.20 General Elastoplastic Constitutive Models. Wiley, 2001.
3. J. Simo and T. Hughes, Computational Inelasticity, Springer, 1998.
4. J. Simo, “Algorithms for Static and Dynamic Multiplicative Plasticity that Preserve the Classical Return Mapping Schemes of the Infinitesimal Theory,” Computer Methods in Applied Mechanics and Engineering, vol. 99, pp. 61–112, 1992.
5. J. Lubliner, Plasticity Theory, Dover, 2008.
6. R. Hill, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. Roy. Soc. London, vol. 193, pp. 281–297, 1948.
7. N. Ottosen and M. Ristinmaa, The Mechanics of Constitutive Modeling, Elsevier Science, 2005.
8. S. Shima and M. Oyane. “Plasticity theory for porous metals,” International Journal of Mechanical Sciences, vol. 18, pp. 285–291, 1976.
9. A. Gurson, “Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media,” Journal of Engineering Materials and Technology, vol. 99, pp. 2–15, 1977.
10. V. Tvergaard and A. Needleman, “Analysis of the cup-cone fracture in a round tensile bar,” Acta Metallurgica, vol. 32, pp. 157–169, 1984.
11. A. Needleman and V. Tvergaard. “An analysis of ductile rupture in notched bars,” Journal of the Mechanics and Physics of Solids, vol. 32, pp. 461– 490, 1984.
12. K. Nahshon and Z. Xue, “A modified Gurson model and its application to punch-out experiments,” Engineering Fracture Mechanics, vol. 76, pp. 997– 1009, 2009.
13. A.E. Huespe, A. Needleman, and J. Oliver, “A finite strain, finite band method for modeling ductile fracture,” International Journal of Plasticity, vol. 28, pp. 53-69, 2012.
14. N. Fleck, L. Kuhn, and R. McMeeking, “Yielding of metal powder bonded by isolated contacts,” Journal of the Mechanics and Physics of Solids, vol. 40, pp. 1139– 1162, 1992.
15. P. Redanz, “Numerical modelling of the powder compaction of a cup,” European Journal of Mechanics - A/Solids, vol. 18, pp.399– 413, 1999.
16. J. Cedergren, N. Sorensen, and A. Bergmark, “Three-dimensional analysis of compaction of metal powder,” Mechanics of Materials, vol. 34, pp. 43–59, 2004.
17. S. Tsai and E. Wu, “A general theory of strength for anisotropic materials,” Journal of Composite Materials, vol. 5, pp. 58-80, 1971.
18. P. Hopkins, “Benchmarks for Membrane and Bending Analysis of Laminated Shells. Part 2: Strength Analysis,” NAFEMS Ltd, 2005.
19. Z. Hashin, “Failure Criteria for Unidirectional Fiber Composites”, Journal of Applied Mechanics, 47, 329,1980.
20. A. J. Sobey, J. I. R. Blake, and R. A. Shenoi, “Implications of failure criteria choices on the rapid concept design of composite grillage structures using multiobjective optimisation”, Structural and Multidisciplinary Optimization, 47, 735–747, 2013.
21. C. G. Davila, P. P. Camanho, and C. A. Rose. “Failure Criteria for FRP Laminates,” Journal of Composites Materials, 39, 2005.
22. R.A.B Engelen, M.G.D. Geers, and F.P.T. Baaijens, “Nonlocal implicit gradient-enhanced elasto-plasticity for modelling of softening behaviour,” International Journal of Plasticity, vol. 19, no. 4, pp. 403-433, 2003.
23. S. Forest, “Micromorphic approach for gradient elasticity, viscoplasticity, and damage,” Journal of Engineering Mechanics, vol. 135, no. 3, pp. 117-131, 2009.
References for Damage Models
1. R. de Borst, M. Crisfield, J. Remmers, and C. Verhoosel, Non-linear Finite Element Analyses of Solids and Structures, John Wiley & Sons, 2012.
2. M. Jirásek, “Damage and smeared crack models,” pp. 1–49 in Numerical Modeling of Concrete Cracking, G. Hofstetter and G. Meschke eds., Springer, 2011.
3. J. Mazars, “A description of micro and macroscale damage of concrete structures,” Engineering Fracture Mechanics, vol. 25, pp. 729–737, 1986.
4. Z. Bazant and B. Oh, “Crack band theory for fracture in concrete,” Materials and Structures, vol. 16, pp. 155–177, 1983.
5. M. Jirásek and M. Bauer, “Numerical aspects of the crack band approach,” Computers and Structures, vol. 110, pp. 60-78, 2012.
6. R. Peerlings and others, “Gradient enhanced damage for quasi-brittle materials,” Int. J. Numer. Meth. Eng., vol. 39, pp. 3391–3403, 1996.
7. C. Miehe, M. Hofhacker, and F. Welschinger, “A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits,” Comput. Methods Appl. Mech. Eng., vol 199, pp. 2765-2778, 2010.
8. C. Miehe, L.S. Schänzel, and H. Ulmer, “Phase field modeling of fracture in multi-physics system. Part 1. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids,” Comput. Methods Appl. Mech. Eng., vol 294, pp. 449-485, 2014.
9. M.J Borden, Analysis of Phase-Field Models for Dynamic Brittle and Ductile Fracture, PhD Thesis, The University of Texas at Austin, 2012.
References for Piezoelectricity
1. R. Holland and E.P. EerNisse, Design of Resonant Piezoelectric Devices, Research Monograph No. 56, The M.I.T. Press, 1969.
