Elastic solutions of a cylindrical rod containing periodically distributed inclusions with axisymmetric eigenstrains |
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| Authors: | Z. Zhong Q. P. Sun X. B. Yu |
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| Affiliation: | (1) Department of Engineering Mechanics and Technology, Tongji University, Key Laboratory of Solid Mechanics of MOE, Shanghai, 200092;(2) Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay Kowloon, Hong Kong SAR, P. R. China |
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| Abstract: | Summary. In this paper, we give the elastic solution for a special type of microstructure – a circular cylindrical rod containing periodically distributed inclusions along its axial direction. Each inclusion has the same uniform axisymmetric transformation strain (eigenstrain). Analytical elastic solutions are obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructure and its evolution (growth of inclusions) on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated. As a result of such microstructure evolution nominal stress-strain relation with strain softening is derived for a rod under uniaxial tension. |
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