Computational bifurcation analysis of hyperelastic thin shells

TL;DR

This paper introduces a novel isogeometric computational approach for analyzing the nonlinear inflation behavior and bifurcations of hyperelastic thin shells, capturing complex deformations and instabilities.

Contribution

It develops a C1-continuous finite element method using Catmull-Clark subdivision bases for hyperelastic shell inflation analysis, including bifurcation detection.

Findings

Successfully validated with benchmarks

Able to simulate large deformations

Effectively detects bifurcations and instabilities

Abstract

The inflation of hyperelastic thin shells is an important and highly nonlinear problem that arises in multiple engineering applications involving severe kinematic and constitutive nonlinearities in addition to various instabilities. We present an isogeometric approach to compute the inflation of hyperelastic thin shells, following the Kirchhoff-Love hypothesis and associated large deformation. Both the geometry and the deformation field are discretized using Catmull-Clark subdivision bases which provide the C1-continuous finite element framework required for the Kirchhoff-Love shell formulation. To follow the complex nonlinear response of hyperelastic thin shells, the inflation is simulated incrementally, and each incremental step is solved via the Newton-Raphson method enriched with arc-length control. Eigenvalue analysis of the linear system after each incremental step allows for inducing bifurcation to a lower energy mode in case stability of the equilibrium is lost. The proposed method is first validated using benchmarks, and then applied to engineering applications, where we demonstrate the ability to simulate large deformation and associated complex instabilities.