Abstract
Composite materials have become indispensable in engineering today. These were originally developed to combine different material properties. A typical example is a reinforced concrete structure. Attempts were made here to improve the poor tensile properties through the reinforcement. Later, lightweight considerations were dominant. For example, aircraft engines were limited in their performance, so that, e.g., sandwich structures were used for the airplane structure. Similar considerations were also made for space structures. Today, composites are used in almost all areas of technology. This often involves the question of substituting traditional construction materials in order to better meet the requirements of use. In this context, there are also increasing considerations to reduce production costs. The actual focus is therefore on foams and functionally graded materials. This chapter gives a brief overview of selected current developments in composite mechanics. This is supplemented by numerous publications (among them the main references from the author’s group), so that one can get a good overview with the references listed within these publications.
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Notes
- 1.
The class of auxetic materials that have a negative Poisson’s ratio (when stretched, they become thicker perpendicular to the applied force), is not in the focus here. However, such values are possible which follows from the positive definiteness of the strain energy.
- 2.
Woldemar Voigt (\(^*\)2 September 1850 Leipzig - \(\dag \)13 December 1919 Göttingen).
- 3.
András (Endre) Reuss (\(^*\)1 July 1900 Budapest - \(\dag \)10 May 1968 Budapest).
- 4.
Stephen Wei-Lun Tsai (\(^*\)6 July 1929, Beijing).
References
Advani SG, Tucker CL (1987) The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 31(8):751–784. https://doi.org/10.1122/1.549945
Altenbach H (1988) Determination of the reduced properties of multilayer viscoelastic sheets. Mech Compos Mater 24(1):52–59
Altenbach H (2000) An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int J Solids Struct 37(25):3503–3520. https://doi.org/10.1016/S0020-7683(99)00057-8
Altenbach H (2000) On the determination of transverse shear stiffnesses of orthotropic plates. Zeitschrift für angewandte Mathematik und Physik ZAMP 51(4):629–649. https://doi.org/10.1007/s000330050021
Altenbach H, Becker W (2003) Modern trends in composite laminates mechanics. In: CISM international centre for mechanical sciences, vol 448. Springer. https://doi.org/10.1007/978-3-7091-2544-1
Altenbach H, Eremeyev VA (2008) Direct approach-based analysis of plates composed of functionally graded materials. Arch Appl Mech 78(10):775–794. https://doi.org/10.1007/s00419-007-0192-3
Altenbach H, Eremeyev VA (2008) On the analysis of viscoelastic plates made of functionally graded materials. ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 88(5):332–341. https://doi.org/10.1002/zamm.200800001
Altenbach H, Eremeyev VA (2008c) On the application of Zhilin’s theory of simple shells to plates made of functionally graded materials. In: Indeitsev DA, Krivtsov AM (eds) Proceedings of 36 international summer school-conference APM 2008, Institute for Problems in Mechanical Engineering, pp 8–49
Altenbach H, Eremeyev VA (2011a) Mechanics of viscoelastic plates made of fgms. In: Murín J, Kompis̆ V, Kutis̆ V (eds) Computational modelling and advanced simulations, computational methods in applied sciences, vol 24. Springer, pp 33–48. https://doi.org/10.1007/978-94-007-0317-9_2
Altenbach H, Eremeyev VA (2011) On the shell theory on the nanoscale with surface stresses. Int J Eng Sci 49(12):1294–1301. https://doi.org/10.1016/j.ijengsci.2011.03.011
Altenbach H, Eremeyev VA (2013a) Cosserat media. In: Altenbach H, Eremeyev VA (eds) Generalized Continua from the theory to engineering applications, CISM international centre for mechanical sciences, vol 541. Springer, pp 65–130. https://doi.org/10.1007/978-3-7091-1371-4_2
Altenbach H, Eremeyev VA (2013b) Cosserat-type shells. In: Altenbach H, Eremeyev VA (eds) Generalized Continua from the theory to engineering applications, CISM international centre for mechanical sciences, vol 541. Springer, pp 131–178. https://doi.org/10.1007/978-3-7091-1371-4_3
Altenbach H, Öchsner A (2010) Cellular and porous materials in structures and processes, CISM international centre for mechanical sciences, vol 521. Springer. https://doi.org/10.1007/978-3-7091-0297-8
Altenbach H, Altenbach J, Rikards R (1996) Einführung in die Mechanik der Laminat- und Sandwichtragwerke: Modellierung und Berechnung von Balken und Platten aus Verbundwerkstoffen. Dt. Verl. für Grundstoffindustrie, Stuttgart
