Micropolar hypo-elasticity |
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Authors: | Shojaa Ramezani Reza Naghdabadi |
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Institution: | 1. Department of Mechanical Engineering and Institute for Nano Science and Technology, Sharif University of Technology, P.O. Box 11365-9567, Tehran, Iran
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Abstract: | In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of
the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose
spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer
attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in
which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation
for large elastic deformation of micropolar hypo-elastic media based on the simplified constitutive equations in conjunction
with Jaumann and gyration rates is presented. As an example, buckling of a shallow arc is examined, and it is shown that an
increase in the micropolar material parameters results in an increase in the buckling load of the arc. Also, it is shown that
micropolar effects become important for deformations taking place at small scales. |
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