A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
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DOI：
10.1098/rspa.2020.0031
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发表时间：
2020-05
期刊：
影响因子：
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通讯作者：
Xiang Yu;Yibin Fu;H. Dai
中科院分区：
文献类型：
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作者：
Xiang Yu;Yibin Fu;H. Dai
本文在前人对静力问题研究的基础上，首先推导了一种包含三种壳本构关系的不可压缩超弹性材料动态有限应变壳方程。为了剔除弯曲效应并减少壳体本构关系的数量，进一步细化，得到了一个只有两个壳体本构关系的动态有限应变壳体理论（可从给定的三维应变能函数推导出），并推导出了一些新的见解。利用壳体方程的弱形式和三维拉格朗日泛函的变分，导出了边界条件和二维壳体虚功原理。作为一个基准问题，我们考虑动脉段的延伸和膨胀。基于壳方程的渐近解与三维精确解之间的良好一致性验证了前者。本文还应用精化壳理论研究了受压动脉的平面应变振动，详细研究了轴向预拉伸、压力和纤维夹角对振动频率的影响。
Based on previous work for the static problem, in this paper, we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.