Summary
The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites. The model is based on the two scale-asymptotic expansions as described by Bensoussan, Lions and Papanicolaou [2], and Sanchez-Palencia [3]. Equations of motion are obtained from the principle of virtual work, while the appropriate incremental constitutive equations are deduced from Reissner’s [4] mixed variational principle. The finite element method is used for the spatial discretization. The resulting semi-discrete equations of motion are then integrated using the explicit method. The fibers are assumed elastic, while the matrix obeys a von Mises yield criterion with linear hardening. A semi-infinite fiber reinforced composite under a step pressure is considered. Stress profiles show the dispersive nature of the waves in the composite.
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References
Murakami, H., and Hegemier, G. A., “A Mixture Model for Unidirectionally Fiber-Reinforced Composites,” ASME Journal of Applied Mechanics,Vol. 53 (1986), 765–773.
Bensoussan, A., Lions, J. L., and Papanicolaou, G., Asymptotic Analysis of Periodic Structures, North-Holland Publishing Co., Amsterdam, 1978.
Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer-Verlag, Berlin, 1980.
Reissner, E., “On a Certain Mixed Variational Theorem and a Proposed Application,” International Journal of Numerical Methods in Engineering, Vol. 20 (1984), 1366–1368.
Hallquist, J. O., User’s Manual for DYNA2D, University of California, LLNL Report, UCID-18756, 1982.
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© 1988 Springer-Verlag Berlin Heidelberg
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Toledano, A., Murakami, H. (1988). Transient Finite Element Analysis of Elastoplastic Fiber Reinforced Composites. In: Atluri, S.N., Yagawa, G. (eds) Computational Mechanics ’88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61381-4_139
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DOI: https://doi.org/10.1007/978-3-642-61381-4_139
Publisher Name: Springer, Berlin, Heidelberg
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