Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

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• 作者：Fabio Sozio^a ; ^b ; Arash Yavari^b ; ^c ; ^{arash.yavari@ce.gatech.edu}
• 关键词：Surface growth ; Accretion mechanics ; Geometric mechanics ; Nonlinear elasticity ; Residual stress
• 刊名：Journal of the Mechanics and Physics of Solids
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：98
• 期：Complete
• 页码：12-48
• 全文大小：1894 K
• 卷排序：98

文摘

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.