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Load Ratios Carried by Each Constituent for Some Problems of a Particulate Composite Modeled as a Mixture of Two Linear Elastic Solids

Published online by Cambridge University Press:  14 October 2020

E. Kurt*
Affiliation:
Faculty of Mechanical Engineering, İstanbul Technical University, İstanbul, Turkey
M. S. Dokuz
Affiliation:
Faculty of Mechanical Engineering, İstanbul Technical University, İstanbul, Turkey
*
*Corresponding author ([email protected])
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Abstract

The basic constitutive equations of theory of mixtures obtained for a mixture of two linear elastic solids can be used as an alternative way to describe the mechanical behavior of binary composite materials. Determining the load ratios carried by each constituent solid of a binary composite is one of challenges of this theory. In this study, the results of directly calculating the ratios of external load carried by each constituent solid for the case of perfectly bonded interface between binary mixture constituents are discussed. Thus, the effects of loading type and volume fraction of the constituent solids to the load ratios carried by each constituent solid are investigated by using three different loading cases and three different volume fractions. Finally, displacement, stress and diffusive force results of two constituent solids using the calculated load ratios are given.

Type
Research Article
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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References

REFERENCES

Steel, T.R., “Applications of a theory of interacting continua”, Quart. J. Mech. Appl. Math., 20, 57-72 (1967).CrossRefGoogle Scholar
Steel, T.R., “Determination of the constitutive coefficients for a mixture of two solids”, International Journal of Solids and Structures, 4, 1149-1160 (1968).CrossRefGoogle Scholar
Bowen, R.M., Theory of mixtures, in continuum physics, vol. III/1, Ed. Eringen, A.C., Academic Press, New York (1976).CrossRefGoogle Scholar
Sadd, M.H., Elasticity: Theory, Applications, and Numerics, Elsevier Inc., Burlington (2005).Google Scholar
Gürgöze, İ.T. and Dokuz, M.S., “An equilibrium solution for the Boussinesq problem for a mixture of an elastic solid and a fluid in an infinite half-space”, International Journal of Engineering Science, 36, 645-653 (1998).CrossRefGoogle Scholar
Dokuz, M.S. and Gürgöze, İ.T., “The galerkin vector solution for a mixture of two elastic solids and Boussinesq problem”, International Journal of Engineering Science, 40, 211-222 (2002).CrossRefGoogle Scholar
Dokuz, M.S., “Thermostatics of an infinite mixture of two solids and a spherical thermal inclusion problem”, International Journal of Engineering Science, 40, 177-191 (2002).CrossRefGoogle Scholar
Dokuz, M.S., “An analytical procedure to determine constitutive coefficients of a mixture of two linear elastic solids”, International Journal of Solids and Structures, 42, 805-817 (2005).CrossRefGoogle Scholar
Binark, N. K. and Dokuz, M.S., “Analytical relations for the undetermined constitutive coefficients of a binary mixture of elastic solids with no relative component motion and an application for semi-infinite mixture continuum”, International Journal of Engineering Science, 111, 1-11 (2017).CrossRefGoogle Scholar
Kurt, E. and Dokuz, M. S., “Analytical Solutions for Axisymmetric Normal Loadings Acting on a Particulate Composite Modeled as a Mixture of Two Linear Elastic Solids”, Journal of Mechanics, 34, 567-578 (2018).10.1017/jmech.2017.31CrossRefGoogle Scholar
Rajagopal, K.R. and Tao, L., Mechanics of mixtures, World Scientific Publishing, Singapore (1995).Google Scholar
Kurt, E. and Dokuz, M. S., “Torsional End Loading Problem for a Prismatic Bar Consisted of a Mixture of Two Linear Elastic Solids.” Proceedings Book of 1th International Conference on Advances in Science and Arts, Oral Presentations, (pp.48-55). Istanbul, March 29-31 (2017).Google Scholar
Kurt, E. and Dokuz, M. S., “Galerkin Vector Solution of Kelvin Problem for a Mixture of Two Linear Elastic Solids”. Proceedings of the 7th International Conference on Applied Analysis and Mathematical Modeling, (pp.9-17). Istanbul, June 20-24 (2018).Google Scholar
Hill, R., “Elastic Properties of Reinforced Solids : Some Theoretical Principles”, Journal of the Mechanics and Physics of Solids, 11, 357-372 (1963).CrossRefGoogle Scholar
Steel, T.R., “Linearised theory of plane strain of a mixture of two solid”, International Journal of Engineering Science, 5, 775-789 (1967).CrossRefGoogle Scholar
Green, A.E. and Steel, T.R., “Constitutive equations for interacting continua”, International Journal of Engineering Science, 4, 483-500 (1966).CrossRefGoogle Scholar
Green, A.E. and Naghdi, P.M., “A dynamical theory of interacting continua”, International Journal of Engineering Science, 3, 231-241 (1965).10.1016/0020-7225(65)90046-7CrossRefGoogle Scholar
Hsieh, C. L., Tuan, W. H. and Wu, T. T., “Elastic Behaviour of a Model Two-Phase Material”, Journal of the European Ceramic Society, 24, 3789-3793 (2004).CrossRefGoogle Scholar