J025011 Computational study of dynamic motion of hyperelastic membrane imposing surface incompressibility

Abstract

This paper presents a sophisticated approach to address a nearly incompressible membrane, based on a pressure-correction approach. Unknown velocities are updated by solving the equation of motion discretized in a step-by-step manner, and the pressure field is determined by solving a discrete Helmholtz equation. In a 2D validation test, it has been confirmed that the present approach is possible to deal with the nearly incompressible membrane without paying attention to numerical instabilities coming from a high stiffness of surface dilation.