Altenbach H, Naumenko K, Lvov GI, Pilipenko SN (2003) Numerical estimation of the elastic properties of thin-walled structures manufactured from short-fiber-reinforced thermoplastics. Mech Compos Mater 39(3):221–234. https://doi.org/10.1023/A:1024566026411
Altenbach H, Naumenko K, Zhilin PA (2003) A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions. Continuum Mech Thermodyn 15(6):539–570. https://doi.org/10.1007/s00161-003-0133-5
Altenbach H, Naumenko K, Pylypenko S (2005) On the numerical prediction of the anisotropic elastic properties in thin-walled structures made from short fiber reinforced plastics. Comput Assist Mech Eng 12(4):87–97
Altenbach H, Naumenko K, Pylypenko S, Renner B (2007) Influence of rotary inertia on the fiber dynamics in homogeneous creeping flows. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 87(2):81–93. https://doi.org/10.1002/zamm.200610303
Altenbach H, Brigadnov I, Naumenko K (2009) Rotation of a slender particle in a shear flow: influence of the rotary inertia and stability analysis. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 89(10):823–832. https://doi.org/10.1002/zamm.200900249
Altenbach H, Eremeyev VA, Lebedev LP (2011) Micropolar shells as two-dimensional generalized continua models. In: Altenbach H, Maugin GA, Erofeev V (eds) Mechanics of generalized Continua, advanced structured materials, vol 7. Springer, pp 23–55. https://doi.org/10.1007/978-3-642-19219-7_2
Altenbach H, Eremeyev VA, Morozov NF (2012) Surface viscoelasticity and effective properties of thin-walled structures at the nanoscale. Int J Eng Sci 59:83–89. https://doi.org/10.1016/j.ijengsci.2012.03.004
Altenbach H, Eremeyev VA, Naumenko K (2015) On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 95(10):1004–1011
Altenbach H, Altenbach J, Kissing W (2018) Mechanics of composite structural elements, 2nd edn. Springer. https://doi.org/10.1007/978-981-10-8935-0
Altenbach H, Öchsner A (2020) Encyclopedia of Continuum mechanics, vol 1–3. Springer. https://doi.org/10.1007/978-3-662-55770-9
Ashby M, Shercliff H, Cebon D (2018) Materials: engineering, science, processing and design, 4th edn. Butterworth-Heinemann
Bay RS, Tucker III CL (1992) Fiber orientation in simple injection moldings. Part I: theory and numerical methods. Polym Compos 13(4):317–331. https://doi.org/10.1002/pc.750130409
Bretherton FP (1962) The motion of rigid particles in a shear flow at low Reynolds number. J Fluid Mech 14:284–304. https://doi.org/10.1017/S002211206200124X
Cristescu ND, Craciun EM, Soós E (2003) Mechanics of elastic composite. Chapman and Hall, New York. https://doi.org/10.1201/9780203502815
Duan H, Yi X, Huang Z, Wang J (2007) A unified scheme for prediction of effective moduli of multiphase composites with interface effects. Part I: theoretical framework. Mech Mater 39(1):81–93. https://doi.org/10.1016/j.mechmat.2006.02.009
Eisenträger J, Naumenko K, Altenbach H, Köppe H (2015a) Application of the first-order shear deformation theory to the analysis of laminated glasses and photovoltaic panels. Int J Mech Sci 96–97:163–171. https://doi.org/10.1016/j.ijmecsci.2015.03.012
Eisenträger J, Naumenko K, Altenbach H, Meenen J (2015b) A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory. Compos Struct 133:265–277. https://doi.org/10.1016/j.compstruct.2015.07.049
Eringen AC (1991) Continuum theory of dense rigid suspensions. Rheologica Acta 30(1):23–32. https://doi.org/10.1007/BF00366791
Halpin JC, Kardos JL (1976) The halpin-tsai equations: a review. Polym Eng Sci 16(5):344–352. https://doi.org/10.1002/pen.760160512
Hashin Z (1990) Thermoelastic properties of fiber composites with imperfect interface. Mechan Mater 8(4):333–348. https://doi.org/10.1016/0167-6636(90)90051-G
Hashin Z (1991) The spherical inclusion with imperfect interface. J Appl Mech 58(2):444–449. https://doi.org/10.1115/1.2897205
Hill R (1963) Elastic properties of reinforced solids: Some theoretical principles. J Mech Phys Solids 11(5):357–372. https://doi.org/10.1016/0022-5096(63)90036-X
Jeffery GB (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proc Roy Soc Lond Ser A Containing Pap Math Phys Charact 102(715):161–179. https://doi.org/10.1098/rspa.1922.0078
Jones RM (2018) Mechanics of composite materials, 2nd edn. CRC Press, Boca Raton. https://doi.org/10.1201/9781498711067
Lakes R (1987) Foam structures with a negative Poisson’s ratio. Science 235(4792):1038–1040. https://doi.org/10.1126/science.235.4792.1038
Lakes RS (2020) Composites and metamaterials. World Scientific, New Jersey
Leal LG (1980) Particle motions in a viscous fluid. Annu Rev Fluid Mech 12(1):435–476. https://doi.org/10.1146/annurev.fl.12.010180.002251
