Finite extension of accreting nonlinear elastic solid circular cylinders
Finite extension of accreting nonlinear elastic solid circular cylinders
复制标题
吸积非线性弹性实心圆柱体的有限延伸
DOI：
10.1007/s00161-023-01208-w
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发表时间：
2023
影响因子：
2.6
通讯作者：
Soleiman Fallah, Arash
中科院分区：
文献类型：
--
作者：
Yavari, Arash;Safa, Yasser;Soleiman Fallah, Arash
本文建立并求解了有限扩展条件下圆筒形增粗杆的初边值问题。我们假设棒材在其边界圆柱上印刷无应力的圆柱层，同时棒材进行随时间的有限扩展。增积引起特征应变，从而产生残余应力。我们首先通过构造生长杆的自然黎曼度规来表述非弹性问题。这个度量明确地依赖于吸积过程中的变形历史。对于吸积过程中的位移控制加载，我们得到了应力的精确分布。对于力控制加载，用非线性积分方程来控制其运动学。卸载后，通常存在残余拉伸和残余应力。对于不同的加载实例，我们用数值方法计算了加载过程中的轴向拉伸、残余拉伸和残余应力。我们还计算了在线性吸积力学条件下的应力分布、残余拉伸和残余应力。在几个吸积算例中对线性解和非线性解进行了数值比较。
In this paper we formulate and solve the initial-boundary value problem of accreting circular cylindrical bars under finite extension. We assume that the bar grows by printing stress-free cylindrical layers on its boundary cylinder while it is undergoing a time-dependent finite extension. Accretion induces eigenstrains, and consequently residual stresses. We formulate the anelasticity problem by first constructing the natural Riemannian metric of the growing bar. This metric explicitly depends on the history of deformation during the accretion process. For a displacement-control loading during the accretion process we find the exact distribution of stresses. For a force-control loading, a nonlinear integral equation governs the kinematics. After unloading there are, in general, a residual stretch and residual stresses. For different examples of loadings we numerically find the axial stretch during loading, the residual stretch, and the residual stresses. We also calculate the stress distribution, residual stretch, and residual stresses in the setting of linear accretion mechanics. The linear and nonlinear solutions are numerically compared in a few accretion examples.
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