Time-Dependent Response of Incompressible Membranes Based on Quasi-Linear Viscoelasticity Theory

In this work, large deformation of incompressible, hyperelastic membranes based on the quasi-linear viscoelasticity (QLV) theory is formulated. Time integration algorithm and the expression for consistent fourth-order tangent tensor are presented. The formulation covers isotropic as well as anisotropic polymeric and biological materials. To solve numerical examples, a nonlinear finite element formulation in the Lagrangian framework is developed. Finally, several examples are provided to investigate the applicability of the present formulation. It is found that the numerical results are in good agreement with the analytical and experimental results available in the literature.

Automated summary

This work formulates the large deformation of incompressible, hyperelastic membranes based on the quasi-linear viscoelasticity theory, covering a wide range of materials. Numerical examples are solved using a nonlinear finite element method, showing good agreement with analytical and experimental results in the literature.