Mikhasev GI, Altenbach H (2019) Thin-walled laminated structures: buckling, vibrations and their suppression, advanced structured materials, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-030-12761-9
Mittelstedt C (2021) Structural mechanics in lightweight engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-75193-7
Mittelstedt C, Becker W (2016) Strukturmechanik ebener Laminate. Technische Universität Darmstadt, Darmstadt, Studienbereich Mechanik
Nazarenko L, Stolarski H (2016) Energy-based definition of equivalent inhomogeneity for various interphase models and analysis of effective properties of particulate composites. Compos Part B Eng 94:82–94. https://doi.org/10.1016/j.compositesb.2016.03.015
Nazarenko L, Bargmann S, Stolarski H (2015) Energy-equivalent inhomogeneity approach to analysis of effective properties of nanomaterials with stochastic structure. Int J Solids Struct 59:183–197. https://doi.org/10.1016/j.ijsolstr.2015.01.026
Nazarenko L, Stolarski H, Altenbach H (2016) Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase. Int J Solids Struct 97–98:75–88. https://doi.org/10.1016/j.ijsolstr.2016.07.041
Nazarenko L, Stolarski H, Altenbach H (2017) A model of cylindrical inhomogeneity with spring layer interphase and its application to analysis of short-fiber composites. Compos Struct 160:635–652. https://doi.org/10.1016/j.compstruct.2016.10.024
Nazarenko L, Stolarski H, Altenbach H (2018) On modeling and analysis of effective properties of carbon nanotubes reinforced materials. Compos Struct 189:718–727. https://doi.org/10.1016/j.compstruct.2018.01.027
Öchsner A (2021) Foundations of classical laminate theory, advanced structured materials, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-030-82631-4
Palanikumar K (2012) Analyzing surface quality in machined composites. In: Hocheng H (ed) Machining technology for composite materials, Woodhead publishing series in composites science and engineering. Woodhead Publishing, pp 154–182. https://doi.org/10.1533/9780857095145.1.154
Reiner M (1960) Deformation, strain and flow: an elementary introduction to rheology. Lewis, London
Reiner M (1967) Rheologie in elementarer Darstellung. Hanser, München
Renner B, Altenbach H, Naumenko K (2005) Numerical treatment of finite rotation for cylindrical particle. Technische Mechanik 25(3/4):151–161
Reuss A (1929) Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Zeitschrift für Angewandte Mathematik und Mechanik 9(1):49–58. https://doi.org/10.1002/zamm.19290090104
Saito M, Kukula S, Kataoka Y, Miyata T (2000) Practical use of statistically modified laminate model for injection moldings. Mater Sci Eng A 285(1):280–287. https://doi.org/10.1016/S0921-5093(00)00646-8
Schulze SH, Pander M, Naumenko K, Altenbach H (2012) Analysis of laminated glass beams for photovoltaic applications. Int J Solids Struct 49(15–16):2027–2036. https://doi.org/10.1016/j.ijsolstr.2012.03.028
Sevostianov I, Kachanov M (2007) Effect of interphase layers on the overall elastic and conductive properties of matrix composites. applications to nanosize inclusion. Int J Solids Struct 44(3):1304–1315. https://doi.org/10.1016/j.ijsolstr.2006.06.020
Shen L, Li J (2005) Homogenization of a fibre/sphere with an inhomogeneous interphase for the effective elastic moduli of composites. Proc Roy Soc A Math Phys Eng Sci 461(2057):1475–1504. https://doi.org/10.1098/rspa.2005.1447
Subramanian G, Koch DL (2005) Inertial effects on fibre motion in simple shear flow. J Fluid Mech 535:383–414. https://doi.org/10.1017/S0022112005004829
Voigt W (1910) Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). Springer, Wiesbaden. https://doi.org/10.1007/978-3-663-15884-4
Weps M, Naumenko K, Altenbach H (2013) Unsymmetric three-layer laminate with soft core for photovoltaic modules. Compos Struct 105:332–339. https://doi.org/10.1016/j.compstruct.2013.05.029
Acknowledgements
This contribution is based on various papers that were created in collaboration with my current and former collaborators (my father Prof. J. Altenbach, Prof. Igor Brigadnov, Prof. Victor A. Eremeyev, Prof. Wolfgang Kissing, Prof. Gennady Lvov, Prof. Konstantin Naumenko, Dr. Lidiia Nazarenko, Prof. Rolands Rikards (\(\dag \)), Prof. Henryk Stolarski, Prof. Pavel Zhilin (\(\dag \))) and former doctoral students (Dr.-Ing. Babara Renner and M.Sc. Sergei Pilipenko).
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Altenbach, H. (2022). Composite Mechanics. In: Altenbach, H., Johlitz, M., Merkel, M., Öchsner, A. (eds) Lectures Notes on Advanced Structured Materials. Advanced Structured Materials, vol 153. Springer, Cham. https://doi.org/10.1007/978-3-031-11589-9_1
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