2. T. Ikeda, Fundamentals of Piezoelectricity, Oxford University Press, 1990.
3. A.V. Mezheritsky, “Elastic, Dielectric, and Piezoelectric Losses in Piezoceramics: How it Works all Together,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 51, no. 6, 2004.
4. K. Uchino and S. Hirose, “Loss Mechanisms in Piezoelectrics: How to Measure Different Losses Separately,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 48, no. 1, pp. 307–321, 2001.
5. P.C.Y. Lee, N.H. Liu, and A. Ballato, “Thickness Vibrations of a Piezoelectric Plate with Dissipation,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 51, no. 1, 2004.
6. P.C.Y. Lee and N.H. Liu, “Plane Harmonic Waves in an Infinite Piezoelectric Plate with Dissipation,” Frequency Control Symposium and PDA Exhibition, IEEE International, pp. 162–169, 2002.
7. C.A. Balanis, “Electrical Properties of Matter,” Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.
8. J. Yang, An Introduction to the Theory of Piezoelectricity, Springer Science and Business Media, N.Y., 2005.
References for Magnetomechanics
1. J.A. Stratton, Electromagnetic Theory, Cambridge, MA, 1941.
2. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, pp. 69–73, 1960.
3. D.J. Griffiths, “Resource Letter EM-1: Electromagnetic Momentum,” Am. J. Phys., vol. 80, pp. 7–18, 2012.
4. L. Dorfmann, R.W. Ogden, Mechanics and Electrodynamics of Electroelastic and Magnetoelastic Interactions, Springer, 2014.
References for Magnetostriction
1. Chikazumi, Physics of Ferromagnetism, Oxford University Press, New York, 1997.
2. H. Kronmüller, “General Micromagnetic Theory”, in Handbook of Magnetism and Advanced Magnetic Materials, edited by H. Kronmüller and S. Parkin, Vol. 2: Micromagnetism, John Wiley & Sons, Chichester, 2007.
3. X.E. Liu and X.J. Zheng, “A Nonlinear Constitutive Model for Magnetostricite Materials”, Acta Mech. Sinica, vol. 21, pp. 278–285, 2005.
4. D.C. Jiles, Introduction to Magnetism and Magnetic Materials, 2nd ed., Chapman & Hall, London, 1998.
5. M.J. Dapino, "Nonlinear and Hysteretic Magnetomechanical Model for Magnetostrictive Transducers," PhD Dissertation, Iowa State University, Ames, Iowa, 1999.
6. C.H. Sherman and J.L. Butler, Appendix A.7, p. 555 in Transducers and Arrays for Underwater Sound, Springer, New York, 2007.
References For Electrostriction
1. J.A. Stratton, Electromagnetic Theory, Cambridge, MA, 1941.
2. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, pp. 69–73, 1960.
3. R.E. Newnham, V. Sundar, R. Yimnirun, J. Su, and Q.M. Zhang, “Electrostriction: Nonlinear Electromechanical Coupling in Solid Dielectrics,” J. Phys. Chem. B, vol. 101, pp. 10141–10150, 1997.
References For Ferroelasticity
1. F. Li, Jin, Z. Xu, and S. Zhang, “Electrostrictive effect in ferroelectrics: An alternative approach to improve piezoelectricity,” Appl. Phys. Reviews, vol. 1, no. 1, pp. 011103-1–011103-21, 2014.
2. C. L. Horn and N. Shankar, “A finite element method for electrostrictive ceramic devices,” Int. J. Solids Structures, vol. 33, pp. 1757–1779, 1995.
3. R.C. Smith and Z. Ounaies. “A Domain Wall Model for Hysteresis in Piezoelectric Materials,” J. Int. Mat. Sys. Struct., vol. 11, no. 1, pp. 62–79, 2000.
References for Boundary Conditions
1. M. Cohen and P.C. Jennings, “Silent Boundary Methods for Transient Analysis,” Computational Methods for Transient Analysis, vol 1 (editors T. Belytschko and T.J.R. Hughes), Nort-Holland, 1983.
2. B. Lalanne and M. Touratier, “Aeroelastic Vibrations and Stability in Cyclic Symmetric Domains,” International Journal of Rotating Machinery, vol. 6, no. 6, pp. 445–452, 2000.
3. Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, 1965, page 99.
References for Contact Analysis and Decohesion
1. L. De Lorenzis, D. Fernando, and J.G. Teng, “Coupled mixed-mode cohesive zone modeling of interfacial debonding in plated beams,” International Journal of Solids and Structures, vol. 50, pp. 2477–2494, 2013.
2. R.D.S.G. Campilho, M.F.S.F. de Moura, and J.J.M.S. Domingues, “Using a cohesive damage model to predict the tensile behavior of CFRP single-strap repairs,” International Journal of Solids and Structures, vol. 45, no. 5, pp. 1497–1512, 2008.
3. S.T. Pinho, L. Iannucci, and P. Robinson, “Formulation and implementation of decohesion elements in an explicit finite code,” Composites Part A: Applied Science and Manufacturing, vol. 37, no. 5, pp. 778–789, 2006.
4. N. Valoroso and L. Champeny, “A damage-mechanics-based approach for modelling decohesion in adhesively bonded assemblies,” Engineering Fracture Mechanics, vol. 73, pp. 2774–2801, 2006.
5. L. Allix and A Corigliano, “Geometrical and interfacial non-linearities in the analysis of delamination in composites,” International Journal of Solids and Structures, vol. 36, pp. 2189–2216, 1999