Computational instability analysis of inflated hyperelastic thin shells using subdivision surfaces

• Published in: Computational mechanics Vol. 73; no. 2; pp. 257 - 276
• Main Authors: Liu, Zhaowei, McBride, Andrew, Ghosh, Abhishek, Heltai, Luca, Huang, Weicheng, Yu, Tiantang, Steinmann, Paul, Saxena, Prashant
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2024; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Computational Science and Engineering; Deformation; Eigenvalues; Engineering; Kinematics; Newton-Raphson method; Nonlinear response; Nonlinearity; Original Paper; Simulation; Stability analysis; Theoretical and Applied Mechanics; Thin walled shells; Isogeometric analysis; Shell buckling; Hyperelastic shells; Stability analysis; Catmull–Clark subdivision surfaces
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-023-02366-z

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 C 1 -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.