The polytopal composite element method for finite strain hyperelastic problems

Abstract

Polygonal elements have emerged as a cutting-edge discretization paradigm in computational solid mechanics, demonstrating significant potential for linear elasticity analyses. This work pioneers a robust computational framework extending polytopal composite elements to finite-strain hyperelasticity. The key idea by constructing a polynomial projection using least squares approximation for linear-compatible strain fields, followed by extending the derived linear operator to large deformation cases involving nonlinear strain. The computational framework of this method is fundamentally consistent with finite elements, allowing it to adapt and extend to various nonlinear problems. Through several numerical investigation we show that this approach maintains the excellent accuracy, convergence and stability, and is potentially offering new insights and references for polygonal elements in future nonlinear problems.