Computational instability analysis of inflated hyperelastic thin shells using subdivision surfaces
Computational instability analysis of inflated hyperelastic thin shells using subdivision surfaces
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DOI：
10.1007/s00466-023-02366-z
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发表时间：
2023-07
影响因子：
4.1
通讯作者：
Zhaowei Liu;A. McBride;A. Ghosh;L. Heltai;Weicheng Huang;Tiantang Yu;P. Steinmann;P. Saxena
中科院分区：
文献类型：
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作者：
Zhaowei Liu;A. McBride;A. Ghosh;L. Heltai;Weicheng Huang;Tiantang Yu;P. Steinmann;P. Saxena
超弹性薄壳的膨胀是一个高度非线性的问题，在许多重要的工程应用中出现。它的特点是严重的运动和本构非线性，并受到各种形式的不稳定性。为了准确地模拟这个具有挑战性的问题，我们提出了一个等几何方法来计算膨胀和相关的大变形的超弹性薄壳以下的Kirchhoff-Love假设。几何形状和变形场离散使用Catmull-Clark细分基地提供所需的连续有限元逼近。为了跟踪超弹性薄壳所表现出的复杂非线性响应，对膨胀进行增量模拟，每个增量步骤都使用具有弧长控制的Newton-Raphson方法求解。线性系统的特征值分析后，每一个增量步骤评估的可能性分叉到一个较低的能量模式时，失去稳定性。所提出的方法首先使用基准问题进行验证，然后应用于工程应用，在那里的能力，模拟大变形和相关的复杂的不稳定性清楚地表明。
The inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required-continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated.