Growth and instability in elastic tissues
Growth and instability in elastic tissues
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DOI：
10.1016/j.jmps.2005.04.008
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发表时间：
2005-10-01
影响因子：
5.3
通讯作者：
Goriely, A
中科院分区：
文献类型：
--
作者：
Ben Amar, M;Goriely, A
研究了生长对弹性材料稳定性的影响。从稳定性的角度来看，生长和再吸收有两个主要影响。首先，质量的变化改变了系统的几何形状，并可能改变了稳定性阈值所涉及的临界长度。其次，生长可能取决于应力，但也可能在材料中引起残余应力。这些应力改变了有效载荷，并且它们可以使材料稳定或不稳定。为了讨论生长中的弹性材料的稳定性，有限弹性理论被用作弹性性质的力学描述的一般框架，并且通过变形梯度的乘法分解来考虑生长。增量变形的形式主义是适应包括增长的影响。作为该方法的一个应用，分析了外压作用下增长的neo-Hookean不可压球壳的稳定性。数值和分析方法相结合，以获得明确的稳定性结果，并确定机械和几何效应的作用。残余应力的重要性是建立在大的各向异性增长的球壳可以成为自发不稳定，没有任何外部负载。(c)2005爱思唯尔有限公司保留所有权利。
The effect of growth in the stability of elastic materials is studied. From a stability perspective, growth and resorption have two main effects. First a change of mass modifies the geometry of the system and possibly the critical lengths involved in stability thresholds. Second, growth may depend on stress but also it may induce residual stresses in the material. These stresses change the effective loads and they may both stabilize or destabilize the material. To discuss the stability of growing elastic materials, the theory of finite elasticity is used as a general framework for the mechanical description of elastic properties and growth is taken into account through the multiplicative decomposition of the deformation gradient. The formalism of incremental deformation is adapted to include growth effects. As an application of the formalism, the stability of a growing neo-Hookean incompressible spherical shell under external pressure is analyzed. Numerical and analytical methods are combined to obtain explicit stability results and to identify the role of mechanical and geometric effects. The importance of residual stress is established by showing that under large anisotropic growth a spherical shell can become spontaneously unstable without any external loading. (c) 2005 Elsevier Ltd. All rights reserved.