Young's modulus of isotropic porous materials with spheroidal pores |
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Affiliation: | 1. Norwegian University of Science and Technology (NTNU), Department of Structural Engineering, NO-7491 Trondheim, Norway;2. NTNU, Department of Marine Technology, NO-7491 Trondheim, Norway;3. NTNU, Department of Civil and Transport Engineering, NO-7491 Trondheim, Norway;1. Department of Physics, Manonmaniam Sundaranar University, Tirunelveli 627012, Tamil Nadu, India;2. Department of Nanoscience and Technology, Bharathiar University, Coimbatore 641046, Tamil Nadu, India |
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Abstract: | Based on the Eshelby solution for the single-inclusion problem and Wu's specification of this solution to spheroidal pores, we show that the Eshelby–Wu coefficients for Young's modulus, in contrast to their counterparts for the bulk and shear moduli, are quite insensitive to changes of the Poisson ratio. Therefore the Eshelby–Wu coefficients of Young's modulus can be described (to a very good approximation) by a unique function of the aspect ratio, which is calculated in this paper and for which a master curve is obtained by segment-wise fitting. Also the implementation of the Eshelby–Wu coefficients into the well-known effective medium approximations (Maxwell, self-consistent, differential) and our exponential relation is discussed. Irrespective of the model into which the Eshelby–Wu coefficients are implemented, prolate pore shape affects the porosity dependence of Young's modulus only very weakly, whereas oblate pore shape can lead to an arbitrary reduction of Young's modulus. |
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Keywords: | Inclusions Porosity Mechanical properties Elastic properties (Young's modulus shear modulus bulk modulus) |
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